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impulse invariance : ウィキペディア英語版
impulse invariance

Impulse invariance is a technique for designing discrete-time infinite-impulse-response (IIR) filters from continuous-time filters in which the impulse response of the continuous-time system is sampled to produce the impulse response of the discrete-time system. The frequency response of the discrete-time system will be a sum of shifted copies of the frequency response of the continuous-time system; if the continuous-time system is approximately band-limited to a frequency less than the Nyquist frequency of the sampling, then the frequency response of the discrete-time system will be approximately equal to it for frequencies below the Nyquist frequency.
==Discussion==

The continuous-time system's impulse response, h_c(t), is sampled with sampling period T to produce the discrete-time system's impulse response, h().
:h()=Th_c(nT)\,
Thus, the frequency responses of the two systems are related by
:H(e^) = \sum_^\infty + j\frack\right)}\,
If the continuous time filter is approximately band-limited (i.e. H_c(j\Omega) < \delta when |\Omega| \ge \pi/T), then the frequency response of the discrete-time system will be approximately the continuous-time system's frequency response for frequencies below π radians per sample (below the Nyquist frequency 1/(2''T'') Hz):
:H(e^) = H_c(j\omega/T)\, for |\omega| \le \pi\,

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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