Next  |  Prev  |  Top  |  JOS Index  |  JOS Pubs  |  JOS Home  |  Search

Remez Multiple Exchange Method

Let's now try the Remez multiple exchange algorithm (``Parks-McClellan algorithm'') for optimal Chebyshev (equiripple) FIR filter design, and compare it to our window-method design.

Step 1: Design an optimal lowpass filter of the desired width (takes quite a while):

  M = 257;      % FIR filter length
  fs = 22050;   % sampling rate (Hz)
  fn = fs/2;    % Nyquist limit (Hz)
  f1 = 530;     % lower passband limit (Hz)
  f2 = fn - f1; % upper passpand limit (see text, p. 136)
  hrm = firpm(M-1, [0,(f2-fs/4)/fn,0.5,1], ...
                          [1,1,0,0], [1,10]);

Step 2: Modulate the impulse response to make it a single-sideband filter. I.e., right-shift by $ \pi/2$ in the frequency domain (rotate the frequency response counterclockwise along the unit circle by 90 degrees):

hr = hrm .* j .^ [0:M-1];

Next  |  Prev  |  Top  |  JOS Index  |  JOS Pubs  |  JOS Home  |  Search

[Comment on this page via email]

``The Window Method for FIR Digital Filter Design}'', by Julius O. Smith III, (From Lecture Overheads, Music 421).
Copyright © 2020-06-27 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
CCRMA  [Automatic-links disclaimer]