Impulse response of Sampled version of a 2nd order Butterworth lowpass filter obtained by the Impulse invariant approximation.

Cuthbert Nyack

The applet below shows the impulse response of a 2nd order Butterworth filter in red and the impulse response of a sampled version of the filter in magenta obtained by using the impulse invariant approximation. The 2 responses are "identical" for all sampling times. I.e. the impulse response of a sampled filter obtained via the impulse invariant method is a sampled version of the analog filter.

Horizontal scale goes from 0 to 5s and with gains = 1, vertical scale goes from -1 to +1.

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