Bilinear Approximation to nth order High Pass Elliptic 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 and zero locations for the continuous Elliptic filter and the discrete Bilinear approximation.

To design a filter which has a gain of ~ -3dB at 0.4ws, ws/wp = 1.25, a minimun stop band attenuation of 80dB and a passband ripple of 0.2dB, proceed as follows:-

Set BL = 235, WL to 300 and R = 0.2 to locate the frequency markers and set the pass band ripple.
Adjust N, fc/fs until the conditions are met.
In this case N = 9, fc/fs = 0.402.

The last entry in the first line of white text shows the gain at 0.4ws as -2.838dB and the second line shows the attenuation at the stop band peak is -82.46dB.

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

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COPYRIGHT 2008 Cuthbert Nyack.