{"id":8600,"date":"2023-07-13T00:23:54","date_gmt":"2023-07-12T22:23:54","guid":{"rendered":"https:\/\/www.euroekonom.sk\/?p=8600"},"modified":"2024-05-14T10:37:39","modified_gmt":"2024-05-14T08:37:39","slug":"informacie-a-jej-prenos","status":"publish","type":"post","link":"https:\/\/www.autoskoly.sk\/news\/informacie-a-jej-prenos\/","title":{"rendered":"Inform\u00e1cie a jej prenos"},"content":{"rendered":"<p>Inform\u00e1cia a jej prenos<\/p>\n<h2>Miera inform\u00e1cie<\/h2>\n<p><span style=\"text-decoration: underline;\">Vhod\u00e9 \u0161trukt\u00fary:<\/span><\/p>\n<ul>\n<li>Nosi\u010d inform\u00e1cie \u2013 v\u00fdroky v telekomunika\u010dn\u00fdch prenosoch, sign\u00e1ly atd.<\/li>\n<li>V\u00fdrok nes\u00faci inform\u00e1ciu m\u00f4\u017eeme sk\u00fama\u0165 z viacer\u00fdch h\u013ead\u00edsk: sch\u00e9matick\u00e9 &#8211; v\u00fdznamov\u00e9, kvantitat\u00edvne \u2013 objemov\u00e9, pravdivostn\u00e9 \u2026<\/li>\n<li>Z kvantitat\u00edvneho h\u013eadiska m\u00f4\u017eeme hovori\u0165 o mno\u017estve inform\u00e1cie<\/li>\n<li>Najm\u00e4 z poh\u013eadu kapacitn\u00fdch prenosov\u00fdch mo\u017enost\u00ed siet\u00ed zauj\u00edma kvantitat\u00edvne h\u013eadisko<\/li>\n<li>Preto\u017ee v\u00fdrok hovor\u00ed o ur\u010ditom jave, existuje tu kore\u0161pondencia medzi v\u00fdrokmi a javmi<\/li>\n<li>Sta\u010d\u00ed n\u00e1m kvalifikova\u0165 javy z h\u013eadiska mno\u017estva inf. t. j. v\u00fdrokov al. javov<\/li>\n<\/ul>\n<p>Vznikaj\u00fa ot\u00e1zky:<\/p>\n<ul>\n<li>Ako mera\u0165 inform\u00e1ciu, v\u00fdrok, jav?<\/li>\n<li>M\u00f4\u017eeme mera\u0165 v\u0161etky javy?<\/li>\n<li>\u010co je to vo v\u0161eobecnosti miera?<\/li>\n<\/ul>\n<p>Zo sk\u00famanosti vieme, \u017ee v\u0161etky syst\u00e9my objektov merate\u013en\u00fdch v ur\u010ditom zmysle tvoria in\u00fa \u0161trukt\u00faru. \u0160trukt\u00fara je mno\u017eina prvkov, pri kt. platia ur\u010dit\u00e9 vlastnosti.<br \/>\n<span style=\"text-decoration: underline;\">Defin\u00edcia miery inform\u00e1cie:<\/span><\/p>\n<ol>\n<li>&#8211; okruh<\/li>\n<li>&#8211; okruh<\/li>\n<li>3.<\/li>\n<li><\/li>\n<\/ol>\n<p>X={{1}, {2}, \u2026, {6}}element8rne javy pri hode kockou<br \/>\n<span style=\"text-decoration: underline;\">Veta<\/span><span style=\"text-decoration: underline;\">:<\/span> je v\u017edy algebra<br \/>\n<span style=\"text-decoration: underline;\">Veta<\/span><span style=\"text-decoration: underline;\">: <\/span><br \/>\n<span style=\"text-decoration: underline;\">D\u00f4kaz:<\/span><br \/>\n<span style=\"text-decoration: underline;\">Veta<\/span><span style=\"text-decoration: underline;\">:<\/span> Nepr\u00e1zdny syst\u00e9m podmno\u017e\u00edn mno\u017einy X je algebra<br \/>\n<span style=\"text-decoration: underline;\">D\u00f4kaz:<\/span><br \/>\n<span style=\"text-decoration: underline;\">Veta<sub>1<\/sub>:<\/span> Ak okruh je g &#8211; okruh alebo &#8211; okruh<br \/>\n<span style=\"text-decoration: underline;\">Veta<sub>2<\/sub>:<\/span> Ka\u017ed\u00fd &#8211; okruh je okruh<br \/>\nKa\u017ed\u00fd okruh je g \u2013 okruh<br \/>\n<span style=\"text-decoration: underline;\">Veta<sub>3<\/sub>:<\/span> Ak je okruh<br \/>\n<span style=\"text-decoration: underline;\">Veta<sub>4<\/sub>:<\/span> Ak<br \/>\n<span style=\"text-decoration: underline;\">Def.:<\/span><sub>V5, V6<\/sub> Okruh e podmno\u017e\u00edn mno\u017einy X (s &#8211; okruh) naz\u00fdvame <span style=\"text-decoration: underline;\">algebra (<\/span><span style=\"text-decoration: underline;\">s<\/span><span style=\"text-decoration: underline;\"> &#8211; algebra)<\/span>, ak X EURe<br \/>\n<span style=\"text-decoration: underline;\">Def.:<\/span> Nech e je syst\u00e9m podmno\u017e\u00edn mno\u017einy X. Funkcia definovan\u00e1 na e, kt.nadob\u00fada hodnoty v R (v\u010d\u00edtane )<br \/>\nNaz\u00fdvame <span style=\"text-decoration: underline;\">mno\u017einovou<\/span> funkciou.<br \/>\n<span style=\"text-decoration: underline;\">Def.:<\/span> Hovor\u00edme, \u017eemno\u017einov\u00e1 funkcia j definovan\u00e1 na syst\u00e9me e je <span style=\"text-decoration: underline;\">kone\u010dn\u00e1<\/span> ak &#8222;E EURe j(E) EURR<br \/>\n<span style=\"text-decoration: underline;\">Def.:<\/span> Mno\u017einov\u00e1 funkcia j definovan\u00e1 na syst\u00e9me e kde \u00c6 EURe naz\u00fdvame <span style=\"text-decoration: underline;\">adit\u00edvnou<\/span> ak j(\u00c6)=0 a &#8222;E, F EURe kde E\u00c7F=\u00c6, E\u00c8F EURe j(E\u00c8F) = j(E) + j(F).<br \/>\n<span style=\"text-decoration: underline;\">Def.:<\/span> Nech U je syst\u00e9m podmno\u017e\u00edn mno\u017einy X, kde \u00c6 EURU. Mno\u017einov\u00fa funkciu j definujeme na U naz\u00fdvame <span style=\"text-decoration: underline;\">s<\/span><span style=\"text-decoration: underline;\"> &#8211; adit\u00edvnou<\/span> ak j(\u00c6)=0 a tak\u00fa , \u017ee<br \/>\n<span style=\"text-decoration: underline;\">Def.:<\/span> Nez\u00e1porn\u00fa s &#8211; adit\u00edvnu funkciu definovan\u00fa na okruhu R pre E, F EURR naz\u00fdvame miernou.<br \/>\n<span style=\"text-decoration: underline;\">Veta<sub>6<\/sub>:<\/span> Nepr\u00e1zdny syst\u00e9m e podmno\u017e\u00edn mno\u017einy X je s algebra &#8222;{E<sub>n<\/sub>} EURe\u00c8E<sub>n<\/sub> EURe<br \/>\n&#8222;E EUReE\u2018 EURe<br \/>\n(d\u00f4kaz tak\u00fd ist\u00fd ako ku Vete<sub>5<\/sub>)<\/p>\n<h2>Miera inform\u00e1cie<\/h2>\n<p>Je zrejm\u00e9, \u017ee nie je adit\u00edvna.<br \/>\nE \u2013 pri hode kockou padla p\u00e1rna hodnota<br \/>\nF \u2013 pri hode kockou padla hodnota 3<br \/>\nj(E\u00c8F) &lt; j(E) j(E\u00c8F) &lt; j(F)<br \/>\nZ anal\u00f3gie vieme, \u017ee sa m\u00f4\u017eeme pok\u00fasi\u0165 nahradi\u0165 vlastnos\u0165 aditivity.<br \/>\nDefinujeme si <span style=\"text-decoration: underline;\">pseudoaditivitu<\/span> na rovnak\u00fdch podmienkach ako aitivitu:<br \/>\nj(E\u00c8F) = j(E) + j(F)<br \/>\nMiera inf. j (mno\u017estvo inform\u00e1cie( <sup>x<\/sup> ) nie je adit\u00edvna mno\u017einov\u00e1 funkcia.<br \/>\nJej vlastnosti:<\/p>\n<ul>\n<li>klesaj\u00faca funkcia<\/li>\n<li>oper\u00e1cia je komutat\u00edvna aj asociat\u00edvna aj distribut\u00edvna<\/li>\n<li>j(W) = 0 (cel\u00fd priestor = 0)<\/li>\n<li>j(A) + j(B) = 0<\/li>\n<li>spojit\u00e1 funkcia<\/li>\n<li>j(E\u00c7F) = j(E) + j(F) pre nez\u00e1visl\u00e9 javy<\/li>\n<\/ul>\n<h2>Oper\u00e1cia \u00b0<\/h2>\n<p>k &gt; 0, k = 1 a \u2013 rozhoduje v ak\u00fdch jednotk\u00e1ch budeme pracova\u0165<br \/>\nak a = 2 [bit] v Shanon<br \/>\na = e = 2,7 [nat]<br \/>\n\u010c\u00edm v\u00e4\u010d\u0161\u00ed jav, t\u00fdm men\u0161ie mno\u017estvo inform\u00e1cie {2} &lt; {2, 4, 6}<br \/>\nj{2} &gt; j{2, 4, 6}<br \/>\nDefin\u00edcia miery inform\u00e1cie vypl\u00fdva z defin\u00edcie oper\u00e1cie \u00b0.<br \/>\n!!! j(E) = &#8211; k.log<sub>a<\/sub>P(E) k = 1 j(E) = &#8211; log<sub>a<\/sub>P(E) \u00de element\u00e1rna !!!<br \/>\nV z\u00e1vislosti od vo\u013eby <strong>a<\/strong> rozozn\u00e1vame jednotky klaicky (?)<br \/>\nAk porovn\u00e1me mieru inform\u00e1cie s klasickou mierou:<br \/>\nP(E\u00c8F) = P(E) + P(F)<\/p>\n<h2>Entropia (neur\u010ditos\u0165)<\/h2>\n<h2>&#8211; je stredn\u00e1 hodnota mno\u017estva inform\u00e1cie (zo \u0161tatistick\u00e9ho h\u013eadiska)<\/h2>\n<p>Entropia \u2013 miera inf. v\u00fddatnosti pokusu, neur\u010ditos\u0165 pokusu<br \/>\nHodnota j(A) predstavuje mno\u017estvo inf., kt. z\u00edskame ak vieme, \u017ee nastane jav A. Touto \u00favahou prij\u00edmate\u013eovi inform\u00e1cie prisudzujeme pas\u00edvnu \u00falohu. Pr\u00edjemca m\u00f4\u017ee by\u0165 akt\u00edvny, ak ide vykona\u0165 pokus pomocou, kt. zist\u00ed, ktor\u00e1 z istejko\u0148e\u010dnej mno\u017einy mo\u017enost\u00ed nastane. Mno\u017eina mo\u017enost\u00ed javov \u2013 v\u00fdsledok pokusu zvy\u010dajne m\u00f4\u017eeme voli\u0165 vhodn\u00fdm v\u00fdberom ot\u00e1zky, pokusu, &#8230; <span style=\"text-decoration: underline;\">V te\u00f3rii inf. definujeme<\/span> pokus P ak kone\u010dn\u00fd merate\u013en\u00fd rozklad ist\u00e9ho javu X \u00de P = {A<sub>1<\/sub>, \u2026, A<sub>n<\/sub>} cez A<sub>i<\/sub> EUR e A<sub>i <\/sub>\u00c7 A<sub>j<\/sub> = \u00c6, i \u00b9 j<br \/>\nPokus je t\u00fdm nev\u00fdhodnej\u0161\u00ed \u010d\u00edm d\u00e1 viac inform\u00e1cie, len\u017ee ak\u00e9 je krit\u00e9rium vhodnosti dan\u00e9ho pokusu? Hodnoty j(A<sub>i<\/sub>) to nem\u00f4\u017eu by\u0165, lebo m\u00f4\u017eu by\u0165 r\u00f4zne a teda pri jednom v\u00fdsledku pokusu P dostaneme viac inf., pri inom menej. Mus\u00edme priradi\u0165 pokusu P nez\u00e1porn\u00e9 \u010d\u00edslo H(P) vyjadruj\u00face priemer \u010d\u00edsel j(A<sub>1<\/sub>)&#8230;j(A<sub>n<\/sub>). \u010c\u00edm je hodnota H(P) vy\u0161\u0161ia, t\u00fdm je pokus P informa\u010dne v\u00fddatnej\u0161\u00ed. Hodnotu H(P) naz\u00fdvame <strong>entropiou<\/strong>.<\/p>\n<h3><strong>Entropia ako stredn\u00e1 hodnota n\u00e1hodnej premennej<\/strong><\/h3>\n<p>Ak m\u00e1me pravdepodobnostn\u00fd priestor (X, e, j) a inform\u00e1ciu j(A) = &#8211; logP(A) m\u00f4\u017eeme uva\u017eova\u0165 o entropii H(P) pokusu P = {A<sub>1<\/sub>, \u2026, A<sub>n<\/sub>} s pravdepodobnos\u0165ou P(A<sub>1<\/sub>)&#8230;P(A<sub>n<\/sub>) \u00de <strong>Shanonova formula<\/strong><br \/>\n<strong> H(P) = Sj(A<sub>i<\/sub>).P(A<sub>i<\/sub>) = &#8211; SP(A<sub>i<\/sub>).logP(A<sub>i<\/sub>)<\/strong><\/p>\n<h3><strong>Axiomatick\u00e1 def. entropie v pravdepodobnostnom priestore<\/strong><\/h3>\n<p>Mnoh\u00ed, kt. nezav\u00e1dzaj\u00fa pojem j(A) v jave A, chc\u00fa tie\u017e pokusu P = {A<sub>1<\/sub>, \u2026, A<sub>n<\/sub>} priradi\u0165 H(P). Vieme, \u017ee H(P) je funkciou pravdep. p<sub>1<\/sub> = P(A<sub>1<\/sub>), &#8230;, p<sub>n<\/sub> = P(A<sub>n<\/sub>) \u00de H(P) = H(p<sub>1<\/sub>, &#8230;, p<sub>n<\/sub>). Funkcia H(P) by mala ma\u0165 ist\u00e9 vlastnosti vypl\u00edvaj\u00face z jej v\u00fdznamu. Z nich m\u00f4\u017eeme postavi\u0165 s\u00fastavu axi\u00f3m, z ktor\u00fdch m\u00f4\u017eeme ur\u010di\u0165 funkciu H. Shannon definoval funkciu (s\u00fastavu) axi\u00f3m. My pou\u017eijeme Fadejevovu z r. 1956:<br \/>\nA<sub>0<\/sub>: H(p<sub>1<\/sub>, &#8230;, p<sub>n<\/sub>) je def. &#8222;n p<sub>i <\/sub>\u00b3 0 &#8222;i EUR {1, \u2026, n} Sp<sub>i<\/sub> = + a nadob\u00fada re\u00e1lne hodnoty<br \/>\nA<sub>1<\/sub>: H(p<sub>1<\/sub>, 1- p) je spojit\u00e1 funkcia premennej p EUR &lt;0, 1&gt;<br \/>\nA<sub>2<\/sub>: H(p<sub>1<\/sub>, \u2026, p<sub>n<\/sub>) je symetrick\u00e1 funkcia, t. j. &#8220; permut\u00e1cie S<sub>1<\/sub>\u2026S<sub>n<\/sub> \u010d\u00edsel 1, \u2026, n<br \/>\nH(p<sub>S1<\/sub>, \u2026, p<sub>Sn<\/sub>) = H(p<sub>1<\/sub>, \u2026, p<sub>n<\/sub>)<br \/>\nA<sub>3<\/sub>: Ak p<sub>n <\/sub>= g<sub>1<\/sub> + g<sub>2<\/sub> &gt; 0 g<sub>1<\/sub> \u00b3 0, g<sub>2<\/sub> \u00b3 0 \u00de<br \/>\nH(p<sub>1<\/sub>, \u2026, p<sub>n-1<\/sub>; g<sub>1<\/sub>, g<sub>2<\/sub>) = H(p<sub>1<\/sub>, \u2026, p<sub>n-1<\/sub>, p<sub>n<\/sub>) + p<sub>n<\/sub>.