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.
http://www.primenet.com/~ericj