Bilinear Approximation to nth order High Pass Butterworth Filter.

Cuthbert Nyack
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 0.36ws and ~ -50dB at 0.3ws, proceed as follows:-

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 0.36ws as -2.76dB and the second line shows the attenuation at 0.3ws is -52.15dB.
Changing Fn to 1 shows the quadratic factors needed to realize the filter and Fn = 2 show the poles.

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COPYRIGHT 2008 Cuthbert Nyack.