<br \/>\nAxi\u00f3my A<sub>0<\/sub> \u2013 A<sub>2<\/sub> s\u00fa prirodzen\u00e9. Axi\u00f3ma A<sub>3<\/sub> tzv. princ\u00edp vetvenia, ohodnocuje pr\u00edrastok entropie, ke\u010f od rozkladu P = {A\u00ad\u00ad\u00ad\u00ad<sub>1<\/sub>\u2026A<sub>n<\/sub>} s pravdep. p<sub>1<\/sub>\u2026p<sub>n<\/sub> prejdeme k rozkladu P\u2019={A<sub>1<\/sub>\u2026A<sub>n-1<\/sub>; B<sub>1<\/sub>, B<sub>2<\/sub>} kde pr\u00edrastok by mal by\u0165 t\u00fdm men\u0161\u00ed, \u010d\u00edm men\u0161\u00ed je p<sub>n<\/sub>. Zrejme ak nastane jav A<sub>n<\/sub>(pravdep. p<sub>n<\/sub>), tak m\u00e1me e\u0161te dostato\u010dn\u00fa neistotu pri pokuse P\u2019, \u010di nastane, ak ja B<sub>1<\/sub> s podmienenou pravdepod. q<sub>1<\/sub> \/ p<sub>n<\/sub> alebo B<sub>2<\/sub> s q<sub>2<\/sub> \/ p<sub>n<\/sub>. T\u00fato neistotu vyjadruje entropia .<\/p>\n<h2>Shanonova entropia<\/h2>\n<p>Uk\u00e1\u017eeme, \u017ee funkcia H je jedin\u00e1 funkcia Shanonovho typu H(P) = &#8211; SP(A<sub>i<\/sub>).logP(A<sub>i<\/sub>)<br \/>\n<span style=\"text-decoration: underline;\">Lema 1:<\/span> H(1, 0) = 0<br \/>\n<span style=\"text-decoration: underline;\">Lema 2:<\/span> H(p<sub>1<\/sub>\u2026p<sub>n<\/sub>, 0) = H(p<sub>1<\/sub>\u2026p<sub>n<\/sub>) <span style=\"text-decoration: underline;\">Def. : <\/span>(pre diskr. sign\u00e1ly) H(P) = &#8211; Sp(A<sub>i<\/sub>).log<sub>2<\/sub>P(A<sub>i<\/sub>)<br \/>\n<span style=\"text-decoration: underline;\">Lema 3:<\/span> Nech p<sub>n<\/sub> = q<sub>1<\/sub> + \u2026+ q<sub>n<\/sub> &gt; 0 \u00de H(p<sub>1<\/sub>\u2026p<sub>n+1,<\/sub>,;q<sub>1<\/sub>\u2026q<sub>n<\/sub>) = H(p<sub>1<\/sub>\u2026p<sub>n<\/sub>) + p<sub>n<\/sub>.<br \/>\n<span style=\"text-decoration: underline;\">Lema 4:<\/span> Nech pre i = 1\u2026n; p<sub>i<\/sub> = q<sub>i<\/sub> + \u2026+ q<sub>i1<\/sub> &gt; 0 potom H(q<sub>1<\/sub>\u2026q<sub>1n1<\/sub>\u2026q<sub>n1<\/sub>\u2026q<sub>nmn<\/sub>) =<br \/>\n= H(p<sub>1<\/sub>\u2026p<sub>n<\/sub>) + Sp<sub>i<\/sub>.<br \/>\n<span style=\"text-decoration: underline;\">Lema 5:<\/span> Pre n \u00ae \u00a5 plat\u00ed A<sub>n<\/sub> = F(n) \u2013 F(n \u2013 1) \u00ae 0<br \/>\n<span style=\"text-decoration: underline;\">Lema 6:<\/span> F(n) = c.log n, kde c je kon\u0161tanta<br \/>\n<span style=\"text-decoration: underline;\">Veta:<\/span> Nech &#8220; i = 1\u2026n; p<sub>i<\/sub> &gt; 0, q<sub>i<\/sub> &gt; 0, Sp<sub>i<\/sub> = 1, Sq<sub>i<\/sub> = 1 \u00de -Sp<sub>i<\/sub>.log p<sub>i<\/sub> = -Sp<sub>i<\/sub>. log q<sub>i<\/sub><br \/>\nD\u00f4sledok: Pri danom <strong>n<\/strong> funkcie H(p<sub>1<\/sub>\u2026p<sub>n<\/sub>) nadob\u00fada max. log n pre p<sub>1<\/sub>\u2026p<sub>n<\/sub> = &#8220; n<br \/>\nmax H(P) =<\/p>\n<ol start=\"3\">\n<li>a) p(X<sub>0<\/sub>) = 2\/3 H(P) = -(2\/3.log 2\/3 + 1\/3.log1\/3) = (2\/3 + 2\/3.log 3 + 1\/3.log) = log 3 \u2013 2\/3 bit (?)<\/li>\n<\/ol>\n<p>p(X<sub>1<\/sub>) = 1\/3<\/p>\n<ol>\n<li>b) p(X<sub>0<\/sub>) = 1\/2 H(P) = log<sub>2<\/sub>2 = 1 bit<\/li>\n<\/ol>\n<p>p(X<sub>1<\/sub>) = 1\/2<br \/>\n<span style=\"text-decoration: underline;\">Def.:<\/span> (pre spojit\u00e9 sign\u00e1ly) <strong>H(P) = <\/strong><br \/>\n<span style=\"text-decoration: underline;\">Pr\u00edklad:<\/span> 27 guli\u010diek rovnakej ve\u013ekosti a farby, 26 m\u00e1 rovnak\u00fa v\u00e1hu a 1 je \u0165a\u017e\u0161ia. N\u00e1jdite t\u00fato 1 guli\u010dku pomocou 2 \u2013 rovnoramenn\u00fdch v\u00e1h, zistite ko\u013eko v\u00e1\u017ei. Ak\u00fdm min. po\u010dtom m\u00f4\u017eeme zisti\u0165, ktor\u00e1 guli\u010dka je \u0165a\u017e\u0161ia.<br \/>\nH(1\/27\u20261\/27) = log<sub>2<\/sub>27 = 3.log 3 \u00de sta\u010dia 3 v\u00e1\u017eenia<br \/>\nH(1\/3 + 1\/3 + 1\/3) = log 3<\/p>\n<h3>Sp\u00f4soby pripojenia<\/h3>\n<p><span style=\"text-decoration: underline;\">Simplexn\u00fd prenos<\/span> \u2013 jednosmern\u00fd prenos<br \/>\n<span style=\"text-decoration: underline;\">Duplexn\u00fd prenos<\/span> \u2013 obojsmern\u00fd prenos, mo\u017enos\u0165 obojsmern\u00e9ho s\u00fa\u010dasn\u00e9ho preonsu<br \/>\n<span style=\"text-decoration: underline;\">Poloduplexn\u00fd prenos<\/span> \u2013 obojsmern\u00fd prenos, mo\u017enos\u0165 prenosu iba jedn\u00fdm smerom s\u00fa\u010dasne<br \/>\nPrenos inf. je realizovan\u00fd prenosom sign\u00e1lu odpovedaj\u00faceho danej prenosovej s\u00fastave. Matemet. popis sign\u00e1lu b\u00fdva \u010dasto zlo\u017eit\u00fd (inf. v\u00fdstup z mikrof\u00f3nu), inokedy formou n\u00e1hodnej postupnosti, kt. \u010dleny s\u00fa sign\u00e1ly definovan\u00e9ho tvaru (tgf. Sign\u00e1l).<br \/>\nS\u00fastavu sign\u00e1lov tvor\u00ed mno\u017eina sign\u00e1lov, kt. v\u00fdberom a usporiadan\u00edm dost\u00e1vame sign\u00e1ly, kt. jednozna\u010dne odpovedaj\u00fa spr\u00e1vam pren\u00e1\u0161an\u00fdm prenosovou s\u00fastavou. Sign\u00e1lom rozumieme ka\u017ed\u00fa fyz. veli\u010dinu nas\u00facu inform\u00e1ciu. Spr\u00e1vou je zostava prvkov (sign\u00e1lov) nes\u00faca inf. Mat. popis s\u00fastavy sign\u00e1lov z\u00e1vis\u00ed od toho, z ak\u00e9ho h\u013eadiska ju chceme sk\u00fama\u0165 a ak\u00e9 mat. prostriedky k tomu potrebujeme. Sign\u00e1lnym priestorom sa naz\u00fdva mno\u017eina sign\u00e1lov, na kt. je vhodne definovan\u00fd pojem vzdialenosti.<br \/>\nMo\u017enosti definovania sign\u00e1lov:<\/p>\n<ol>\n<li>Ak n\u00e1s zauj\u00edma v ur\u010ditom okamihu vyhodnoten\u00e1 amplit\u00fada sign\u00e1lov, m\u00f4\u017eeme definova\u0165 vzdialenos\u0165 ako d(x, y) = (x \u2013 y); kde x, y s\u00fa ve\u013ekosti amplit\u00fad sign\u00e1lov x a y.<\/li>\n<li>V sign\u00e1lnom priestore, kt. k\u00f3dov\u00e9 zlo\u017eky maj\u00fa kon\u0161tantn\u00fa v\u00e1hu a s\u00fa zlo\u017een\u00e9 z line\u00e1rnych symbolov 0 a 1. M\u00f4\u017eeme definova\u0165 <strong>Hamingovu vzdialenos\u0165<\/strong>: ak x = {x<sub>1<\/sub>, \u2026,x<sub>n<\/sub>}, y = {y<sub>1<\/sub>, \u2026,y<sub>n<\/sub>} \u00de d(x, y) = S(xi \u00c5 y<sub>i<\/sub>), \u00c5 &#8211; s\u00fa\u010det Modulu 2<\/li>\n<\/ol>\n<p><strong> Hamingova vzd.<\/strong> Ud\u00e1va na ko\u013ek\u00fdch miestach sa pr\u00edslu\u0161n\u00e9 k\u00f3dov\u00e9 zlo\u017eky navz\u00e1jom l\u00ed\u0161ia.<\/p>\n<ol start=\"3\">\n<li>Majme sign\u00e1ly definovan\u00e9 ako komplexn\u00e9 funkcie x(t), y(t) re\u00e1lnej premennej t (\u010das) na intervale (0, T). Potom mo\u017eno definova\u0165 vzdialenos\u0165: . Ak x(t) bol vyslan\u00fd sign\u00e1l y(t) jemu odpovedaj\u00faci prijat\u00fd, potom d(x, y) definujeme ako mieru odli\u0161nosti t\u00fdch sign\u00e1lov.<\/li>\n<\/ol>\n<p><strong>Z\u00e1kladnou \u00falohou<\/strong> pri prenose spr\u00e1v: pren\u00e1\u0161a\u0165 po \u0161umiv\u00fdch kan\u00e1loch r\u00fdchlo, ekonomicky, pri zachovan\u00ed po\u017eadovanej spr\u00e1vnosti prenosu.<br \/>\n<strong>K\u00f3dovanie<\/strong> \u2013 proces prira\u010fovania kombin\u00e1ciou prvkov mno\u017einy sign\u00e1lov X = {x<sub>1<\/sub>\u2026x<sub>n<\/sub>} mno\u017eine spr\u00e1v I = {i<sub>1<\/sub>\u2026\u00ad\u00adi<sub>n<\/sub>}<br \/>\n<strong>K\u00f3dom<\/strong> naz\u00fdvame pravidlo jednozna\u010dne prira\u010fuj\u00face ka\u017edej spr\u00e1ve z mno\u017einy I jedin\u00fa postupnos\u0165 prvkov (k\u00f3dov\u00e9 slovo) z mno\u017einy X.<br \/>\nK\u00f3dovan\u00edm prisp\u00f4sobujeme vlastnosti spr\u00e1v vlastnostiam kan\u00e1lu, \u010d\u00edm dosahujeme v\u00e4\u010d\u0161iu odolnos\u0165 spr\u00e1v v \u0161umivom kan\u00e1li.<br \/>\n<strong>Shanonova veta o k\u00f3dovan\u00ed:<\/strong><br \/>\nExistuje \u010d\u00edslo, ktor\u00e9 sa naz\u00fdva kapacitou tak\u00e9, \u017ee ak je v\u00e4\u010d\u0161ie ako entropia zdroja, mo\u017eno pou\u017eit\u00edm vhodn\u00e9ho k\u00f3dovania pren\u00e1\u0161a\u0165 spr\u00e1vy s \u013eubovo\u013enou malou pravdepodobnos\u0165ou chyby.<br \/>\nK\u00f3dovan\u00e9 s\u00fastavy del\u00edme do 2 kateg\u00f3ri\u00ed:<\/p>\n<ol>\n<li><strong>spojit\u00e9<\/strong> \u2013 zobrazenie z nekone\u010dnej mno\u017einy inf. do nkone\u010dnej mno\u017einy sign\u00e1lov (AM, FM\u2026)<\/li>\n<li><strong>diskr\u00e9tne<\/strong> \u2013 zobrazenie z kone\u010dnej mno\u017einy inform\u00e1cie do kone\u010dnej mno\u017einy sign\u00e1lov<\/li>\n<\/ol>\n<p>Spojit\u00e9 s\u00fastavy mo\u017eno previes\u0165 na diskr\u00e9tnu s ur\u010ditou chybou vzorkovan\u00edm a kvantovan\u00edm.<br \/>\nI(x<sub>i<\/sub>) je mno\u017estvo inf., kt. potrebujeme z\u00edska\u0165, aby sme ur\u010dili v\u00fdskyt konkr\u00e9tneho x<sub>i<\/sub> zo s\u00faboru X. Ak pr\u00edjmeme y<sub>i<\/sub>, potom podmienen\u00fa pravdepodobnos\u0165 P(x<sub>i<\/sub>, y<sub>i<\/sub>) naz\u00fdvame podmieneou inform\u00e1ciou<br \/>\nI(x<sub>i<\/sub>, y<sub>i<\/sub>) = &#8211; log P(x<sub>i<\/sub>, y<sub>i<\/sub>). Ud\u00e1va n\u00e1m mno\u017estvo inf., kt. budeme potrebova\u0165, aby sme ur\u010dili x<sub>i<\/sub> zo s\u00faboru X, aby sme prijali y<sub>i<\/sub>. \u010ci\u017ee mno\u017estvo inf. I(x<sub>i<\/sub>) \u2013 I(x<sub>i<\/sub>\/y<sub>i<\/sub>) sme u\u017e prijat\u00edm y<sub>i<\/sub> z\u00edskali. Preto mno\u017estvo inf. pri vysielanom x<sub>i<\/sub> a prijatom y<sub>i<\/sub> je I(x<sub>i<\/sub>\/y<sub>i<\/sub>) = I(x<sub>i<\/sub>) \u2013 I(xi\/y<sub>i<\/sub>) = , kde I(x<sub>i<\/sub>\/y<sub>i<\/sub>) naz\u00fdvame <strong> vz\u00e1jomnou inform\u00e1ciou<\/strong>. Je to vlastne log. pravdep. ur\u010denie x<sub>i<\/sub> po prijat\u00ed y<sub>i<\/sub> s pravdep. ur\u010denia x<sub>i<\/sub> pred prijat\u00edm y<sub>i<\/sub>.