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.