DSP Trick: Simple Filter Coefficient Interpolation

From: ericj@primenet.com.nospam (Eric Jacobsen)
Subject: DSP Trick - Simple Filter Coefficient Interpolation
Date: 23 Oct 1999 00:00:00 GMT
Newsgroups: comp.dsp
THIS WORK IS PLACED IN THE PUBLIC DOMAIN

Often it is necessary to design a FIR filter coefficient set that is longer than can be practically computed using common automated routines like Parks-McLellan or its Remez subroutine. In most cases this problem can be alleviated by using P-M or Remez to design a short coefficient set and then interpolating it up to the desired length. A simple interpolation method that avoids some of the distortions that may be associated with linear, spline, or polynomial interpolation utilizes the interpolating capabilities of the DFT. The procedure may be achieved as follows:

  1. Design a shortened FIR filter that can be computed using an appropriate design technique.
  2. Take a forward DFT of this shortened FIR coefficient set.
  3. Zero pad the result up to the desired length of the final filter.
  4. Take the inverse-DFT of the zero-padded vector.
  5. The real part of the inverse-DFT is the interpolated coefficient set of the desired length.

It is always prudent to verify that the interpolated filter has the desired response.

Eric Jacobsen Minister of Algorithms, EF Data Corp.

Editor's Note: This trick has some similarities to another dspGuru article, "How to Interpolate in the Time-Domain by Zero-Padding in the Frequency Domain".