<\/p>\n<h4>Entropia zdroja<\/h4>\n<p>Je stredn\u00e9 mno\u017estvo inf. pripadaj\u00face na 1 sign\u00e1l zdroja inf. je definovan\u00e1 ako stredn\u00e1 hodnota I(x<sub>i<\/sub>),<br \/>\nH(X) = &#8211; S p(x<sub>i<\/sub>).log p(x<sub>i<\/sub>).<br \/>\nDefin\u00edciu H(X) mo\u017eno roz\u0161\u00edri\u0165 aj pre spojit\u00e9 sign\u00e1ly (veli\u010diny) kde j(X) je rozlo\u017eenie hustoty pravdepodobnosti.<\/p>\n<h2>Spektr\u00e1lna anal\u00fdza sign\u00e1lov<\/h2>\n<ol>\n<li><span style=\"text-decoration: underline;\">Determinovan\u00fd sign\u00e1l<\/span> \u2013 v z\u00e1vislosti na \u010dase t je definovan\u00fd predpisom g(t), v\u0161etky sign\u00e1ly n\u00e1s bud\u00fa zauj\u00edma\u0165 z poh\u013eadu funkcie \u010dasu z poh\u013eadu ich spektr\u00e1lnu anal\u00fdzu. Analytick\u00fdm n\u00e1strojom s\u00fa Furrierove rady a integr\u00e1ly.<\/li>\n<li><span style=\"text-decoration: underline;\">Harmonick\u00fd sign\u00e1l<\/span> \u2013 je od ot\u00e1\u010dania vektora v komplexnej rovine. Oto\u010denie o p\/2 odpoved\u00e1 n\u00e1sobeniu imag. jednotkami, lebo ak v po\u010diato\u010dnom stave z = 1 oto\u010den\u00edm 2x p\/2 prejde z = -1 \u00dek = -1 \u00de pri oto\u010den\u00ed<\/li>\n<\/ol>\n<p>p\/2 \u00de<br \/>\n\u013dubovo\u013enou polohou vektora na jednotkovej kru\u017enici mo\u017eno definova\u0165 s\u00faradnicami x + jy kde x = cos a,<br \/>\ny = sin a, a &#8211; uhol oto\u010denia vektora od z\u00e1kl. polohy.<br \/>\n<strong>obr\u00e1zok<\/strong><br \/>\nv\u00fdchodzia poloha vektora v osi x: s\u00faradnice (x = 1, y = 0) \u00de a = 0<br \/>\nEulerov vz\u0165ah: x + jy = e<sup>j<\/sup><sup>a<\/sup> d\u00f4kaz: x+jy=cosa+jsina=e<sup>j<\/sup><sup>a<\/sup><br \/>\nx \u2013 jy = e<sup>-j<\/sup><sup>a<\/sup> rovnos\u0165 je zrejm\u00e1 rozpisom do <strong>Taylorovho radu<\/strong><br \/>\nZavedieme do ot\u00e1\u010dania \u010das t a kruhov\u00fd kmito\u010det w. Doba ot\u00e1\u010dania vektora o 2p &#8211; peri\u00f3da T \u00de 2p = wt.<br \/>\nObecne za \u010das t sa oto\u010d\u00ed vektor o uhol a = wt, ve\u013ekos\u0165 zlo\u017eiek ot\u00e1\u010daj\u00faceho sa vektora v rovine kruh. r\u00fdchlos\u0165ou (w [rad\/s]) s\u00fa: x = cos wt, y = sin wt. Tnto sign\u00e1l odvoden\u00fd od rovnomern\u00e9ho kmitav\u00e9ho pohybu naz\u00fdvame <strong> harmonick\u00fdm sign\u00e1lom<\/strong>. Predpokl. V nejakom \u010dase t ur\u010dit\u00fa polohu ota\u010d. sa vektora ve\u013ekosti (c). Potom <strong> polohu vektora<\/strong> m\u00f4\u017eeme definova\u0165:<br \/>\n(g(t) = c.e<sup>j<\/sup><sup>w<\/sup><sup>t<\/sup>; kde c = |c|.e<sup>j<\/sup><sup>w<\/sup>) \u00de <strong>\u013eavoto\u010div\u00fd pohyb<\/strong><br \/>\n(g<sup>*<\/sup>(t) = c<sup>*<\/sup>.e<sup>-j<\/sup><sup>w<\/sup><sup>t<\/sup>; kde c = |c|.e<sup>-j<\/sup><sup>w<\/sup>) \u00de <strong> pravoto\u010div\u00fd pohyb<\/strong><br \/>\nHarmonick\u00fd sign\u00e1l je periodicky, \u010dasovo neohrani\u010d. sign\u00e1l. Pri z\u00e1pise v spektr. oblasti sa oprieme o t\u00fato \u00favahu: G(w) = &#8211; predpoklad\u00e1me. \u017ee t<sub>0<\/sub> je kon\u0161t. a men\u00ed sa w. Dan\u00e9mu z\u00e1pisu v \u010das. oblasti odpoved\u00e1 z\u00e1pisu v ur\u010ditom w. Pozn\u00e1me 3 parametre zvuku: 1. hlasitos\u0165 \u00de intenzita zvuku<\/p>\n<ol start=\"2\">\n<li>t\u00f3n \u00de frekvencia zvuku<\/li>\n<li>zafarbenie \u00de harmonickos\u0165 zvuku<\/li>\n<\/ol>\n<p><strong>Absol\u00fatna hodnota g<sub>1<\/sub>(t) = c<sub>1<\/sub>.e<sup>j<\/sup><sup>w<\/sup><sup>t<\/sup> je rovn\u00e1 |c<sub>1<\/sub>| lebo vektor sa men\u00ed \u010do do d\u013e\u017eky (len sa ot\u00e1\u010da). Stredn\u00fd v\u00fdkon harm. sign\u00e1lu nap\u00e4tia al. sign\u00e1lu g<sub>1<\/sub>(t) na odpore 1W je rovn\u00fd strednej hodnote \u0161tvorca jeho obsahu.<\/strong><br \/>\n<strong>Zlo\u017een\u00fd sign\u00e1l<\/strong> \u2013 zlo\u017een\u00edm 2 sign\u00e1lov neschopn\u00fdch vies\u0165 inf., sign\u00e1l, kt. men\u00ed ve\u013ekos\u0165 aj kmito\u010det \u00de kmito\u010det v okamihu = difirenci\u00e1lne mal\u00fd kmito\u010det g<sub>1<\/sub>(t) = |c<sub>1<\/sub>|, a<sub>1<\/sub>, w<sub>1<\/sub><br \/>\ng<sub>2<\/sub>(t) = |c<sub>2<\/sub>|, a<sub>2<\/sub>, w<sub>2<\/sub> g<sub>1<\/sub>(t), g<sub>2<\/sub>(t) nebude harmonick\u00fd (lan ak w<sub>1<\/sub> = w<sub>2<\/sub>)<br \/>\n<strong>obr\u00e1zok<\/strong><br \/>\nV\u00fdsl. Vektor men\u00ed ve\u013ekos\u0165 aj kruhov\u00fd kmito\u010det \u00de mo\u017eno zavies\u0165 pojem okam\u017eit\u00e9ho kruh. kmito\u010dtu<br \/>\n<strong>V\u00fdsledn\u00fd sign\u00e1l bude op\u00e1\u0165 periodick\u00fd.<\/strong><br \/>\nOrigin\u00e1lom budeme naz\u00fdva\u0165 \u010das. funkciu g(t), <strong>obrazom<\/strong> je mat. predpis , kt. n\u00e1s informuje o ve\u013ekosti amplit\u00fady a o f\u00e1ze zlo\u017ekov\u00fdch harmonick\u00fdch(?), \u010di\u017ee o <strong>SPEKTRE<\/strong>. Origin\u00e1l n\u00e9m ud\u00e1va \u010dasov\u00fa z\u00e1vyslos\u0165:<br \/>\nobraz \u2013 kmito\u010dtov\u00fa \u00de , kde c<sub>g<\/sub> je vektor amplit\u00fady g &#8211; tej harmonickej<br \/>\n, T<sub>0<\/sub> je doba peri\u00f3dy uva\u017eovan\u00e9ho per. sign\u00e1lu g(t) a s\u00fa\u010dasne I peri\u00f3da z\u00e1kl. harm. zlo\u017eky s kmito\u010dtom F<sub>0<\/sub><br \/>\nAk je priebeh sign\u00e1lu dan\u00fd graficky alebo postupnos\u0165ou okam\u017eit\u00fdch amplit\u00fad sign\u00e1lz, m\u00f4\u017eene dosaden\u00edm t\u00fdchto \u00fadajov do predo\u0161l\u00fdch vz\u0165ahov vypo\u010d\u00edta\u0165 vektory amplit\u00fad c<sub>g<\/sub> jednotliv\u00fdch harmon. a t\u00fdm je ur\u010den\u00fd \u010dasov\u00fd priebeh periodick\u00e9ho sign\u00e1lu g(t).<br \/>\nV\u00fdkon na odpore R = 1 W :<br \/>\nPre re\u00e1lny periodick\u00fd sign\u00e1l: (c<sub>&#8211;<\/sub><sub>g<\/sub> = c<sup>*<\/sup><sub>g<\/sub>) plat\u00ed:<br \/>\n, pre g = 0 dosad\u00edme a<sub>g<\/sub> = a<sub>0<\/sub> a Fourrierov rad v re\u00e1lnej forme je:<br \/>\nPeriodick\u00e9 sign\u00e1ly pre svoju determinovanos\u0165 <strong>nem\u00f4\u017eu by\u0165 nosite\u013emi inform\u00e1ci\u00ed<\/strong>. N\u00e1hodn\u00fd sled sign\u00e1lov je realizovan\u00fd len sign\u00e1lmi kone\u010dn\u00e9ho tvarovania. K jeho anal\u00fdze vyu\u017eijeme Fourrierive rady s predpokladom, \u017ee priebeh sign\u00e1lu v intervale t predstavuje 1 peri\u00f3du sign\u00e1lu g(t). Fourrierov rad g(t) bude odpoveda\u0165 sign\u00e1lu v ohrani\u010denom \u010dasovom intervale, ak v spektr\u00e1lnej oblasti by tento rad rprezentoval obraz odpovedaj\u00faci uva\u017eovan\u00e9mu sign\u00e1lu. Uva\u017eujeme takto: vyn\u00e1sobme rovnicu pre v\u00fdpo\u010det amplit\u00fady g &#8211; tej harmonickej z\u00e1kladnou peri\u00f3dou T<sub>0<\/sub>: .<br \/>\nS\u00fa\u010din c<sub>g<\/sub>.T<sub>0<\/sub> = c<sub>g<\/sub>\/F<sub>0<\/sub> je fikt\u00edvna stredn\u00e1 hodnota amplit\u00fad na 1 Hz v oblasti g &#8211; tej harmonickej periodick\u00e9ho dign\u00e1lu g(t). Ozna\u010dujeme G(gw<sub>0<\/sub>) stredn\u00fa hodnotu amplit\u00fad v intervale spektra (g &#8211; 1).F<sub>0<\/sub> \u010di\u017ee gF<sub>0<\/sub>. Pracujeme s \u010dasov\u00fdm ohrani\u010den\u00fdm sign\u00e1lom, \u010do sa prejav\u00ed v spojitosti spektra. Ak bude r\u00e1s\u0165 peri\u00f3da T<sub>0<\/sub> \u00de spektr\u00e1lne intervaly sa bud\u00fa <strong>SKRACOVA\u0164<\/strong>, w<sub>0<\/sub> prejde na \u00a5 \u010di\u017ee . V mieste gw<sub>0<\/sub> bude<br \/>\nc<sub>g<\/sub> = F<sub>0<\/sub>.G(gw<sub>0<\/sub>), a preto tu bude hustota amplit\u00fad <strong>NEKONE\u010cN\u00c1<\/strong> \u00de &#8211; to je Fourrierov rad (integr\u00e1l) pre transf. origin\u00e1lu na obraz<br \/>\nG(w) = F{g(t)}<br \/>\nPo aplik\u00e1cii podobn\u00fdch \u00favah na vz\u0165ah: , roz\u0161\u00edren\u00edm pravej strany rovnice o w<sub>0<\/sub> zmen\u00ed: \u00de pre limitu pre T<sub>0<\/sub> \u00ae \u00a5:<br \/>\nG(t) = F<sup>-1<\/sup>{G(w)}. Pre $ integr\u00e1lu mus\u00ed by\u0165 splnen\u00e1 <strong>Dirchletova podmienka<\/strong>:<br \/>\nV praxi je t\u00e1to podmienka splnen\u00e1 v\u017edy.