Discussion
The continuous-time system's impulse response, is sampled with sampling period to produce the discrete-time system's impulse response, .
Thus, the frequency responses of the two systems are related by
If the continuous time filter is approximately band-limited (i.e. when ), 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/(2T) Hz):
- for
Read more about this topic: Impulse Invariance
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