DSP Trick: Using Parks-McClellan to Design a Non-Linear Phase FIR Filter

From: ericj@primenet.com.nospam (Eric Jacobsen)
Subject: DSP Trick - Using P-M to design a non-linear phase FIR filter.
Date: 23 Oct 1999 00:00:00 GMT
Newsgroups: comp.dsp
THIS WORK IS PLACED IN THE PUBLIC DOMAIN

It is possible to use the Parks-McClellan algorithm to design FIR filters with non-linear phase response. For example, a FIR filter with the equivalent response of a Butterworth filter can be designed using the P-M routine.

First, take a common Butterworth description like that in Parks and Burrus where H(x) is a complex function. Create two PM input grids using the real and imaginary components of the Butterworth response. Use PM (or "remez" or whatever it's called on your favorite system) to design two FIR filters using the respective input grids, but turn the 'Hilbert' switch on for the one derived from the imaginary component. Sum the results, i.e., add together the nth coefficients of each filter to create a single N-tap filter.

The resulting FIR filter (assuming you've done your job to make sure everything converges) will have the desired response from the original expression used to generate the PM input grids.

Eric Jacobsen
Minister of Algorithms