<\/p>\n<h2>Triedenie modul\u00e1ci\u00ed<\/h2>\n<table width=\"592\">\n<tbody>\n<tr>\n<td width=\"92\">Typ modul\u00e1cie<\/td>\n<td width=\"119\">Pren\u00e1\u0161an\u00e1 inform\u00e1cia<\/td>\n<td width=\"107\">Nosi\u010d<\/td>\n<td width=\"128\">Modulovan\u00fd parameter<\/td>\n<td width=\"147\">Typ modul\u00e1cie<\/td>\n<\/tr>\n<tr>\n<td rowspan=\"8\" width=\"92\">Analogick\u00e1<\/td>\n<td width=\"119\"><\/td>\n<td rowspan=\"4\" width=\"107\">S\u00ednusoida<\/td>\n<td rowspan=\"2\" width=\"128\">Amplit\u00fada<\/td>\n<td width=\"147\">AM<\/td>\n<\/tr>\n<tr>\n<td width=\"119\"><\/td>\n<td width=\"147\">SSB<\/td>\n<\/tr>\n<tr>\n<td width=\"119\">Analogick\u00e1:<\/td>\n<td width=\"128\">Frekvencia<\/td>\n<td width=\"147\">FM<\/td>\n<\/tr>\n<tr>\n<td width=\"119\">hovor<\/td>\n<td width=\"128\">F\u00e1za<\/td>\n<td width=\"147\">PM<\/td>\n<\/tr>\n<tr>\n<td width=\"119\">hudba<\/td>\n<td rowspan=\"4\" width=\"107\">Impulz<\/td>\n<td width=\"128\">Amplit\u00fada<\/td>\n<td width=\"147\">PAM<\/td>\n<\/tr>\n<tr>\n<td width=\"119\">video<\/td>\n<td width=\"128\">Frekvencia<\/td>\n<td width=\"147\">PFM<\/td>\n<\/tr>\n<tr>\n<td width=\"119\"><\/td>\n<td width=\"128\">F\u00e1za<\/td>\n<td width=\"147\">PPM<\/td>\n<\/tr>\n<tr>\n<td width=\"119\"><\/td>\n<td width=\"128\">Doba<\/td>\n<td width=\"147\">PDM<\/td>\n<\/tr>\n<tr>\n<td rowspan=\"7\" width=\"92\">Numerick\u00e1<\/td>\n<td width=\"119\">Numerick\u00e1:<\/td>\n<td rowspan=\"3\" width=\"107\">S\u00ednusoida<\/td>\n<td width=\"128\">Amplit\u00fada<\/td>\n<td width=\"147\">ASK<\/td>\n<\/tr>\n<tr>\n<td width=\"119\">\u00fadaje<\/td>\n<td width=\"128\">Frekvencia<\/td>\n<td width=\"147\">FSK<\/td>\n<\/tr>\n<tr>\n<td width=\"119\">text<\/td>\n<td width=\"128\">F\u00e1za<\/td>\n<td width=\"147\">PSK<\/td>\n<\/tr>\n<tr>\n<td rowspan=\"4\" width=\"119\">Analogick\u00e1 \u00de Numerick\u00e1<\/td>\n<td rowspan=\"4\" width=\"107\">Hodiny<\/td>\n<td rowspan=\"4\" width=\"128\">K\u00f3d<\/td>\n<td width=\"147\">PCM<\/td>\n<\/tr>\n<tr>\n<td width=\"147\">DPCM<\/td>\n<\/tr>\n<tr>\n<td width=\"147\">DM<\/td>\n<\/tr>\n<tr>\n<td width=\"147\">SDM<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h3><\/h3>\n<h3><span style=\"text-decoration: underline;\">Modul\u00e1cie so s\u00ednusov\u00fdm nosi\u010dom \u2013 ANAL\u00d3GOV\u00c9<\/span><\/h3>\n<ul>\n<li>nosi\u010dom je s\u00ednusoida<\/li>\n<\/ul>\n<p>u<sub>p<\/sub>(t) = up.cos u<sub>p<\/sub>.t = u<sub>p<\/sub>.cos 2pfp + 2<br \/>\nu<sub>2<\/sub>(t) = w<sub>2<\/sub>(t).cos [j<sub>2<\/sub>(t)] kde w<sub>2<\/sub>(t) = 2p.f<sub>2<\/sub>(t) =<\/p>\n<table>\n<tbody>\n<tr>\n<td width=\"34\"><\/td>\n<td width=\"93\">u<sub>2<\/sub>(t)<\/td>\n<td width=\"93\">f<sub>2<\/sub>(t)<\/td>\n<td width=\"93\">j<sub>2<\/sub>(t)<\/td>\n<\/tr>\n<tr>\n<td width=\"34\">AM<\/td>\n<td width=\"93\">u<sub>p<\/sub> + Du(t)<\/td>\n<td width=\"93\">f<sub>p<\/sub><\/td>\n<td width=\"93\">u<sub>p<\/sub>(t)<\/td>\n<\/tr>\n<tr>\n<td width=\"34\">FM<\/td>\n<td width=\"93\">u<sub>p<\/sub><\/td>\n<td width=\"93\">f<sub>p<\/sub> + D(t)<\/td>\n<td width=\"93\">u<sub>p<\/sub>(t) + Dj(t)<\/td>\n<\/tr>\n<tr>\n<td width=\"34\">PM<\/td>\n<td width=\"93\">u<sub>p<\/sub><\/td>\n<td width=\"93\">f<sub>p<\/sub> + D(t)<\/td>\n<td width=\"93\">u<sub>p<\/sub>(t) + Dj(t)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><strong><span style=\"text-decoration: underline;\">Apmlit\u00fadov\u00e1 modul\u00e1cia<\/span> \u2013 AM<\/strong><\/p>\n<ul>\n<li>pou\u017e\u00edva sa pre rozhlasov\u00e9 vysielanie na dlh\u00fdch stredn\u00fdch <strong>obr\u00e1zok<\/strong><\/li>\n<\/ul>\n<p>kr\u00e1tkych vln\u00e1ch<\/p>\n<ul>\n<li>v\u00fdhody: jednoduch\u00e1 modul\u00e1cia, demodul\u00e1cia, dobr\u00e9 \u0161\u00edrenie<\/li>\n<li>nev\u00fdhody: energetick\u00e1 n\u00e1ro\u010dnos\u0165, zl\u00e1 kvalita (vplyv na<\/li>\n<\/ul>\n<p>amplit\u00fadu, mal\u00e1 \u0161\u00edrka p\u00e1sma)<br \/>\n<strong><span style=\"text-decoration: underline;\">Amplit\u00fadov\u00e1 modul\u00e1cia<\/span> \u2013 SSB<\/strong><\/p>\n<ul>\n<li>vyu\u017e\u00edvan\u00e1 telef\u00f3nmi, modul\u00e1cia s jedn\u00fdm postrann\u00fdm p\u00e1smom<\/li>\n<li>ide o to, \u017ee \u0161\u00edrku p\u00e1sma potrebujeme z\u00fa\u017ei\u0165, aby sme si vymedzili prvky pre jednotliv\u00e9 hovory<\/li>\n<li>cie\u013e: <strong>frekven\u010dn\u00fd multiplex<\/strong> \u2013 jedn\u00fdm kan\u00e1lom sa m\u00e1 pren\u00e1\u0161a\u0165 viacero hovorov s\u00fa\u010dasne<\/li>\n<\/ul>\n<p><strong><span style=\"text-decoration: underline;\">Frekven\u010dn\u00e1 modul\u00e1cia<\/span> \u2013 FM<\/strong><\/p>\n<ul>\n<li>je ovplyv\u0148ovan\u00e1 frekvenciou <strong>obr\u00e1zok<\/strong><\/li>\n<li>vyu\u017e\u00edva sa pri vysielan\u00ed (iba pre kr\u00e1tke vlny VKV)<\/li>\n<li>v\u00fdhody: energetick\u00e1 nen\u00e1ro\u010dnos\u0165, vysok\u00e1 kvalita<\/li>\n<li>nev\u00fdhody: \u0161\u00edri sa len do mal\u00e9ho \u00fazemia, n\u00e1ro\u010dnos\u0165<\/li>\n<\/ul>\n<p>spracovania sign\u00e1lu<\/p>\n<ul>\n<li>\u010d\u00edm je vy\u0161\u0161\u00ed sign\u00e1l, t\u00fdm je frekvencia ni\u017e\u0161ia<\/li>\n<\/ul>\n<p><strong><span style=\"text-decoration: underline;\">Impulzn\u00e1 modul\u00e1cia<\/span> obr\u00e1zky<\/strong><br \/>\n<strong>PAM<\/strong>: pulzne amplit\u00fadov\u00e1 modul\u00e1cia &#8211; men\u00ed sa v\u00fd\u0161ka amplit\u00fady<br \/>\n<strong>PFM<\/strong>: pulzne f\u00e1zov\u00e1 modul\u00e1cia &#8211; v\u00fd\u0161ka zost\u00e1va rovnak\u00e1, men\u00ed sa frekvencia<br \/>\n<strong>PPM<\/strong>: pulzne polohov\u00e1 modul\u00e1cia &#8211; men\u00ed sa poloha impulzu<br \/>\n&#8211; ak je <strong>kladn\u00e1<\/strong> hodnota, stred impulze sa pos\u00fava <strong>doprava<\/strong><br \/>\n&#8211; ak je <strong>z\u00e1porn\u00e1<\/strong> hodnota, stred impulze sa pos\u00fava <strong>do\u013ealva<\/strong><br \/>\n<strong>PDM<\/strong>: pulzne dobov\u00e1 modul\u00e1cia &#8211; men\u00ed sa \u0161\u00edrka impulzu<\/p>\n<h3><span style=\"text-decoration: underline;\">Numerick\u00e1 modul\u00e1cia<\/span><\/h3>\n<p>Z\u00e1kladn\u00fd princ\u00edp je zmena anal\u00f3gov\u00e9ho sign\u00e1lu nes\u00faceho inform\u00e1ciu na numerick\u00fd sign\u00e1l (t. j. postupnos\u0165 diskr\u00e9tnych znakov. Teda spojit\u00fd sign\u00e1l, nekone\u010dn\u00e9 mno\u017estvo prvkov, transformujeme na diskr\u00e9tny sign\u00e1l s kone\u010dn\u00fdm mno\u017estvom prvkov.<br \/>\nT\u00e1to zmena je realizovan\u00e1:<\/p>\n<ul>\n<li>vzorkovan\u00edm (frekvencie f<sub>e<\/sub>)<\/li>\n<li>kvantovan\u00edm (line\u00e1rne, neline\u00e1rne)<\/li>\n<li>k\u00f3dovan\u00edm do bin\u00e1rneho sign\u00e1lu<\/li>\n<\/ul>\n<p><span style=\"text-decoration: underline;\">Vyu\u017eitie modul\u00e1cie<\/span><\/p>\n<ol>\n<li>telef\u00f3nia: &#8211; anal\u00f3gov\u00e9 p\u00e1smo 300 \u2013 3400 Hz je vzorkovan\u00e9 f<sub>e<\/sub> = 8kHz<\/li>\n<\/ol>\n<p>&#8211; vz\u0165ah sign\u00e1l \u2013 hluk: 10 ? \u00b3 35 dB<br \/>\n&#8211; q = 2<sup>8<\/sup> = 256 \u00farovn\u00ed, kvantovanie neline\u00e1rne<br \/>\n&#8211; r\u00fdchlos\u0165 prenosu D = f<sub>e<\/sub>.ln g = 64 kbit\/s<\/p>\n<ol>\n<li>audio prenos: &#8211; f<sub>e<\/sub> = 32 kHz, k\u00f3dovanie: line\u00e1rne na 14 bitov \u00de D = 448 kbit\/s<\/li>\n<\/ol>\n<p>neline\u00e1rne na 12 bitov \u00de D = 384 kbit\/s<br \/>\nneline\u00e1rne na 10 bitov \u00de D= 320 kbit\/s<\/p>\n<ol>\n<li>video prenos: &#8211; f<sub>e<\/sub> = 13,3 MHz, k\u00f3dovanie line\u00e1rne na 8 alebo 9 bitov<\/li>\n<\/ol>\n<p><span style=\"text-decoration: underline;\">V\u00fdhody<\/span>:<\/p>\n<ul>\n<li>ekonomick\u00e9 (spracovanie jedn\u00e9ho typu sign\u00e1lu)<\/li>\n<li>kvalita (rekon\u0161truovanie sign\u00e1lu, odolnos\u0165, vyradi\u0165 star\u00e9 sign\u00e1ly(?))<\/li>\n<li>TDM (\u010dasov\u00e9 delenie sign\u00e1lov)<\/li>\n<\/ul>\n<h4>Numerick\u00e9 rozdielov\u00e9 modul\u00e1cie<\/h4>\n<p>Z\u00e1kladn\u00fdm princ\u00edpom je, \u017ee nekvantujeme hodnoty z\u00e1kl. anal\u00f3gov\u00e9ho sign\u00e1lu, ale rozdiel medzi<br \/>\nu<sub>1<\/sub>(t) \u2013 z\u00e1kl. sign\u00e1l a g(t) \u2013 odhadnut\u00e1 hodnota extrapol\u00e1ciou na z\u00e1kl. predch\u00e1dzaj\u00facich hodn\u00f4t<br \/>\n<strong><span style=\"text-decoration: underline;\">Delta modul\u00e1cia<\/span><\/strong> <strong>&#8211; DM <\/strong>&#8211; ide o rozdielov\u00e9 modul\u00e1cie s extrapol\u00e1ciou nulov\u00e9ho radu, t. j. odhadnut\u00e1 hodnota sa rovn\u00e1 predo\u0161lej kvantifikovanej hodnote<br \/>\nf\u00ade\u00ad \u2013 vzorkovacia frekvencia, D = f<sub>e<\/sub>, kvantovanie:<br \/>\n<strong>obra\u00e1zok<\/strong> ak sign\u00e1l rastie = 1, ak kles\u00e1 = 0<br \/>\nak je skuto\u010dn\u00fd sign\u00e1l nad odhadom \u00de st\u00fapa (1)<br \/>\nak je skuto\u010dn\u00fd sign\u00e1l pod odhadom \u00de kles\u00e1 (0)<\/p>\n<p><span style=\"text-decoration: underline;\">Nev\u00fdhoda<\/span> \u00de ak sign\u00e1l rastie alebo kles\u00e1 ve\u013emi pruko, kvantovac\u00ed sign\u00e1l nest\u00edha a je to na \u00fakor kvality<br \/>\nPCM \u2013 ten ist\u00fd princ\u00edp, ale po\u010det \u00farovn\u00ed je q + 2<\/p>\n<p><strong><span style=\"text-decoration: underline;\">DPCM <\/span><\/strong>\u2013 ten ist\u00fd princ\u00edp, zv\u00e4\u010d\u0161enie po\u010dtu \u00farovn\u00ed<\/p>\n<p><strong><span style=\"text-decoration: underline;\">D<\/span><span style=\"text-decoration: underline;\">S<\/span><span style=\"text-decoration: underline;\">M<\/span><\/strong> \u2013 ten ist\u00fd princ\u00edp, ale n\u00e1sob\u00edme spektrum 1\/F, \u010do sa rovn\u00e1 intefr\u00e1cii p\u00f4vodn\u00e9ho sign\u00e1lu u<sub>p<\/sub>(t) a potom realizujeme DM<\/p>\n<h2>Anal\u00f3gov\u00e1 modul\u00e1cia diskr\u00e9tnych sign\u00e1lov<\/h2>\n<ul>\n<li>p\u00f4vodn\u00fd sign\u00e1l je numerick\u00fd (bin\u00e1rny, M \u2013 \u00e1rny)<\/li>\n<li>nosi\u010dom je sign\u00e1l u<sub>p<\/sub>(t) = U<sub>p<\/sub>.cos (w<sub>p<\/sub>t &#8211; a<sub>p<\/sub>)<\/li>\n<li>madulovan\u00fd sign\u00e1l je z\u00edskan\u00fd diskr\u00e9tnou zmenou jedn\u00e9ho z parametrov (amplit\u00fada, frekvencia, f\u00e1za)<\/li>\n<li>exzistenciu hod\u00edn zabezpe\u010duje TAKT<\/li>\n<\/ul>\n<p><span style=\"text-decoration: underline;\">Diskr\u00e9tne modul\u00e1cie:<\/span><\/p>\n<p><strong><span style=\"text-decoration: underline;\">ASK<\/span>:<\/strong> &#8211; \u0161peci\u00e1lny pr\u00edpad je <strong>OOK<\/strong>, kde m = 2 \u2013 bin\u00e1rny sign\u00e1l<br \/>\n&#8211; m \u2013 hodn\u00f4t amplit\u00fady, pri m = 2 je to 0 a u<sub>2<\/sub>(t) = a<sub>k<\/sub>.cos w<sub>p<\/sub>(t), kde a<sub>k<\/sub> EUR{0, 1}<br \/>\n<strong><span style=\"text-decoration: underline;\">FSK<\/span>:<\/strong> &#8211; pri m = 2: 1. sign\u00e1l: f<sub>p<\/sub> + Df v\u00fdsledn\u00fd sign\u00e1l u<sub>2<\/sub>(t) = U<sub>p<\/sub>.cos (2p(f<sub>p<\/sub> + a<sub>k<\/sub>Df)t)<\/p>\n<ol start=\"2\">\n<li>sign\u00e1l: f<sub>p<\/sub> &#8211; Df<\/li>\n<\/ol>\n<p>&#8211; vyu\u017e\u00edva sa na riadenie mobiln\u00fdch siet\u00ed<br \/>\n<strong><span style=\"text-decoration: underline;\">PSK<\/span>:<\/strong> &#8211; pre m \u2013 \u00e1rny sign\u00e1l<br \/>\n&#8211; f\u00e1zov\u00e9 rozdiely<br \/>\n&#8211; 2x ur\u00fdch\u013euje prenos<br \/>\nK\u00d3DOVANIE<br \/>\nZmysel k\u00f3dovania a z\u00e1klady te\u00f3rie k\u00f3dovania:<\/p>\n<ul>\n<li>vych\u00e1dzame zo z\u00e1kladnej \u00falohy pri prenose spr\u00e1v: pren\u00e1\u0161a\u0165 spr\u00e1vy po \u0161umov\u00fdch kan\u00e1loch