. . . . . . "16448"^^ . . . "In mathematics and signal processing, an analytic signal is a complex-valued function that has no negative frequency components. The real and imaginary parts of an analytic signal are real-valued functions related to each other by the Hilbert transform. The analytic representation of a real-valued function is an analytic signal, comprising the original function and its Hilbert transform. This representation facilitates many mathematical manipulations. The basic idea is that the negative frequency components of the Fourier transform (or spectrum) of a real-valued function are superfluous, due to the Hermitian symmetry of such a spectrum. These negative frequency components can be discarded with no loss of information, provided one is willing to deal with a complex-valued function instead. That makes certain attributes of the function more accessible and facilitates the derivation of modulation and demodulation techniques, such as single-sideband. As long as the manipulated function has no negative frequency components (that is, it is still analytic), the conversion from complex back to real is just a matter of discarding the imaginary part. The analytic representation is a generalization of the phasor concept: while the phasor is restricted to time-invariant amplitude, phase, and frequency, the analytic signal allows for time-variable parameters."@en . . "Dans le domaine du traitement du signal et plus particuli\u00E8rement en t\u00E9l\u00E9communications, le signal analytique est un signal satisfaisant un certain nombre de propri\u00E9t\u00E9s, mais qui peut \u00EAtre tout d'abord vu comme le prolongement d'un signal r\u00E9el dans le plan complexe : Exemple : Soit un signal r\u00E9el de la forme: On peut le consid\u00E9rer comme \u00E9tant la partie r\u00E9elle du signal complexe:Cependant, le choix se portera sur les fonctions r\u00E9guli\u00E8res dans le demi-plan complexe sup\u00E9rieur; soit pour , le signal complexe . Introduisons certaines notions pour argumenter ce choix."@fr . "Sygna\u0142 analityczny"@pl . . . . . "Analytic signal"@en . . "La se\u00F1al anal\u00EDtica de Gabor correspondiente a una se\u00F1al temporal real, es una se\u00F1al compleja cuyo espectro de frecuencias es nulo para frecuencias negativas, y cuya parte real es igual a la se\u00F1al original."@es . . . "\u0410\u043D\u0430\u043B\u0438\u0442\u0438\u0447\u0435\u0441\u043A\u0438\u0439 \u0441\u0438\u0433\u043D\u0430\u043B (\u0430\u043D\u0430\u043B\u0438\u0442\u0438\u0447\u0435\u0441\u043A\u043E\u0435 \u043F\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043B\u0435\u043D\u0438\u0435 \u0441\u0438\u0433\u043D\u0430\u043B\u0430) \u2014 \u0438\u0441\u043F\u043E\u043B\u044C\u0437\u0443\u0435\u043C\u043E\u0435 \u0432 \u0442\u0435\u043E\u0440\u0438\u0438 \u043E\u0431\u0440\u0430\u0431\u043E\u0442\u043A\u0438 \u0441\u0438\u0433\u043D\u0430\u043B\u043E\u0432 \u043C\u0430\u0442\u0435\u043C\u0430\u0442\u0438\u0447\u0435\u0441\u043A\u043E\u0435 \u043F\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043B\u0435\u043D\u0438\u0435 \u0430\u043D\u0430\u043B\u043E\u0433\u043E\u0432\u043E\u0433\u043E \u0441\u0438\u0433\u043D\u0430\u043B\u0430 \u0432 \u0432\u0438\u0434\u0435 \u043A\u043E\u043C\u043F\u043B\u0435\u043A\u0441\u043D\u043E\u0437\u043D\u0430\u0447\u043D\u043E\u0439 \u0430\u043D\u0430\u043B\u0438\u0442\u0438\u0447\u0435\u0441\u043A\u043E\u0439 \u0444\u0443\u043D\u043A\u0446\u0438\u0438 \u0432\u0440\u0435\u043C\u0435\u043D\u0438. \u041E\u0431\u044B\u0447\u043D\u044B\u0439, \u0434\u0435\u0439\u0441\u0442\u0432\u0438\u0442\u0435\u043B\u044C\u043D\u044B\u0439 \u0441\u0438\u0433\u043D\u0430\u043B x \u044F\u0432\u043B\u044F\u0435\u0442\u0441\u044F \u043F\u0440\u0438 \u044D\u0442\u043E\u043C \u0434\u0435\u0439\u0441\u0442\u0432\u0438\u0442\u0435\u043B\u044C\u043D\u043E\u0439 \u0447\u0430\u0441\u0442\u044C\u044E \u0430\u043D\u0430\u043B\u0438\u0442\u0438\u0447\u0435\u0441\u043A\u043E\u0433\u043E \u043F\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043B\u0435\u043D\u0438\u044F xa. \u0418\u0434\u0435\u044F \u043F\u0440\u0435\u043E\u0431\u0440\u0430\u0437\u043E\u0432\u0430\u043D\u0438\u044F \u2014 \u043E\u0441\u0442\u0430\u0432\u0438\u0442\u044C \u043B\u0438\u0448\u044C \u043D\u0435\u043E\u0442\u0440\u0438\u0446\u0430\u0442\u0435\u043B\u044C\u043D\u044B\u0435 \u0447\u0430\u0441\u0442\u043E\u0442\u044B \u0432 \u0441\u043F\u0435\u043A\u0442\u0440\u0435 \u0441\u0438\u0433\u043D\u0430\u043B\u0430, \u0434\u043E\u0441\u0442\u0430\u0442\u043E\u0447\u043D\u044B\u0435 \u0434\u043B\u044F \u0435\u0433\u043E \u0432\u043E\u0441\u0441\u0442\u0430\u043D\u043E\u0432\u043B\u0435\u043D\u0438\u044F \u0432 \u0441\u0438\u043B\u0443 \u044D\u0440\u043C\u0438\u0442\u043E\u0432\u043E\u0439 \u0441\u0438\u043C\u043C\u0435\u0442\u0440\u0438\u0438: . \u0410\u043D\u0430\u043B\u0438\u0442\u0438\u0447\u0435\u0441\u043A\u0438\u0439 \u0441\u0438\u0433\u043D\u0430\u043B \u044F\u0432\u043B\u044F\u0435\u0442\u0441\u044F \u043E\u0431\u043E\u0431\u0449\u0435\u043D\u0438\u0435\u043C \u043F\u043E\u043D\u044F\u0442\u0438\u044F \u043A\u043E\u043C\u043F\u043B\u0435\u043A\u0441\u043D\u043E\u0439 \u0430\u043C\u043F\u043B\u0438\u0442\u0443\u0434\u044B \u043D\u0430 \u0441\u043B\u0443\u0447\u0430\u0439 \u0441\u0438\u0433\u043D\u0430\u043B\u043E\u0432, \u043E\u0442\u043B\u0438\u0447\u043D\u044B\u0445 \u043E\u0442 \u0433\u0430\u0440\u043C\u043E\u043D\u0438\u0447\u0435\u0441\u043A\u043E\u0433\u043E."@ru . "Dans le domaine du traitement du signal et plus particuli\u00E8rement en t\u00E9l\u00E9communications, le signal analytique est un signal satisfaisant un certain nombre de propri\u00E9t\u00E9s, mais qui peut \u00EAtre tout d'abord vu comme le prolongement d'un signal r\u00E9el dans le plan complexe : Exemple : Soit un signal r\u00E9el de la forme: On peut le consid\u00E9rer comme \u00E9tant la partie r\u00E9elle du signal complexe:Cependant, le choix se portera sur les fonctions r\u00E9guli\u00E8res dans le demi-plan complexe sup\u00E9rieur; soit pour , le signal complexe . Introduisons certaines notions pour argumenter ce choix."