Butterworth Response

Cuthbert Nyack
The Butterworth filter has maximally flat response at zero frequency. In the s plane the poles of a normalised Nth order filter are on the unit circle. The poles derived from the magnitude squared transfer function lie on the entire unit circle. A stable filter is derived from the poles on the unit circle and in the left half of the s plane.

Poles are located at:-
-sin((2n - 1)p/2N) + j cos((2n - 1)p/2N) ; n = 1, 2, ... N

In the applet above, the magnitude response is shown in red and pink with different scales. Phase delay is in green, group delay in cyan and impulse response in yellow.

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COPYRIGHT 2005 Cuthbert Nyack.