r\u00fdchlo, ekonomicky, so zachovan\u00edm po\u017eadovanej spr\u00e1vnosti, rie\u0161enie Shannon z\u00edskame pou\u017eit\u00edm vhodn\u00e9ho k\u00f3dovania<\/li>\n<li><strong>k\u00f3dovanie<\/strong> = zobrazenie z I = {i<sub>1<\/sub>, \u2026, i<sub>n<\/sub>} \u00ae X = {x<sub>1<\/sub>, \u2026, x<sub>n<\/sub>}, X \u2013 mno\u017eina sign\u00e1lov, I \u2013 mno\u017eina spr\u00e1v<\/li>\n<li>pravidlo priradenia naz\u00fdvame <strong>k\u00f3dom<\/strong><\/li>\n<li>postupnos\u0165 symbolov mno\u017einy X naz\u00fdvame <strong>k\u00f3dov\u00fdm slovom<\/strong><\/li>\n<li>k\u00f3dovan\u00edm prisp\u00f4sob\u00edme vlastnosti spr\u00e1v vlastnostiam kan\u00e1lu<\/li>\n<li>k\u00f3dov\u00e9 s\u00fastavy: <strong>diskr\u00e9tna<\/strong> a <strong>spojit\u00e1<\/strong><\/li>\n<\/ul>\n<h4>Diskr\u00e9tne k\u00f3dy<\/h4>\n<ul>\n<li>s\u00fa tvoren\u00e9 na kartezi\u00e1nskom s\u00fa\u010dine A x X, kde A = {a<sub>1<\/sub>, \u2026, a<sub>n<\/sub>} je mno\u017eina \u010dasov\u00fdch prvkov k\u00f3d. slova a X = {x<sub>1<\/sub>, \u2026, x<sub>n<\/sub>} je mno\u017eina \u00farov\u0148ov\u00fdch stavov<\/li>\n<li>ka\u017ed\u00fd prvok z A m\u00f4\u017ee ma\u0165 <strong>Z<\/strong> stavov \u00de m\u00f4\u017eeme vytvori\u0165 <strong>Z<sup>n<\/sup> <\/strong>r\u00f4znych <strong>n<\/strong> prvkov\u00fdch slov, po\u010det<\/li>\n<\/ul>\n<p>L = Z<sup>n<\/sup> sa naz\u00fdva <strong> d\u013e\u017eka k\u00f3du<\/strong><\/p>\n<ul>\n<li>k\u00f3d zlo\u017een\u00fd z neronako dlh\u00fdch k\u00f3dov\u00fdch slov m\u00e1 d\u013e\u017eku<\/li>\n<\/ul>\n<p><strong><span style=\"text-decoration: underline;\">Pln\u00fd k\u00f3d<\/span><\/strong> \u00ae k\u00f3d, ke\u010f v\u0161etk\u00fdm slov\u00e1m s\u00fa priraden\u00e9 informa\u010dn\u00e9 prvky.<br \/>\nZrejme, aby sme mohli zak\u00f3dova\u0165 N prvkov mno\u017einy I, m\u00e1 N \u00a3 L. K\u00f3d zad\u00e1vame: vzorom, obrazom, tabu\u013ekou, grafom, mnoho\u010dlenom alebo maticou. Pre \u013eubovo\u013en\u00fa \u010d\u00edseln\u00fa s\u00fastavu so z\u00e1kladom Z, pri existencii<br \/>\nn r\u00f4znych znakov a<sub>i<\/sub> \u00de k\u00f3dov\u00e9 slovo .<\/p>\n<h4>Bin\u00e1rny k\u00f3d<\/h4>\n<ul>\n<li>optim\u00e1lny z h\u013eadiska hospod\u00e1rnosti<\/li>\n<\/ul>\n<p>Pri k\u00f3dovan\u00ed a dek\u00f3dovan\u00ed treba ulo\u017ei\u0165 k\u00f3dov\u00e9 slov\u00e1 dok pam\u00e4te. Jej cena(?) je ur\u010den\u00e1 po\u010dtu pam\u00e4\u0165ov\u00fdch miest, ten z\u00e1vis\u00ed na organiz\u00e1cii pam\u00e4te a t\u00e1 je ur\u010den\u00e1 pou\u017eit\u00fdm z\u00e1kladom k\u00f3dovej s\u00fastavy, Pok\u00fasime sa n\u00e1js\u0165 optim\u00e1lny z\u00e1klad k\u00f3d. s\u00fastavy. Majme prvok, ktor\u00fd m\u00f4\u017ee na\u0165 <strong>z<\/strong> \u00farov\u0148ov\u00fdch stavov. Ak pou\u017eijeme <strong>n<\/strong> tak\u00fdch prvkov, dostaneme <strong>n.z<\/strong> pam\u00e4\u0165ov\u00fdch miest. Pou\u017eit\u00edm n symbolov o z stavoch vytvor\u00edme k\u00f3d o d\u013e\u017eke <strong>L = Z<sup>n<\/sup><\/strong>. M\u00e1me teda g(z) = n.z = Z.(ln L \/ ln z) pam\u00e1\u0165ov\u00fdch miest.<br \/>\nN\u00e1jdime minimum danej funkcie \u00de<br \/>\n\u010ci\u017ee minimum dosiahneme pre z = 2,7\u2026 Ak po\u010det stavov mus\u00ed by\u0165 <strong>cel\u00e9 \u010d\u00edslo<\/strong> \u00de <strong>z = 2<\/strong> al. <strong>3.<\/strong><br \/>\nVo\u013eba z = 2 m\u00e1 viacero v\u00fdhod pri mat. \u00fakonoch a tie\u017e pri realiz\u00e1cii pam\u00e4\u0165ov\u00fdch prvkov \u00de najpou\u017e\u00edvanej\u0161\u00edm k\u00f3dom je bin\u00e1rny k\u00f3d.<\/p>\n<h4>Transform\u00e1cie<\/h4>\n<p>Pri prenose je \u010dasto treba transformova\u0165 k\u00f3d o <strong>z<sub>1<\/sub> <\/strong>stavoch a <strong>n<sub>1<\/sub><\/strong> prvkov\u00fdch slov\u00e1ch na k\u00f3d o <strong>z<sub>2<\/sub><\/strong> stavoch a <strong>n<sub>2<\/sub><\/strong> prvkov\u00fdch slov\u00e1ch. Potom je nutn\u00e9 aby .<br \/>\n<span style=\"text-decoration: underline;\">Pr\u00edklad:<\/span> PCM vznik\u00e1 vzorkovan\u00edm a kvantovan\u00edm, po \u0148om m\u00e1me jednoprvkov\u00fd k\u00f3d (n = 1) o z<sub>1<\/sub><br \/>\n(z<sub>1<\/sub> = 127 stavov). Potrebn\u00fd v\u00fdkon plynie zo vz\u0165ahu , N<sub>s<\/sub> \u2013 v\u00fdkon sign\u00e1lu, &#8211; v\u00fdkon \u0161umu, . Ak vzkon\u00e1me transform\u00e1ciu do bin\u00e1rneho d\u00f3du (z<sub>2<\/sub> = 2) , m\u00f4\u017ee sa zn\u00ed\u017ei\u0165 v\u00fdkon. Mus\u00edme roz\u0161\u00edri\u0165 \u0161\u00edrku p\u00e1sma Df.Dt = z.<br \/>\nPred zv\u00e4\u010d\u0161en\u00edm p\u00e1sma zrastie \u0161um. Ak z<sub>1<\/sub> = 128 a N<sub>s1<\/sub> = 1 \u00de Ak Z<sub>2<\/sub> = 2, potrebn\u00fd v\u00fdkon<br \/>\n.<br \/>\nPri zak\u00f3dovan\u00ed 128 stavov do bin. s\u00fastavy treba n = 7 prvkov\u00e9 slov\u00e1 \u00de p\u00e1smo sa roz\u0161\u00edri 7x a \u0161um tie\u017e 7x \u00de .<br \/>\n<strong><span style=\"text-decoration: underline;\">\u00daloha k\u00f3dovania m\u00e1 3 varianty:<\/span><\/strong><\/p>\n<ol>\n<li>pozn\u00e1me L \u2013 d\u013e\u017eka k\u00f3du, l &#8211; pravdepodobnost chyby a h\u013ead\u00e1me n \u2013 min. d\u013e\u017eku d\u00f3d. slova<\/li>\n<li>pozn\u00e1me n, l a h\u013ead\u00e1me L<\/li>\n<li>pozn\u00e1me L, n a h\u013ead\u00e1me l<\/li>\n<\/ol>\n<p>Pre dosiahnutie max. r\u00fdchlosti prenosu n\u00e1s zauj\u00edma N prvkov\u00e1 inform\u00e1cia I = {i<sub>1<\/sub>, \u2026, i<sub>i<\/sub>} k\u00f3dom o 7 stavoch. Pou\u017eijeme k\u00f3d o nerovnako dlh\u00fdch k\u00f3dov\u00fdch slov\u00e1ch, krit\u00e9riom hospod\u00e1rnosti je priemer. D\u013e\u017eka k\u00f3dov\u00e9ho slova. , kde n<sub>i<\/sub> je po\u010det prvkov v i \u2013 tom k\u00f3dovom slove a p<sub>i<\/sub> je pravdepodobnos\u0165 jeho v\u00fdskytu. Ak polo\u017e\u00edme n<sub>i<\/sub> = n \u2013 kon\u0161t. a p<sub>i<\/sub> = 1\/N \u00de , vieme N \u00a3 L je podmienkou jednozna\u010dnosti k\u00f3dovania, ak ale L = Z<sup>n<\/sup> \u00de . Ak nast\u00e1va rovnos\u0165, je optim\u00e1lnou d\u013e\u017ekou k\u00f3du.<br \/>\n<strong><span style=\"text-decoration: underline;\">Optim\u00e1lny nerovnomern\u00fd k\u00f3d<\/span> \u2013 ONK<\/strong><br \/>\n<strong>S\u00fa to k\u00f3dy jednozna\u010dne dek\u00f3dovate\u013en\u00e9 s nulovou nadbyto\u010dnos\u0165ou. Optim\u00e1lnos\u0165<\/strong> zaru\u010duje, \u017ee neexistuje in\u00e1 jednozna\u010dne dek\u00f3dovate\u013en\u00e1 mno\u017eina slov s men\u0161ou d\u013a\u017ekou k\u00f3du. <strong>Nerovnomernos\u0165<\/strong> je vlastnos\u0165 slov s r\u00f4znou d\u013a\u017ekou. Existuj\u00fa i ORK, ale po\u010det inform\u00e1cie mus\u00ed by\u0165 rovn\u00fd mocnine z\u00e1kladu Z. Optim\u00e1lny k\u00f3d je jednozna\u010dne <strong>dek\u00f3dovate\u013en\u00fd<\/strong>, t. j. r\u00f4zne k\u00f3dov\u00e9 slov\u00e1 odpovedaj\u00fa r\u00f4znym spr\u00e1vam. To v\u017edy plat\u00ed u k\u00f3dov s vlastnos\u0165ou <strong>prefixu<\/strong>, kde prefixom k \u2013 teho slova je \u013eubovo\u013en\u00e1 postupnos\u0165 po\u010diato\u010dn\u00fdch prvkov slova. K\u00f3d s vlastnos\u0165ou prefixu je tak\u00fd, \u017ee \u017eiadne k\u00f3dov\u00e9 slovo nie je prefixom in\u00e9ho k\u00f3dov\u00e9ho slova. OK je prefixn\u00fdm k\u00f3dom \u00de OK je jednozna\u010dne dek\u00f3dovate\u013en\u00fd bez odde\u013eovac\u00edch znakov (opa\u010dne to neplat\u00ed).<br \/>\nHUFFMANOVA met\u00f3da<\/p>\n<ol>\n<li>prvky zostav\u00edme s klesaj\u00facou pravdepodobnos\u0165ou v\u00fdskytu<\/li>\n<li>s\u010d\u00edtame pravdepodobnos\u0165 posledn\u00fdch dvoch a usporiadame ako v 1.<\/li>\n<li>opakujeme krok 2. pokia\u013e mo\u017eno s\u010d\u00edta\u0165<\/li>\n<li>ur\u010d\u00edme ko\u013ekokr\u00e1t sa p\u00f4vodn\u00fd symbol z\u00fa\u010dastnil s\u010d\u00edtania \u00de to ur\u010d\u00ed d\u013e\u017eku jeho k\u00f3d. slova<\/li>\n<li>zostav\u00edme k\u00f3dov\u00e9 slov\u00e1 tak, aby boli jesnozna\u010dn\u00e9<\/li>\n<\/ol>\n<p><span style=\"text-decoration: underline;\">Pr\u00edklad:<\/span> Zak\u00f3dujte do ONK t\u00fato abecedu A, B, C, P, K, O s t\u00fdmito pravdepodobnos\u0165ami v\u00fdskytu:<\/p>\n<table>\n<tbody>\n<tr>\n<td width=\"443\"><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>A p(A) = 16\/32 A 16\/32 \u00ae 16\/32 \u00ae 16\/32 \u00ae 16\/32 \u00ae 16\/32 32\/32 = <strong>1<\/strong><\/p>\n<table>\n<tbody>\n<tr>\n<td width=\"527\"><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>B p(B) = 1\/32 O 8\/32 \u00ae 8\/32 \u00ae 8\/32 \u00ae 8\/32 16\/32 +<\/p>\n<table>\n<tbody>\n<tr>\n<td width=\"443\"><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>C p(C) = 2\/32 K 3\/32 \u00ae 3\/32 5\/32 8\/32 +<\/p>\n<table>\n<tbody>\n<tr>\n<td width=\"0\"><\/td>\n<td width=\"20\"><\/td>\n<td width=\"16\"><\/td>\n<td width=\"14\"><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td rowspan=\"3\"><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>P p(P) = 2\/32 C 2\/32 3\/32 3\/32 + <strong>A = 0 al. 1<\/strong><br \/>\n<strong>O = 10 <\/strong><br \/>\nK p(K) = 3\/32 P 2\/32 2\/32 + <strong>K = 110<\/strong><br \/>\n<strong>C = 1110<\/strong><br \/>\nO p(O) = 8\/32 B 1\/32 + <strong>P = 11110<\/strong><br \/>\n<strong>B = 11111 <\/strong><br \/>\nA \u00ae sa z\u00fa\u010dastnilo s\u010d\u00edtania A = 1, O = 2, K = 3, C = 4, P = 5, B = 5<\/p>\n<h3><strong>SHANNON \u2013 FANNONOVA met\u00f3da<\/strong><\/h3>\n<p>&nbsp;<\/p>\n<ol>\n<li>informa\u010dn\u00e9 prvky zostav\u00edme s klesaj\u00facou pravdepodobnos\u0165ou v\u00fdskytu<\/li>\n<li>vytvor\u00edme 2 skupiny s rovnakou pravdepodobnos\u0165ou, horn\u00fdm prvkom prirad\u00edme 1 a doln\u00fdm 0<\/li>\n<\/ol>\n<table width=\"576\">\n<tbody>\n<tr>\n<td width=\"64\">A<\/td>\n<td width=\"64\">16\/32<\/td>\n<td width=\"64\">1<\/td>\n<td width=\"64\">\/<\/td>\n<td rowspan=\"2\" width=\"64\">\/<\/td>\n<td rowspan=\"2\" width=\"64\">\/<\/td>\n<td rowspan=\"6\" width=\"64\"><\/td>\n<td width=\"64\">A<\/td>\n<td width=\"64\">1<\/td>\n<\/tr>\n<tr>\n<td>O<\/td>\n<td>8\/32<\/td>\n<td