Frequency Response of Low Pass Elliptic Filter 1

Cuthbert Nyack
The Elliptic Filter has Poles in the passband and zeros in the stopband resulting in both passband and stopband ripples in the frequency response. The Elliptic filter is characterised by 4 parameters, As the minimum stopband attenuation, Ap the passband ripple, n the order of the filter and ws/wp the ratio of the lowest frequency where the attenuation reaches its minimum value divided by the highest frequency where the attenuation is less than the passband ripple.

The poles can be derived by specifying 3 of the 4 parameters. The 4th parameter can then be derived from the other 3.

In the applet below the parameters As, Ap, and ws/wp are specified and the smallest value of n is calculated.

The relevant equations can be found in :- C. Britton Rorabaugh - Digital Filter Designer's Handbook - Publ by Mc Graw Hill.

In the applet, the magnitude response is shown in red and pink, the phase shift is shown as bright green(for the poles) and darker green(for the zeros), the group delay is shown in cyan.

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COPYRIGHT 2005 Cuthbert Nyack.