Butterworth Filter, magnitude response in complex plane

Cuthbert Nyack
The poles of a Butterworth filter lie on a circle in the complex s plane. When the magnitude squared transfer function is plotted in the s plane, the result is shown below. It looks like a "plateau" held up by poles on the unit circle.

In the applet, the black line shows the real s axis and the magenta line shows the filter response along the +ve imaginary s axis.
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COPYRIGHT 2005 Cuthbert Nyack.