rowspan=\"5\">0<\/td>\n<td>1<\/td>\n<td>O<\/td>\n<td>01<\/td>\n<\/tr>\n<tr>\n<td>K<\/td>\n<td>3\/32<\/td>\n<td rowspan=\"4\">0<\/td>\n<td rowspan=\"2\">1<\/td>\n<td>1<\/td>\n<td>K<\/td>\n<td>001<\/td>\n<\/tr>\n<tr>\n<td>C<\/td>\n<td>2\/32<\/td>\n<td>0<\/td>\n<td>C<\/td>\n<td>0010<\/td>\n<\/tr>\n<tr>\n<td>P<\/td>\n<td>2\/32<\/td>\n<td rowspan=\"2\">0<\/td>\n<td>1<\/td>\n<td>P<\/td>\n<td>0001<\/td>\n<\/tr>\n<tr>\n<td>B<\/td>\n<td>1\/32<\/td>\n<td>0<\/td>\n<td>B<\/td>\n<td>0000<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h4>V\u00fdhody ONK<\/h4>\n<ol>\n<li>naj\u010dastej\u0161ie sa vyskytuj\u00faci prvok m\u00e1 najkrat\u0161ie slovo<\/li>\n<li>k\u00f3dov\u00e9 slovo nie je prefixom \u00de slov\u00e1 mo\u017eno vysiela\u0165 bez medzery<\/li>\n<li>ONK s\u00fa optim\u00e1lne z h\u013eadiska r\u00fdchlosti, ale vy\u017eaduj\u00fa bez\u0161umov\u00fd kan\u00e1l<\/li>\n<\/ol>\n<h4>Nev\u00fdhody ONK<\/h4>\n<ol>\n<li>vy\u017eaduje vysoko kvalitn\u00fd kan\u00e1l<\/li>\n<\/ol>\n<p><strong><span style=\"text-decoration: underline;\">K\u00f3dy so zlo\u017ekami kon\u0161tantnej v\u00e1hy<\/span> \u2013 IZO k\u00f3dy<\/strong><br \/>\nMaj\u00fa kon\u0161tantn\u00fa v\u00e1hu \u2013 <strong>HAMMINGOVU<\/strong>, <strong>n<\/strong> \u2013 d\u013a\u017eka slova, <strong>m <\/strong>\u2013 po\u010det jednotiek, hovor\u00edme im tie\u017e k\u00f3dy <strong>m <\/strong>z <strong>n<\/strong>. D\u013a\u017eka k\u00f3du m z n je . Najpou\u017e\u00edvanej\u0161\u00ed je <strong>2<\/strong> z <strong>5<\/strong>, <strong>3<\/strong> z <strong>5<\/strong> a k\u00f3d <strong>3<\/strong> zo <strong>7<\/strong> ozna\u010den\u00fd<br \/>\n<strong>MTA 3<\/strong>, kde &#8211; z toho 32 slov pou\u017e\u00edvame na prenos \u010d\u00edslic znakov a riadiacich symbolov.<br \/>\n<strong>MTA 3<\/strong> \u2013 medzin\u00e1rodn\u00e1 telegrafn\u00e1 abeceda doporu\u010den\u00e1 CCITT<br \/>\nK\u00f3dy s pravidelnou zmenou v P \u2013 r\u00e1doch<br \/>\nU t\u00fdchto k\u00f3dov sa 2 susedn\u00e9 slov\u00e1 l\u00ed\u0161ia v P \u2013 radoch, tak\u017ee vzdialenos\u0165 susedn\u00fdch slov je v\u017edy<br \/>\nd(c<sub>i<\/sub>, c<sub>i<\/sub> + 1) = P. D\u013a\u017eka k\u00f3du z\u00e1vis\u00ed od vo\u013eby P a n.<\/p>\n<h4>GREYOV k\u00f3d<\/h4>\n<p>P = 1, v\u00fdhodn\u00fd pre anal\u00f3govo \u2013 \u010d\u00edslicov\u00e9 prevody \u00de pou\u017eitie PCM syst\u00e9my<\/p>\n<h4>Ekvidi\u0161tantn\u00e9 k\u00f3dy<\/h4>\n<p>Dve \u013eubovo\u013en\u00e9 zlo\u017eky maj\u00fa kon\u0161tantn\u00fa vzdialenos\u0165 d(c<sub>i<\/sub>, c<sub>j<\/sub>) = k. D\u013a\u017eka k\u00f3du z\u00e1vis\u00ed od <strong>k<\/strong>. Ich nev\u00fdhodou je relat\u00edvne mal\u00e1 d\u013a\u017eka.<\/p>\n<h4>\u010ealekopisn\u00fd k\u00f3d MTA 2<\/h4>\n<p>MTA 2 je rovnomern\u00fd k\u00f3d s d\u013a\u017ekou n = 5, L<sub>z<\/sub> = 2<sup>n<\/sup> = 32, z toho u\u017e\u00edvame 31 slov pre 2 v\u00fdznamy (p\u00edsmeno \u2013 \u010d\u00edslo). 5 inform. symbolov ka\u017ed\u00e9ho slova je doplnen\u00e1 symbolom \u0160TART a STOP, nenes\u00fa inform\u00e1ciu a t\u00fdm zni\u017euj\u00fa v\u00fdkon. MTA nie je redundantn\u00fd, nem\u00f4\u017ee odhali\u0165 chybu, Dnes pri prenose d\u00e1t je nahr\u00e1dzan\u00fd k\u00f3dom MTA 5 s d\u013a\u017ekou slova n = 7 + <strong>1<\/strong> \u00ae paritn\u00fd bit.<\/p>\n<h4>K\u00f3dy s kontrolou p\u00e1rnosti a nep\u00e1rnosti<\/h4>\n<p>S\u00fa modern\u00e9 so zabezpe\u010dovac\u00edmi vlastnos\u0165ami.<\/p>\n<h4>Redundancia \u00de vznik\u00e1 kontrolou modulu 2 z ur\u010den\u00e9ho po\u010dtu prvkov (symbolov)<\/h4>\n<p><strong>Paritn\u00fd k\u00f3d<\/strong> \u2013 napr. na koniec ka\u017ed\u00e9ho slova prid\u00e1me kontroln\u00fd symbol, paritu vol\u00edme pod\u013ea \u0161trukt\u00fary slov tak, aby sa zlep\u0161ili prenosov\u00e9 podmienky<\/p>\n<h4>Itera\u010dn\u00e9 k\u00f3dy<\/h4>\n<p>Zabezpe\u010denie kr\u00e1tkych slov zni\u017euje v\u00fdkon \u00de pri prenose s\u00fa vytv\u00e1ran\u00e9 <strong>BLOKY<\/strong> a tie zabezpe\u010dujeme ako celok. Inter\u00e1cia m\u00f4\u017ee by\u0165 n \u2013 n\u00e1sobn\u00e1, ale \u010dasto 2 \u2013 n\u00e1sobn\u00e1 (m\u00e1 dobr\u00e9 vlastnosti). D\u013a\u017eka bloku sa rob\u00ed tak, aby odpovedala <strong>matici<\/strong> rozmeru: <strong>po\u010det k\u00f3dov\u00fdch slov x po\u010det symbolov zo slova<\/strong>. Pri prenose id\u00fa slov\u00e1 za sebou, ako posledn\u00e9 ide k\u00f3dov\u00e9 slovo pozd\u013a\u017enych par\u00edt.<br \/>\nPri pou\u017eit\u00ed 3 \u2013 n\u00e1sobnej inter\u00e1cie dok\u00e1\u017eeme odhali\u0165 prakticky v\u0161etky chyby.<\/p>\n<h4>Line\u00e1rne (grupov\u00e9) k\u00f3dy<\/h4>\n<ul>\n<li>redukovan\u00e9 k\u00f3dy, systematick\u00e9, blokov\u00e9, d\u013a\u017eka bloku N<\/li>\n<\/ul>\n<p>Zobrazenie informa\u010dn\u00fdch postupnost\u00ed do k\u00f3dov\u00fdch slov je line\u00e1rne. Line\u00e1rnou kombin\u00e1ciou slov. k\u00f3du<br \/>\nVznik\u00e1 nov\u00e9 k\u00f3dov\u00e9 slovo. Zabezpe\u010dovacie symboly tvor\u00edme ako line\u00e1rnu kombin\u00e1ciu inf. symbolov. Lin. K\u00f3dy so z\u00e1kladom z = 2 tvoria <strong>GRUPU<\/strong> s oper\u00e1ciou s\u00fa\u010dtu modulu 2. Ozna\u010d\u00edme (n, k) \u00de n \u2013 d\u013a\u017eka \u013eubovo\u013en\u00e9ho slova, k \u2013 po\u010det inform. symbolov. Regul\u00e1rnos\u0165 grupov\u00fdch k\u00f3dov umo\u017e\u0148uje \u013eahko n\u00e1js\u0165 K\u00d3DER a DEK\u00d3DER. Zabezpe\u010denie je ur\u010den\u00e9 min. k\u00f3dovou vzdialenos\u0165ou = min. v\u00e1ha k\u00f3du, lebo d(c<sub>i<\/sub>, c<sub>j<\/sub>) = c<sub>i<\/sub> \u00c5 c<sub>j<\/sub> = |c<sub>k<\/sub>| = w.<br \/>\n<span style=\"text-decoration: underline;\">Pr\u00edklad:<\/span><\/p>\n<table width=\"158\">\n<tbody>\n<tr>\n<td width=\"26\">b<sub>1<\/sub><\/td>\n<td width=\"26\">b<sub>2<\/sub><\/td>\n<td width=\"26\">b<sub>3<\/sub><\/td>\n<td width=\"26\"><\/td>\n<td width=\"26\">e<sub>1<\/sub><\/td>\n<td width=\"26\">e<sub>2<\/sub><\/td>\n<\/tr>\n<tr>\n<td>0<\/td>\n<td>0<\/td>\n<td>0<\/td>\n<td>=<\/td>\n<td>0<\/td>\n<td>0<\/td>\n<\/tr>\n<tr>\n<td>1<\/td>\n<td>0<\/td>\n<td>0<\/td>\n<td>=<\/td>\n<td>1<\/td>\n<td>1<\/td>\n<\/tr>\n<tr>\n<td>0<\/td>\n<td>1<\/td>\n<td>0<\/td>\n<td>=<\/td>\n<td>1<\/td>\n<td>0<\/td>\n<\/tr>\n<tr>\n<td>1<\/td>\n<td>1<\/td>\n<td>0<\/td>\n<td>=<\/td>\n<td>0<\/td>\n<td>1<\/td>\n<\/tr>\n<tr>\n<td>0<\/td>\n<td>0<\/td>\n<td>1<\/td>\n<td>=<\/td>\n<td>0<\/td>\n<td>1<\/td>\n<\/tr>\n<tr>\n<td>1<\/td>\n<td>0<\/td>\n<td>1<\/td>\n<td>=<\/td>\n<td>1<\/td>\n<td>0<\/td>\n<\/tr>\n<tr>\n<td>0<\/td>\n<td>1<\/td>\n<td>1<\/td>\n<td>=<\/td>\n<td>1<\/td>\n<td>1<\/td>\n<\/tr>\n<tr>\n<td>1<\/td>\n<td>1<\/td>\n<td>1<\/td>\n<td>=<\/td>\n<td>0<\/td>\n<td>0<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>b<sub>1<\/sub> b<sub>2<\/sub> b<sub>3<\/sub><\/p>\n<ol>\n<li>a) 1 0 1 1 0<\/li>\n<\/ol>\n<table>\n<tbody>\n<tr>\n<td width=\"112\">\n<table width=\"100%\">\n<tbody>\n<tr>\n<td>1 a ko\u013eko je 1 = 0<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>\u00ae 0 a ko\u013eko je 0<br \/>\nS = (S<sub>1<\/sub>, S<sub>2<\/sub>)<br \/>\nS<sub>i<\/sub>=e<sub>1<\/sub>+;ak bolo &#8220; prenesen\u00e9 dobre \u00deS=(0,0) b<sub>1<\/sub> b<sub>2<\/sub> b<sub>3<\/sub><\/p>\n<ol>\n<li>b) ak 1 1 1 1 0<\/li>\n<\/ol>\n<table>\n<tbody>\n<tr>\n<td width=\"100\">\n<table width=\"100%\">\n<tbody>\n<tr>\n<td>0 a ko\u013eko je 0 = 0<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>S = (1, 0)<\/p>\n<table>\n<tbody>\n<tr>\n<td width=\"100\">\n<table width=\"100%\">\n<tbody>\n<tr>\n<td>0 a ko\u013eko je 1 = 1<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h4>Cyklick\u00e9 k\u00f3dy<\/h4>\n<p>S\u00fa to bin\u00e1rne systematick\u00e9 k\u00f3dy, jednoduch\u00e1 realiz\u00e1cia k\u00f3deru a dek\u00f3deru, zabezpe\u010denie i proti zhlukom ch\u00fdb, kde ich d\u013a\u017eka je \u00a3 ako po\u010det vlo\u017een\u00fdch kontroln\u00fdch symbolov \u00de po\u010det kontroln\u00fdch symbolov z\u00e1vis\u00ed od po\u017eadovan\u00e9ho stup\u0148a zabezpe\u010denia. Pri kon\u0161trukcii s\u00fa vyu\u017eit\u00e9 poznatky algebraick\u00fdch syst\u00e9mov. Postupnos\u0165 bin\u00e1rnych inf. znakov vyjadrujeme v tvare mnoho\u010dlena pou\u017e\u00edvan\u00e9ho na zobrazenie dvohkob\u00e9ho \u010d\u00edsla v desiatkovej s\u00fastave.<br \/>\n<span style=\"text-decoration: underline;\">Pr\u00edklad:<\/span><br \/>\n1 0 1 0 0 1 1 1 1.2<sup>7<\/sup> + 0.2<sup>6<\/sup> + 1.2<sup>5<\/sup> + 0.2<sup>4<\/sup> + 0.2<sup>3<\/sup> + 1.2<sup>2<\/sup> + 1.2<sup>1<\/sup> + 1.2<sup>0<\/sup><br \/>\nZobrazenie mnoho\u010dlenom: G(x) = x<sup>7<\/sup> + x<sup>5<\/sup> + x<sup>2<\/sup> + x + 1<br \/>\nIde o mnoho\u010dleny, ktor\u00fdch koeficient je spracovan\u00fd modulom 2, Preto mo\u017eno n\u00e1sobi\u0165, deli\u0165, a s\u010d\u00edta\u0165 modulo 2.<br \/>\n<span style=\"text-decoration: underline;\">Poz.:<\/span> Tieto oper\u00e1cie mo\u017eno vykon\u00e1va\u0165 i priamo s bin\u00e1rnymi \u010d\u00edslami. V praxi tieto oper\u00e1cie realizujeme pomocou line\u00e1rnych sekven\u010dn\u00fdch automatov.<br \/>\n<strong>Kon\u0161trukcia cyklick\u00fdch k\u00f3dov<\/strong><br \/>\nNech G(x) \u2013 mnoho\u010dlen zobrazuje <strong>k<\/strong> inf. znakov (ST = k \u2013 1)<br \/>\nR(x) \u2013 mnoho\u010dlen zobrazuje <strong>r<\/strong> kontroln\u00fdch znakov (r \u2013 1)<br \/>\nF(x) \u2013 mnoho\u010dlen zobrazuje pren\u00e1\u0161an\u00fd blok (n \u2013 1 = k + r \u2013 1)<br \/>\n<span style=\"text-decoration: underline;\">Pr\u00edklad:<\/span><br \/>\nChceme prenies\u0165 slovo, ktor\u00e9 chceme zak\u00f3dova\u0165 do kontroln\u00e9ho slova.<br \/>\nG(x) = x<sup>7<\/sup> + x<sup>5<\/sup> + x<sup>2<\/sup> + x + 1 1 0 1 0 0 1 1 1<br \/>\nR(x) = x + 1 1 1<br \/>\nF(x) vytvor\u00edme ako R(x) + x<sup>r<\/sup>.G(x) \u00de F(x) = x<sup>9<\/sup> + x<sup>7<\/sup> + x<sup>4<\/sup> + x<sup>3<\/sup> + x<sup>2<\/sup> + x + 11 0 1 0 0 1 1 1 1 1 \u00de<br \/>\n\u00de vysielame v opa\u010dnom porad\u00ed \u00de<br \/>\n, P(x) \u2013 vytvoren\u00fd mnoho\u010dlen z tabuliek<br \/>\nZabezpe\u010denie je zalo\u017een\u00e9 na tom, \u017ee mo\u017en\u00e9 F(x) s\u00fa delite\u013en\u00e9 tzv. vytv\u00e1raj\u00facim mnoho\u010dlenom P(x) bez<br \/>\nzvy\u0161ku.