Frequency Response, Transfer function and pole locations are shown by the applet below.

Fn = 0 shows the frequency response.

Fn = 1 shows the transfer function represented as a product of quadratic factors.

Fn = 2 shows the pole locations for the continuous Butterworth filter and the discrete Bilinear approximation.

To design a filter which has a gain of ~ -3dB at 0.36w

Set BL = 225 and WL to 270 to locate the frequency markers.

Adjust N, fc/fs until the conditions are met.

In this case N = 14 and fc/fs = 0.359.

The last entry in the first line of white text shows the gain at 0.36w

Changing Fn to 1 shows the quadratic factors needed to realize the filter and Fn = 2 show the poles.

COPYRIGHT © 2008 Cuthbert Nyack.