The Butterworth filter has maximally flat response at zero frequency. In the s plane the poles of a normalised N

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.

COPYRIGHT © 2005 Cuthbert Nyack.