<\/p>\n<table>\n<tbody>\n<tr>\n<td width=\"316\">\n<table width=\"100%\">\n<tbody>\n<tr>\n<td>(x<sup>11<\/sup> + x<sup>9<\/sup> + x<sup>6<\/sup> + x<sup>5<\/sup> + x<sup>4<\/sup>) : (x<sup>3<\/sup> + x + 1) = x<sup>8<\/sup> + x<sup>5<\/sup> + x<br \/>\nx<sup>11<\/sup> + x<sup>9<\/sup> + x<sup>8<\/sup><br \/>\nx<sup>8<\/sup> + x<sup>6<\/sup> + x<sup>5<\/sup><br \/>\nx<sup>4<\/sup> + x<sup>2<\/sup> + x<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><span style=\"text-decoration: underline;\">Pr\u00edklad:<\/span><br \/>\n1 0 1 0 0 1 1 1<br \/>\nG(x) = x<sup>7<\/sup> + x<sup>5<\/sup> + x<sup>2<\/sup> + x + 1 r = 4<br \/>\nG(x).x<sup>4<\/sup> = x<sup>11<\/sup> + x<sup>9<\/sup> + x<sup>6<\/sup> + x<sup>5<\/sup> + x<sup>4<\/sup><br \/>\nP(x) = x<sup>3<\/sup> + x + 1<br \/>\nF(x) = G(x).x<sup>r<\/sup> + R(x)<br \/>\n<strong>ANTENY<\/strong><br \/>\nAnt\u00e9na je tak\u00e1 usporiadan\u00e1 s\u00fastava vodi\u010dov a izolantov, kt. je schopn\u00e1 meni\u0165 energiu priveden\u00e9ho vysokofrekven\u010dn\u00e9ho el. pr\u00fadu na energiu vo\u013en\u00e9ho elektromag. po\u013ea alebo naopak.<br \/>\nROZDELENIE: a) pod\u013ea smeru premeny energie: vysielacie a prij\u00edmacie<\/p>\n<ol>\n<li>b) pod\u013ea kmito\u010dtov\u00e9ho rozsahu: dlhovlnn\u00e9<\/li>\n<\/ol>\n<p>strednovlnn\u00e9<br \/>\nkr\u00e1tkovlnn\u00e9<br \/>\npre VKV<br \/>\ndecimetrov\u00e9, centimetrov\u00e9 vlny<\/p>\n<ol>\n<li>c) pod\u013ea smeru vy\u017earovania: v\u0161esmerov\u00e9 a viac \u010di menej smerov\u00e9<\/li>\n<li>d) pod\u013ea rozlo\u017eenia vf. nap\u00e4tia: so stojacou vlnou (rezonan\u010dn\u00e9)<\/li>\n<\/ol>\n<p>s postupnou vlnou (nerezonan\u010dn\u00e9)<\/p>\n<ol>\n<li>e) pod\u013ea pou\u017eitia: rozhlasov\u00e9, telev\u00edzne, zameriavacie, lietadlov\u00e9,<\/li>\n<\/ol>\n<p>lodn\u00e9<br \/>\n<strong>DELENIE PODLA VEDLAJSICH HLADISK:<\/strong><\/p>\n<ol>\n<li>pod\u013ea po\u010dtu \u010dlenov: jednoduch\u00e9 a zlo\u017een\u00e9<\/li>\n<li>pod\u013ea druhu \u010dlenov: zlo\u017een\u00e9 z akt\u00edvnych\/ z pas\u00edvnych prvkov<\/li>\n<li>pod\u013ea \u0161\u00edrky p\u00e1sma: \u0161irokop\u00e1smov\u00e9 a \u00fazkop\u00e1smov\u00e9<\/li>\n<li>pod\u013ea druhu akt\u00edvnych prvkov: dipol\u00f3v\u00e9, slu\u010dkov\u00e9, \u0161tvrtinov\u00e9<\/li>\n<\/ol>\n<p><strong>Z\u00e1kladn\u00e9 vlastnosti ant\u00e9n:<\/strong><\/p>\n<ol>\n<li>elektrick\u00e1 vstupn\u00e1 impedencia Z z\u00e1vis\u00ed od kmito\u010dtu, druhu, rozmer a po\u010dtu vy\u017earovan\u00fdch \u010dlenov<\/li>\n<li>smerovos\u0165 F ur\u010duje rozlo\u017eenie vf. energie<\/li>\n<li>zisk ant\u00e9ny G ako pomer intenzity vysielan\u00e9ho po\u013ea v ur\u010d. smere k intenzite ide\u00e1lneho v\u0161esmerov\u00e9ho \u017eiari\u010da<\/li>\n<li>efekt\u00edvna plocha ant\u00e9ny A je ur\u010den\u00e1 plocha ant\u00e9ny, kde je schopn\u00e1 zachyti\u0165energiu<\/li>\n<li>\u00fa\u010dinnos\u0165 ant\u00e9ny \u03b7 ako pomer medzi privedenou a vy\u017eiarenou energiou<\/li>\n<\/ol>\n<p>Ant\u00e9na je obojsmern\u00fd meni\u010d energie a jeho vlastnosti nez\u00e1visia od smeru premeny. Hustota \u017eiarenia S vo vzdialenosti R pri vysielacom v\u00fdkone P zo v\u0161esmerov\u00e9ho (izotropn\u00e9ho) \u017eiari\u010da je dan\u00e1 vz\u0165ahom . Hustota \u017eiarenia \u013eubovo\u013enej ant\u00e9ny so ziskom G<sub>is<\/sub>, is-izotropny , pri\u010dom uisk G<sub>is<\/sub> je z\u00e1visl\u00fd na smere definovanom horizont\u00e1nlou odch\u00fdlkou \u03c6 a vertik\u00e1lnou elev\u00e1ciou \u03b4 od smeru ant\u00e9ny. Z\u00e1vislos\u0165 na smer vykazuje aj efekt\u00edvna plocha ant\u00e9ny A, pre kt. platia rovnako vy\u017earovacia diagramy. Medzi ziskom a plochou A plat\u00ed vz\u0165ah . V hlavnom smere ant\u00e9ny \u03c6=0, \u03b3=0 (\u03b3-theta) b\u00fdva zisk i efekt\u00edvna plocha ant\u00e9ny najv\u00e4\u010d\u0161ia. \u010c\u00edm v\u00e4\u010d\u0161\u00ed je tento zisk, t\u00fdm viac je vysielan\u00fd v\u00fdkon s\u00fastreden\u00fd do hlavn\u00e9ho smeru a t\u00fdm menej v\u00fdkonu ost\u00e1va pre ostatn\u00e9 smery.<br \/>\nZ\u00e1kladn\u00e9 ant\u00e9ny so stojatou vlnou:<br \/>\nZa ant\u00e9nu mo\u017eno pova\u017eova\u0165 ka\u017ed\u00fd vodi\u010d vo vo\u013enom priestore. Vy\u017earovanie vf. v\u00fdkonu do priestoru z vodi\u010da je t\u00fdm \u00fa\u010dinnej\u0161\u00ed, \u010d\u00edn s\u00fa v\u00e4\u010d\u0161ie rozmery vodi\u010da v pomere k d\u013a\u017eke vlny. Z praktic. d\u00f4vodov \u2013 ant\u00e9ny mal\u00fdch rozmerov.<br \/>\n3 z\u00e1kladn\u00e9 typy \u017eiari\u010dov: element\u00e1rny dip\u00f3l *1<br \/>\nelement\u00e1rna slu\u010dka *2<br \/>\nelement\u00e1rna \u0161trbina *3<br \/>\n*1-tvoria ho 2 priamkov\u00e9 vodi\u010de o d\u013a\u017eke d nap\u00e1jan\u00e9 vf. pr\u00fadom I. Elektromag. pole tohto dip\u00f3lu vo vzdialenosti R a v smere ur\u010denom uhlom \u03b3 je ur\u010den\u00e9 rovnicou , kde je d\u013a\u017eka vlny ur\u010den\u00e1 kmito\u010dtom f nap\u00e1jacieho pr\u00fadu I. Tejto itenzite po\u013ea odpoved\u00e1 celkov\u00fd vy\u017eiaren\u00fd v\u00fdkon vypo\u010d\u00edtan\u00fd integr\u00e1ciouv\u00fdkonu vy\u017eiaren\u00e9ho do v\u0161etk\u00fdch smerov . Vy\u017earovan\u00edm v\u00fdkonu rastie re\u00e1lny odpor ant\u00e9ny o tzv. vy\u017earovac\u00ed odpor, kt.reprezentuje \u010das\u0165<br \/>\n*2 doch\u00e1dza tu k podobn\u00fdm vz\u0165ahom o ploche S . Porovn\u00e1van\u00edm s element\u00e1rnym dipolom zist\u00edme, \u017ee slu\u010dka sa chov\u00e1 ako element. dipol o dl\u017eke<br \/>\n*3 podobn\u00e9 vz\u0165ahy s dl\u017ekou d<br \/>\n\u0160trbina je nap\u00e1jan\u00e1 uprostred nap\u00e4t\u00edm U a plat\u00ed . Porovnan\u00edm s elment.dipolom zist\u00edme, \u017ee elemen. \u0161trbina nap\u00e1jan\u00e1 U=188V sa chov\u00e1 rovnako ako element. dipol rovnakej d\u013a\u017eky nap\u00e1jan\u00fd pr\u00fadom 1A.<br \/>\nV\u0161etky tieto \u010dleny maj\u00fa rovnak\u00fd vy\u017earovac\u00ed diagram -pre d\u013a\u017eky.<br \/>\n\u010eal\u0161ou skupinou \u017eiari\u010dov s\u00fa <span style=\"text-decoration: underline;\">\u017eiari\u010de rezonan\u010dn\u00e9:<\/span> povlnen\u00e9 dipoly a \u0161tvrtinov\u00e9 monopoly.<br \/>\nPOVLNENE DIPOL o dl\u017eke , m\u00e1 nap\u00e1jaciu impedanciu \u010disto re\u00e1lnu R=72\u03a9, pou\u017e\u00edva sa na KV a VKV a v p\u00e1sme decimetrov\u00fdch vln.<br \/>\n<strong>STVRTVLNOVY MONOPOL<\/strong> je vertik\u00e1lny \u017eiari\u010d o dl\u017eke nap\u00e1jan\u00fd medzi p\u00e4tou a zemou, m\u00e1 vy\u017earovac\u00ed odpor R=36 \u03a9, pou\u017e\u00edva sa ako vysielacia ant\u00e9na pre KV, SV a DV.<br \/>\nD\u00f4le\u017eit\u00fdm \u010dlenom je tie\u017e SKLADANY DIPOL, kt. m\u00e1 vstupn\u00fa impedanciu 300 \u03a9 a hod\u00ed sa pre nap\u00e1janie ploch\u00fdm dvojit\u00fdm vodi\u010dom s polyetyl\u00e9nov\u00fdm dialektikom. Jeho vstupn\u00e1 impedancia je menej z\u00e1visl\u00e1 od kmito\u010dtu ne\u017e u jednoduch\u00fdch dipolov, je teda \u0161irokop\u00e1smov\u00fd a vyu\u017e\u00edva sa najm\u00e4 pre TV ant\u00e9ny.<br \/>\n<strong>ANTENNE SUSTAVY<\/strong><br \/>\nNajd\u00f4le\u017eitej\u0161\u00edmi zlo\u017een\u00fdmi s\u00fastavami s\u00fa rady dipolov, dipolove steny, Jagiho ant\u00e9ny a s\u00fastavy s ploch\u00fdmi reflektormi. Pri suf\u00e1rovom nap\u00e1jam\u00ed radov dipolov sa intentzity po\u013ea, kt. vzniklo v kolmom smere na os radu s\u010d\u00edtaj\u00fa a tak sa dosahuje najv\u00e4\u010d\u0161\u00ed zisk. Vy\u017earovac\u00ed diagram v smere radu sa v\u0161ak zu\u017euje. Tieto syst\u00e9my sa pou\u017e\u00edvaj\u00fa u TV vysielac\u00edch ant\u00e9n a u rozhlasov\u00fdch vysiela\u010doch na VKV. Na ka\u017edej strane vysielacieho sto\u017eiara sa vytvor\u00ed rad dipolov,kt. spolu vytvoria v\u0161esmerov\u00fd vy\u017earovac\u00ed diagram,kt. intenzita je 3 a\u017e 5-kr\u00e1t v\u00e4\u010d\u0161ia ako u v\u0161esmerov\u00e9ho \u017eiari\u010da. \u00da\u010dinn\u00fd vy\u017earovac\u00ed v\u00fdkon ERP sa zv\u00fd\u0161i 10 a\u017e 50 kr\u00e1t oproti skuto\u010dn\u00e9mu v\u00fdkonu vysiela\u010da. Podobn\u00fd \u00fa\u010dinok maj\u00fa dip\u00f3lov\u00e9 steny usmer\u0148uj\u00face v\u00fdkon do \u00fazkeho zv\u00e4zku. \u010casto sa st\u00e1vaj\u00fa za sebou dve steny s odstupom l\/4, kde zadn\u00e1 stena sa nap\u00e1ja s f\u00e1zov\u00fdm predstihom p\/2, \u010do p\u00f4sob\u00ed, \u017ee v\u00fdkony vpred sa s\u010d\u00edtaj\u00fa a vzad sa ru\u0161ia.<br \/>\n<strong>DRUZICOVE SPOJE<\/strong><br \/>\nS\u00fa zalo\u017een\u00e9 na vyu\u017eit\u00ed elektromag. vlnenia pre prenos inform\u00e1cie. V\u00fdrazn\u00fd rozvoj t\u00fdchto syst\u00e9mov sa datuje do ned\u00e1vnej minulosti a je ve\u013emi \u00fazko sp\u00e4t\u00fd s obdob\u00edm n\u00e1stupu integrovanl\u00fdch obvodov a vysokou hustotou integr\u00e1cie. Tieto syst\u00e9my sl\u00fa\u017eia pre prenos info na ve\u013ek\u00e9 vzdialenosti.<br \/>\nNaj\u010dastej\u0161ie pou\u017eitie: rozhlas a TV prenosy, komunik.kan\u00e1ly, navig\u00e1cia dopr. prostriedkov, ur\u010dovanie polohy.<br \/>\nPASIVNE DRUZICOVE SPOJE \u2013 najm\u00e4 balony v pokovovan\u00fdm povrchom, kt. odr\u00e1\u017ea elektromag. vlny,kvalita tak\u00fdchto prenosov\u00fdch syst\u00e9mov bola nedostato\u010dn\u00e1, ovl\u00e1danie ve\u013emi zlo\u017eit\u00e9 a aj ich \u017eivotnos\u0165 bola ve\u013emi mal\u00e1, z t\u00fdchto d\u00f4vodov sa komer\u010dne nevyu\u017e\u00edvali.<br \/>\nAKTIVNE DRUZICOVE SPOJE- pracuj\u00fa na princ\u00edpe sign\u00e1lu z pozemnej stanice na vzostupnej frekvencii jeho zosilnenia a n\u00e1slednej transform\u00e1cii na zostupn\u00fa frekvenciu a odvysielanie smerom k zemi.