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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Group delay and phase delay ： ウィキペディア英語版 Group delay and phase delay In signal processing, group delay is a measure of the time delay of the amplitude envelopes of the various sinusoidal components of a signal through a device under test, and is a function of frequency for each component. Phase delay is similar, however it is a measure of the time delay of the ''phase'' as opposed to the time delay of the ''amplitude envelope''. All frequency components of a signal are delayed when passed through a device such as an amplifier, a loudspeaker, or propagating through space or a medium, such as air. This signal delay will be different for the various frequencies unless the device has the property of being linear phase. (Linear phase and minimum phase are often confused. They are quite different.) The delay variation means that signals consisting of multiple frequency components will suffer distortion because these components are not delayed by the same amount of time at the output of the device. This changes the shape of the signal in addition to any constant delay or scale change. A sufficiently large delay variation can cause problems such as poor fidelity in audio or intersymbol interference (ISI) in the demodulation of digital information from an analog carrier signal. High speed modems use adaptive equalizers to compensate for non-constant group delay. == Introduction == Group delay is a useful measure of time distortion, and is calculated by differentiating, with respect to frequency, the phase response of the device under test (DUT): the group delay is a measure of the slope of the phase response at any given frequency. Variations in group delay cause signal distortion, just as deviations from linear phase cause distortion. In linear time-invariant (LTI) system theory, control theory, and in digital or analog signal processing, the relationship between the input signal, $\backslash displaystyle\; x(t)$, to output signal, $\backslash displaystyle\; y(t)$, of an LTI system is governed by a convolution operation: : $y(t)\; =\; (h$ *x)(t) \ \stackrel\ \int_^ x(u) h(t-u) \, du Or, in the frequency domain, : $Y(s)\; =\; H(s)\; X(s)\; \backslash ,$ where : $X(s)\; =\; \backslash mathcal\backslash left\; \backslash \; \backslash \; \backslash stackrel\backslash \; \backslash int\_^\; x(t)\; e^\backslash ,\; dt$ : $Y(s)\; =\; \backslash mathcal\backslash left\; \backslash \; \backslash \; \backslash stackrel\backslash \; \backslash int\_^\; y(t)\; e^\backslash ,\; dt$ and : $H(s)\; =\; \backslash mathcal\backslash left\; \backslash \; \backslash \; \backslash stackrel\backslash \; \backslash int\_^\; h(t)\; e^\backslash ,\; dt$. Here $\backslash displaystyle\; h(t)$ is the time-domain impulse response of the LTI system and $\backslash displaystyle\; X(s)$, $\backslash displaystyle\; Y(s)$, $\backslash displaystyle\; H(s)$, are the Laplace transforms of the input $\backslash displaystyle\; x(t)$, output $\backslash displaystyle\; y(t)$, and impulse response $\backslash displaystyle\; h(t)$, respectively. $\backslash displaystyle\; H(s)$ is called the transfer function of the LTI system and, like the impulse response $\backslash displaystyle\; h(t)$, ''fully'' defines the input-output characteristics of the LTI system. Suppose that such a system is driven by a quasi-sinusoidal signal, that is, a sinusoid whose amplitude envelope $\backslash displaystyle\; a(t)$ is slowly-changing relative to the phase frequency $\backslash displaystyle\; \backslash omega$ of the sinusoid. Mathematically, this means that the driving signal has the form : $x(t)\; =\; a(t)\; \backslash cos(\backslash omega\; t\; +\; \backslash theta)\; \backslash$ subject to the assumption : $\backslash left|\; \backslash frac\; \backslash right|\; \backslash ll\; \backslash omega\backslash ;.$ Then the output of such an LTI system is very well approximated as : $y(t)\; =\; |H(i\; \backslash omega)|\; \backslash \; a(t\; -\; \backslash tau\_g)\; \backslash cos\; \backslash left(\; \backslash omega\; (t\; -\; \backslash tau\_\backslash phi)\; +\; \backslash theta\; \backslash right)\; \backslash ;\; .$ Here $\backslash displaystyle\; \backslash tau\_g$ and $\backslash displaystyle\; \backslash tau\_\backslash phi$, the group delay and phase delay respectively, are given by the expressions below (and potentially are functions of the angular frequency $\backslash displaystyle\; \backslash omega$). In a linear phase system (with non-inverting gain), both $\backslash displaystyle\; \backslash tau\_g$ and $\backslash displaystyle\; \backslash tau\_\backslash phi$ are constant (i.e. independent of ω) and equal, and their common value equals the overall delay of the system; and the unwrapped phase shift of the system (namely ''-ωτφ'') is negative, with magnitude increasing linearly with frequency $\backslash displaystyle\; \backslash omega$. More generally, it can be shown that for an LTI system with transfer function $\backslash displaystyle\; H(s)$ driven by a complex sinusoid of unit amplitude, : $x(t)\; =\; e^\; \backslash$ the output is : $\backslash begin$ y(t) & = H(i \omega) \ e^ \ \\ & = \left( |H(i \omega)| e^ \right) \ e^ \ \\ & = |H(i \omega)| \ e^ \ \\ \end \ where the phase shift $\backslash displaystyle\; \backslash phi$ is : $\backslash phi(\backslash omega)\; \backslash \; \backslash stackrel\backslash \; \backslash arg\; \backslash left\backslash \; \backslash ;.$ Additionally, it can be shown that the group delay, $\backslash displaystyle\; \backslash tau\_g$, and phase delay, $\backslash displaystyle\; \backslash tau\_\backslash phi$, are frequency-dependent, and they can be computed from the phase shift $\backslash displaystyle\; \backslash phi$ by : $\backslash tau\_g(\backslash omega)\; =\; -\; \backslash frac\; \backslash$ : $\backslash tau\_\backslash phi(\backslash omega)\; =\; -\; \backslash frac\; \backslash$ . 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Group delay and phase delay」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. 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