Impulse response of Bilinear approximation to a Butterworth 2nd order lowpass.

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 bilinear approximation. The 2 responses are "identical" for small sampling times but some differences develop as the sampling time is increased.

Applet below is similar to the one above but frequency prewarping was not applied when calculating the sampled Transfer Function. In both applets the horizontal scale is from 0 to 10s and the vertical is from -1 to +1 when gains are 1.

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COPYRIGHT © 1999 Cuthbert A. Nyack.