<br \/>\nPre obojsmern\u00fd prenos s\u00fa potrebn\u00e9 parabolick\u00e9 ant\u00e9ny s priemerom 3 a\u017e 15 m. Zivotnost dru\u017eice bez korekcie dr\u00e1hy z\u00e1vis\u00ed od po\u010diato\u010dnej v\u00fd\u0161ky (pri 500km asi 10 rokov). Dru\u017eice sa pohybuj\u00fa po eliptickej alebo kruhovej dr\u00e1he okolo zeme. Najm\u00e4 dru\u017eice vypusten\u00e9 pre komer\u010dn\u00e9 \u00fa\u00fa\u010dely sa pohybuj\u00fa po kruhov\u00fdch dr\u00e1hach r\u00fdchlos\u0165ou toto\u017enou s r\u00fdchlos\u0165ou ot\u00e1\u010dania zeme. Tieto dru\u017eice sa naz\u00fdvaj\u00fa <span style=\"text-decoration: underline;\">geostacion\u00e1rne, <\/span>lebo sa relat\u00edvne pohybuj\u00fa vo\u010di povrchu zeme. Geostacion\u00e1rne dru\u017eice na uchovanie kon\u0161tantnej v\u00fd\u0161ky vzh\u013eadom k zemi a kon\u0161tantnej r\u00fdchlosti ot\u00e1\u010dania nemusia by\u0165 umiestnen\u00e9 vo v\u00fd\u0161ke 35820km nad povrchom zeme. Satelit na obe\u017enej dr\u00e1he m\u00e1 pridelen\u00fa ur\u010dit\u00fa polohu \u2013 \u201eslot\u201c \u0161\u00edrky 2 a\u017e 4 stupne s presnos\u0165ou 0,05 a\u017e 0,2 stup\u0148a. Pre frekven\u010dn\u00e9 p\u00e1smo 14\/12 GHz je potrebn\u00e1 presnos\u0165 0,05 stup\u0148a. P\u00f4soben\u00edm gravit\u00e1cie sa men\u00ed poloha dru\u017eice. Satelit pomocou motorov raz za dva a\u017e \u0161tyri t\u00fd\u017edne vykon\u00e1va korekcie dr\u00e1hy. Z\u00e1soba paliva posta\u010duje na nieko\u013eko desiatok rokov.<br \/>\nV s\u00fa\u010dasnosti vyu\u017e\u00edvame dva typy komunik. satelitov \u2013 rota\u010dn\u00e9 a stabilizovan\u00e9.<br \/>\nOBRAZOK by tu mal byt.. chm..<br \/>\nPre navig\u00e1ciu lietadiel a dru\u017e\u00edc sa pou\u017e\u00edvaj\u00fa min 4 dru\u017eice.<br \/>\nOBRAZOK<br \/>\nV s\u00fa\u010dasnosti je na orbit\u00e1lnej dr\u00e1he ve\u013ek\u00fd po\u010det satelitov. CCR ur\u010duje polohy pre nov\u00e9 dru\u017eice, kde ich vz\u00e1jomn\u00e1 vzdialenost je 4 stupne. Pou\u017e\u00edvaj\u00fa sa \u0161tandardn\u00e9 frekven\u010dn\u00e9 p\u00e1sma<br \/>\n\u201eC\u201c 6\/4 GHz (3,8 \u2013 4,2)<br \/>\n\u201ekv\u201c 14\/12 GHz (10,95 \u2013 12,75)<br \/>\n\u010c\u00edm v\u00e4\u010d\u0161ia frekvencia, t\u00fdm men\u0161ia ant\u00e9na. Dru\u017eice s\u00fa vybaven\u00e9 prev\u00e1dza\u010dmi,kt. zabezpe\u010duj\u00fa prenos pre nieko\u013eko kan\u00e1lov \u2013 <span style=\"text-decoration: underline;\">transpond\u00e9rov<\/span>.<br \/>\n<strong>POCITACOVE SIETE<\/strong><br \/>\npozn\u00e1me 3 typy: LAN-lok\u00e1lne siete (z\u00e1vodn\u00e1 doprava)<br \/>\nMAN- mestsk\u00e9 siete (mestsk\u00e1 doprava)<br \/>\nWAN \u2013 celosvetov\u00e9 siete (medzin\u00e1rodn\u00e1 doprava)<br \/>\nTopologia sieti: &#8211; hviezda, &#8211; kruhov\u00e1, -diagon\u00e1lna, -zbernicov\u00e1,<br \/>\n<strong>ETERNET<\/strong>-najjednoduch\u0161ia sie\u0165 typu LAN, topologia je line\u00e1rne, ka\u017ed\u00fd PC m\u00e1 sie\u0165ov\u00fa kartu<br \/>\ndruh kabel\u00e1\u017ee &#8211; koaxi\u00e1l, konektory BNC<br \/>\nv\u00fdhody: ekonomicky nen\u00e1ro\u010dn\u00e1 sie\u0165,<br \/>\nnev\u00fdhody: v\u00fdpadok jedn\u00e9ho PC \u2013nefunguj\u00fa ostatn\u00e9, slab\u00e1 bezpe\u010dnos\u0165,<br \/>\nsp\u00f4sob riadenia: riadenie zabezpe\u010den\u00e9 ak jeden PC chce posla\u0165 data in\u00e9mu, v\u00fdzva do siete, ak do ur\u010ditej \u010dasovej doby nedostal v\u00fdzvu, za\u010dne vysiela\u0165, ke\u010f jeden vysiela, ostatn\u00e9 \u010dakaj\u00fa.<br \/>\n<strong>TOOKEN RING<\/strong>-topologia je kruhova,kabel\u00e1\u017e koaxi\u00e1l, BNC a R45<br \/>\nv\u00fdhody:kvalita, spolahlivost, bezpecnost,<br \/>\nnev\u00fdhody: ekon. n\u00e1rocnost,<br \/>\nsp\u00f4sob riadenia: tooken-zvuk, z toho vypl\u00fdva kto m\u00e1 tooken m\u00f4\u017eu vysiela\u0165, ostatn\u00e9 \u010dakaj\u00fa, ke\u010f odvysiela pod\u00e1va tooken \u010fal\u0161iemu<br \/>\nARCNET-topologia je hviezda,z\u00e1kl. PC,kt. riadi a na\u0148 s\u00fa pripojen\u00e9 ostatn\u00e9<br \/>\nkabel\u00e1\u017e: BNC a RJ45<br \/>\nv\u00fdhody: spolahlivost, bezpecnost, kvalita<br \/>\nnev\u00fdhody: ekon, n\u00e1ro\u010dnos\u0165,<br \/>\nsposob riadenia: centr\u00e1lne, server riadi cel\u00fa sie\u0165<br \/>\n<strong>SIETOVA KARTA<\/strong>-(adapter)-z\u00e1kl. \u00faloha \u2013transform\u00e1cia s\u00e9riov\u00e9ho prenosu na paraleln\u00fd, nevyhnutn\u00e1 podmienka preLAN:sie\u0165ov\u00fd opera\u010dn\u00fd syst\u00e9m \u2013 NT,LINUX,UNIX.<br \/>\nLINUX-otvoren\u00fd opera\u010dn\u00fd syst\u00e9m, bol vyroben\u00fd amat\u00e9rom a m\u00f4\u017ee sa roz\u0161irova\u0165 a \u013eubovo\u013ene do\u0148 vstupova\u0165.<br \/>\nOS-rozdelenie- otvoren\u00e9 a uzavret\u00e9, -polootvoren\u00e9 a polouzavret\u00e9,<br \/>\nMETODA EDI-met\u00f3da v\u00fdmeny info, u n\u00e1s ju vyu\u017e\u00edvaj\u00fa len firmy,kt. s\u00fa n\u00faten\u00e9 komunikova\u0165 so zahrani\u010d\u00edm (VS\u017d,\u010cSOB), PC ka\u017ed\u00e9ho \u00fa\u010dastn\u00edka mus\u00ed by\u0165 pripojen\u00fd na prenosov\u00fa sie\u0165 (telegrafn\u00e1, komunika\u010dn\u00e1 &#8211; telefonna, komunika\u010dn\u00e1 \u2013 paraleln\u00e1, ISDN). Dva typy prenosov (prostredie telekomunik. sieti) a) priame \u2013 spojenie jednej stanice s inou b) spojenie s vyu\u017eit\u00edm slu\u017eieb s tzv. pridanou hodnotou. V\u00e4\u010d\u0161inou sa vyu\u017e\u00edva druhl\u00fd sp\u00f4sob spojenia (b) \u2013 menej siete prepojen\u00ed, m\u00e1me prepojenie len na jedin\u00e9ho u\u010dastn\u00edka a potrebujeme vytv\u00e1ra\u0165 spojenie len s n\u00edm, aby sme uskuto\u010dnili zasielanie spr\u00e1v,kt. bud\u00fa potom distribuovan\u00e9 ku v\u0161etk\u00fdm ostatn\u00fdm be\u017en\u00fdm partnerom \u2013 obr.<br \/>\nEDI &#8211; medzin\u00e1rodne vypracovan\u00e9 \u0161tandardn\u00e9 dokumenty<br \/>\nTyp 132 \u2013 len toto prenesie a vie, \u017ee je to napr. objedn\u00e1vka, obsahuje len potrebn\u00e9 \u00fadaje bez \u201eom\u00e1\u010dok.\u201c<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Inform\u00e1cia a jej prenos Miera inform\u00e1cie Vhod\u00e9 \u0161trukt\u00fary: Nosi\u010d inform\u00e1cie \u2013 v\u00fdroky v telekomunika\u010dn\u00fdch prenosoch, sign\u00e1ly atd. V\u00fdrok nes\u00faci inform\u00e1ciu m\u00f4\u017eeme sk\u00fama\u0165 z viacer\u00fdch h\u013ead\u00edsk: &hellip; <\/p>\n","protected":false},"author":28,"featured_media":27601,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[632,636],"tags":[641,640,639],"class_list":["post-8600","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-informacne-systemy","category-komunikacia","tag-informacie","tag-informacny-system","tag-is"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.6 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Inform\u00e1cie a jej prenos - Auto\u0161koly.sk<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.autoskoly.sk\/news\/informacie-a-jej-prenos\/\" \/>\n<meta property=\"og:locale\" content=\"sk_SK\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Inform\u00e1cie a jej prenos - Auto\u0161koly.sk\" \/>\n<meta property=\"og:description\" content=\"Inform\u00e1cia a jej prenos Miera inform\u00e1cie Vhod\u00e9 \u0161trukt\u00fary: Nosi\u010d inform\u00e1cie \u2013 v\u00fdroky v telekomunika\u010dn\u00fdch prenosoch, sign\u00e1ly atd. V\u00fdrok nes\u00faci inform\u00e1ciu m\u00f4\u017eeme sk\u00fama\u0165 z viacer\u00fdch h\u013ead\u00edsk: &hellip;\" \/>\n<meta property=\"og:url\" content=\"https:\/\/www.autoskoly.sk\/news\/informacie-a-jej-prenos\/\" \/>\n<meta property=\"og:site_name\" content=\"Auto\u0161koly.sk\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/www.facebook.com\/vrtulniky\/\" \/>\n<meta property=\"article:published_time\" content=\"2023-07-12T22:23:54+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2024-05-14T08:37:39+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/www.autoskoly.sk\/news\/wp-content\/uploads\/2022\/08\/komunikacia-autoskoly-15.jpg\" \/>\n\t<meta property=\"og:image:width\" content=\"1600\" \/>\n\t<meta property=\"og:image:height\" content=\"1066\" \/>\n\t<meta property=\"og:image:type\" content=\"image\/jpeg\" \/>\n<meta name=\"author\" content=\"Frederik\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Autor\" \/>\n\t<meta name=\"twitter:data1\" content=\"Frederik\" \/>\n\t<meta name=\"twitter:label2\" content=\"Predpokladan\u00fd \u010das \u010d\u00edtania\" \/>\n\t<meta name=\"twitter:data2\" content=\"36 min\u00fat\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\\\/\\\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\\\/\\\/www.autoskoly.sk\\\/news\\\/informacie-a-jej-prenos\\\/#article\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/www.autoskoly.sk\\\/news\\\/informacie-a-jej-prenos\\\/\"},\"author\":{\"name\":\"Frederik\",\"@id\":\"https:\\\/\\\/www.autoskoly.sk\\\/news\\\/#\\\/schema\\\/person\\\/2a94f3f8738a3241d1f656aef8d54497\"},\"headline\":\"Inform\u00e1cie a jej prenos\",\"datePublished\":\"2023-07-12T22:23:54+00:00\",\"dateModified\":\"2024-05-14T08:37:39+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\\\/\\\/www.autoskoly.sk\\\/news\\\/informacie-a-jej-prenos\\\/\"},\"wordCount\":7603,\"commentCount\":0,\"publisher\":{\"@id\":\"https:\\\/\\\/www.autoskoly.sk\\\/news\\\/#organization\"},\"image\":{\"@id\":\"https:\\\/\\\/www.autoskoly.sk\\\/news\\\/informacie-a-jej-prenos\\\/#primaryimage\"},\"thumbnailUrl\":\"https:\\\/\\\/www.autoskoly.sk\\\/news\\\/wp-content\\\/uploads\\\/2022\\\/08\\\/komunikacia-autoskoly-15.jpg\",\"keywords\":[\"inform\u00e1cie\",\"informa\u010dn\u00fd syst\u00e9m\",\"IS\"],\"articleSection\":[\"Informa\u010dn\u00e9 syst\u00e9my\",\"Komunik\u00e1cia\"],\"inLanguage\":\"sk-SK\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"https:\\\/\\\/www.autoskoly.sk\\\/news\\\/informacie-a-jej-prenos\\\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"https:\\\/\\\/www.autoskoly.sk\\\/news\\\/informacie-a-jej-prenos\\\/\",\"url\":\"https:\\\/\\\/www.autoskoly.sk\\\/news\\\/informacie-a-jej-prenos\\\/\",\"name\":\"Inform\u00e1cie a jej prenos - 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