@fr . "Se\u00F1al anal\u00EDtica"@es . . "1124895742"^^ . . "Ka\u017Cdemu sygna\u0142owi rzeczywistemu odpowiada zespolony sygna\u0142 analityczny (inny zapis ), kt\u00F3rego cz\u0119\u015B\u0107 rzeczywist\u0105 stanowi sygna\u0142 a cz\u0119\u015B\u0107 urojon\u0105 \u2013 jego transformata Hilberta Wa\u017Cn\u0105 w\u0142a\u015Bciwo\u015Bci\u0105 sygna\u0142u analitycznego jest posta\u0107 jego widma: gdzie oznacza widmo cz\u0119stotliwo\u015Bciowe sygna\u0142u za\u015B widmo Reasumuj\u0105c: Jak wida\u0107, widmo sygna\u0142u analitycznego charakteryzuje si\u0119 tym, \u017Ce dla ujemnych cz\u0119stotliwo\u015Bci jest zerowe, a dla dodatnich jest podwojonym widmem oryginalnego sygna\u0142u. Fakt ten jest wykorzystywany do modulacji amplitudowej typu SSB (jednowst\u0119gowej)."@pl . "Signal analytique"@fr . . . . . . . . . "La se\u00F1al anal\u00EDtica de Gabor correspondiente a una se\u00F1al temporal real, es una se\u00F1al compleja cuyo espectro de frecuencias es nulo para frecuencias negativas, y cuya parte real es igual a la se\u00F1al original."@es . . . . "Analytisches Signal"@de . "950777"^^ . . . . . . "\u89E3\u6790\u4FE1\u53F7"@zh . . "\u5728\u6570\u5B66\u548C\u4FE1\u53F7\u5904\u7406\u4E2D\uFF0C\u89E3\u6790\u4FE1\u53F7\uFF08\u82F1\u8A9E\uFF1Aanalytic signal\uFF09\u662F\u6CA1\u6709\u8D1F\u9891\u7387\u5206\u91CF\u7684\u590D\u503C\u51FD\u6570\u3002 \u89E3\u6790\u4FE1\u53F7\u7684\u5B9E\u90E8\u548C\u865A\u90E8\u662F\u7531\u5E0C\u723E\u4F2F\u7279\u8F49\u63DB\u76F8\u5173\u8054\u7684\u5B9E\u503C\u51FD\u6570\u3002 \u5B9E\u503C\u51FD\u6570\u7684\u89E3\u6790\u8868\u793A\u662F\u89E3\u6790\u4FE1\u53F7\uFF0C\u5305\u542B\u539F\u59CB\u51FD\u6570\u548C\u5B83\u7684\u5E0C\u5C14\u4F2F\u7279\u53D8\u6362\u3002\u8FD9\u79CD\u8868\u793A\u4FC3\u8FDB\u4E86\u8BB8\u591A\u6570\u5B66\u53D8\u6362\u7684\u53D1\u5C55\u3002\u57FA\u672C\u7684\u60F3\u6CD5\u662F\uFF0C\u7531\u4E8E\u9891\u8C31\u7684\u57C3\u5C14\u7C73\u7279\u5BF9\u79F0\uFF0C\u5B9E\u503C\u51FD\u6570\u7684\u5085\u91CC\u53F6\u53D8\u6362\uFF08\u6216\u9891\u8C31\uFF09\u7684\u8D1F\u9891\u7387\u6210\u5206\u662F\u591A\u4F59\u7684\u3002\u82E5\u662F\u4E0D\u4ECB\u610F\u5904\u7406\u590D\u503C\u51FD\u6570\u7684\u8BDD\uFF0C\u8FD9\u4E9B\u8D1F\u9891\u7387\u5206\u91CF\u53EF\u4EE5\u4E22\u5F03\u800C\u4E0D\u635F\u5931\u4FE1\u606F\u3002\u8FD9\u4F7F\u5F97\u51FD\u6570\u7684\u7279\u5B9A\u5C5E\u6027\u66F4\u6613\u7406\u89E3\uFF0C\u5E76\u4FC3\u8FDB\u4E86\u8C03\u5236\u548C\u89E3\u8C03\u6280\u672F\u7684\u884D\u751F\uFF0C\u5982\u5355\u8FB9\u5E26\u3002\u53EA\u8981\u64CD\u4F5C\u7684\u51FD\u6570\u6CA1\u6709\u8D1F\u9891\u7387\u5206\u91CF\uFF08\u4E5F\u5C31\u662F\u5B83\u4ECD\u662F\u201C\u89E3\u6790\u51FD\u6570\u201D\uFF09\uFF0C\u4ECE\u590D\u6570\u8F6C\u6362\u56DE\u5B9E\u6570\u5C31\u53EA\u9700\u8981\u4E22\u5F03\u865A\u90E8\u3002\u89E3\u6790\u8868\u793A\u662F\u5411\u91CF\u6982\u5FF5\u7684\u4E00\u4E2A\u63A8\u5E7F\uFF1A \u5411\u91CF\u9650\u5236\u5728\u65F6\u4E0D\u53D8\u7684\u632F\u5E45\u3001\u76F8\u4F4D\u548C\u9891\u7387\uFF0C\u89E3\u6790\u4FE1\u53F7\u5141\u8BB8\u6709\u65F6\u53D8\u53C2\u6570\u3002"@zh . . "In mathematics and signal processing, an analytic signal is a complex-valued function that has no negative frequency components. The real and imaginary parts of an analytic signal are real-valued functions related to each other by the Hilbert transform."@en . . "\u0410\u043D\u0430\u043B\u0438\u0442\u0438\u0447\u0435\u0441\u043A\u0438\u0439 \u0441\u0438\u0433\u043D\u0430\u043B (\u0430\u043D\u0430\u043B\u0438\u0442\u0438\u0447\u0435\u0441\u043A\u043E\u0435 \u043F\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043B\u0435\u043D\u0438\u0435 \u0441\u0438\u0433\u043D\u0430\u043B\u0430) \u2014 \u0438\u0441\u043F\u043E\u043B\u044C\u0437\u0443\u0435\u043C\u043E\u0435 \u0432 \u0442\u0435\u043E\u0440\u0438\u0438 \u043E\u0431\u0440\u0430\u0431\u043E\u0442\u043A\u0438 \u0441\u0438\u0433\u043D\u0430\u043B\u043E\u0432 \u043C\u0430\u0442\u0435\u043C\u0430\u0442\u0438\u0447\u0435\u0441\u043A\u043E\u0435 \u043F\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043B\u0435\u043D\u0438\u0435 \u0430\u043D\u0430\u043B\u043E\u0433\u043E\u0432\u043E\u0433\u043E \u0441\u0438\u0433\u043D\u0430\u043B\u0430 \u0432 \u0432\u0438\u0434\u0435 \u043A\u043E\u043C\u043F\u043B\u0435\u043A\u0441\u043D\u043E\u0437\u043D\u0430\u0447\u043D\u043E\u0439 \u0430\u043D\u0430\u043B\u0438\u0442\u0438\u0447\u0435\u0441\u043A\u043E\u0439 \u0444\u0443\u043D\u043A\u0446\u0438\u0438 \u0432\u0440\u0435\u043C\u0435\u043D\u0438. \u041E\u0431\u044B\u0447\u043D\u044B\u0439, \u0434\u0435\u0439\u0441\u0442\u0432\u0438\u0442\u0435\u043B\u044C\u043D\u044B\u0439 \u0441\u0438\u0433\u043D\u0430\u043B x \u044F\u0432\u043B\u044F\u0435\u0442\u0441\u044F \u043F\u0440\u0438 \u044D\u0442\u043E\u043C \u0434\u0435\u0439\u0441\u0442\u0432\u0438\u0442\u0435\u043B\u044C\u043D\u043E\u0439 \u0447\u0430\u0441\u0442\u044C\u044E \u0430\u043D\u0430\u043B\u0438\u0442\u0438\u0447\u0435\u0441\u043A\u043E\u0433\u043E \u043F\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043B\u0435\u043D\u0438\u044F xa. \u0418\u0434\u0435\u044F \u043F\u0440\u0435\u043E\u0431\u0440\u0430\u0437\u043E\u0432\u0430\u043D\u0438\u044F \u2014 \u043E\u0441\u0442\u0430\u0432\u0438\u0442\u044C \u043B\u0438\u0448\u044C \u043D\u0435\u043E\u0442\u0440\u0438\u0446\u0430\u0442\u0435\u043B\u044C\u043D\u044B\u0435 \u0447\u0430\u0441\u0442\u043E\u0442\u044B \u0432 \u0441\u043F\u0435\u043A\u0442\u0440\u0435 \u0441\u0438\u0433\u043D\u0430\u043B\u0430, \u0434\u043E\u0441\u0442\u0430\u0442\u043E\u0447\u043D\u044B\u0435 \u0434\u043B\u044F \u0435\u0433\u043E \u0432\u043E\u0441\u0441\u0442\u0430\u043D\u043E\u0432\u043B\u0435\u043D\u0438\u044F \u0432 \u0441\u0438\u043B\u0443 \u044D\u0440\u043C\u0438\u0442\u043E\u0432\u043E\u0439 \u0441\u0438\u043C\u043C\u0435\u0442\u0440\u0438\u0438: . \u0410\u043D\u0430\u043B\u0438\u0442\u0438\u0447\u0435\u0441\u043A\u0438\u0439 \u0441\u0438\u0433\u043D\u0430\u043B \u044F\u0432\u043B\u044F\u0435\u0442\u0441\u044F \u043E\u0431\u043E\u0431\u0449\u0435\u043D\u0438\u0435\u043C \u043F\u043E\u043D\u044F\u0442\u0438\u044F \u043A\u043E\u043C\u043F\u043B\u0435\u043A\u0441\u043D\u043E\u0439 \u0430\u043C\u043F\u043B\u0438\u0442\u0443\u0434\u044B \u043D\u0430 \u0441\u043B\u0443\u0447\u0430\u0439 \u0441\u0438\u0433\u043D\u0430\u043B\u043E\u0432, \u043E\u0442\u043B\u0438\u0447\u043D\u044B\u0445 \u043E\u0442 \u0433\u0430\u0440\u043C\u043E\u043D\u0438\u0447\u0435\u0441\u043A\u043E\u0433\u043E."@ru . . . . . . . "\u0410\u043D\u0430\u043B\u0438\u0442\u0438\u0447\u0435\u0441\u043A\u0438\u0439 \u0441\u0438\u0433\u043D\u0430\u043B"@ru . "Ein analytisches Signal ist in der Signaltheorie eine komplexwertige Funktion der Zeit, dessen Imagin\u00E4rteil die Hilbert-Transformierte des Realteils ist. Die Bezeichnung analytisch dr\u00FCckt aus, dass die Funktion im Komplexen differenzierbar ist (siehe analytische Funktion). Hieraus ergibt sich, dass im Spektrum eines analytischen Signals im Gegensatz zu einem reellen Signal keine negativen Frequenzen auftreten. Das analytische Signal stellt einen Spezialfall aus der Gruppe der monogenen Signale dar."@de . "Un segnale analitico, in matematica e nella teoria dei segnali, \u00E8 un segnale (in generale una funzione del tempo), ad esempio un segnale elettrico, che non possiede componenti a frequenza negativa. La rappresentazione analitica di una funzione (non correlata con la nozione di funzione analitica) consiste in una funzione complessa di frequenza positiva; ci\u00F2 facilita spesso il trattamento e le manipolazioni matematiche sul segnale stesso. L'idea di base \u00E8 che le componenti a frequenze negative dello spettro del segnale, cio\u00E8 della trasformata di Fourier del segnale, possono essere trascurate a causa della propriet\u00E0 di simmetria complessa coniugata (simmetria Hermitiana) dello spettro stesso: per un segnale reale la parte reale e il modulo della trasformata sono simmetrici rispetto all'origin"@it . . . . "Un segnale analitico, in matematica e nella teoria dei segnali, \u00E8 un segnale (in generale una funzione del tempo), ad esempio un segnale elettrico, che non possiede componenti a frequenza negativa. La rappresentazione analitica di una funzione (non correlata con la nozione di funzione analitica) consiste in una funzione complessa di frequenza positiva; ci\u00F2 facilita spesso il trattamento e le manipolazioni matematiche sul segnale stesso. L'idea di base \u00E8 che le componenti a frequenze negative dello spettro del segnale, cio\u00E8 della trasformata di Fourier del segnale, possono essere trascurate a causa della propriet\u00E0 di simmetria complessa coniugata (simmetria Hermitiana) dello spettro stesso: per un segnale reale la parte reale e il modulo della trasformata sono simmetrici rispetto all'origine (funzione pari), mentre la parte immaginaria e la fase sono antisimmetriche (dispari). In questo modo trascurando met\u00E0 dello spettro non vi \u00E8 perdita di informazione. Tuttavia il segnale ricostruito antitrasformando il segnale analitico non \u00E8 pi\u00F9 un segnale reale, ma \u00E8 un segnale complesso di variabile complessa, sebbene la conversione alla rispettiva funzione reale consista in pratica nell'eliminazione della sola parte immaginaria. Tale rappresentazione analitica rende certe caratteristiche del segnale pi\u00F9 accessibili e facilita la derivazione delle tecniche di modulazione/demodulazione, specialmente a singola banda laterale (single-sideband). La rappresentazione analitica \u00E8 una generalizzazione della notazione dei fasori propria dell'elettrotecnica (notazione di Steinmetz): mentre quest'ultima \u00E8 ristretta a segnali con ampiezza, fase e frequenza tempo-invarianti, la notazione analitica consente di avere parametri tempo-varianti ovvero non costanti."@it . . . . . . . "Segnale analitico"@it . . . . . . . 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"Ka\u017Cdemu sygna\u0142owi rzeczywistemu odpowiada zespolony sygna\u0142 analityczny (inny zapis ), kt\u00F3rego cz\u0119\u015B\u0107 rzeczywist\u0105 stanowi sygna\u0142 a cz\u0119\u015B\u0107 urojon\u0105 \u2013 jego transformata Hilberta Wa\u017Cn\u0105 w\u0142a\u015Bciwo\u015Bci\u0105 sygna\u0142u analitycznego jest posta\u0107 jego widma: gdzie oznacza widmo cz\u0119stotliwo\u015Bciowe sygna\u0142u za\u015B widmo Reasumuj\u0105c: Jak wida\u0107, widmo sygna\u0142u analitycznego charakteryzuje si\u0119 tym, \u017Ce dla ujemnych cz\u0119stotliwo\u015Bci jest zerowe, a dla dodatnich jest podwojonym widmem oryginalnego sygna\u0142u. Fakt ten jest wykorzystywany do modulacji amplitudowej typu SSB (jednowst\u0119gowej)."@pl . . . . . "Ein analytisches Signal ist in der Signaltheorie eine komplexwertige Funktion der Zeit, dessen Imagin\u00E4rteil die Hilbert-Transformierte des Realteils ist. Die Bezeichnung analytisch dr\u00FCckt aus, dass die Funktion im Komplexen differenzierbar ist (siehe analytische Funktion). Hieraus ergibt sich, dass im Spektrum eines analytischen Signals im Gegensatz zu einem reellen Signal keine negativen Frequenzen auftreten. Das analytische Signal stellt einen Spezialfall aus der Gruppe der monogenen Signale dar. Anwendungen von analytischen Signalen in der Signalverarbeitung liegen im Bereich der Einseitenbandmodulation."@de . . . . . . . . . . . . . .