remez

remez
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Name

remez — Remez exchange algorithm for the weighted chebyshev approximation of a continuous function with a sum of cosines.

Calling Sequence

an=remez(guess,mag,fgrid,weight)

Parameters

guess: real array of size n+2 the initial guess
fgrid: real array of size ng: the grid of normalized frequency points in [0,.5[
mag: real array of size ng: the desired magnitude on grid fg
weight: real array of size ng: weighting function on error on grid fg
an: real array of size n: cosine coefficients

Description

Minimax approximation of a frequency domain magnitude response. The approximation takes the form

 h = sum[a(i)*cos(weight)], i=1:n

An FIR, linear-phase filter can be obtained from the the output of remez by using the following commands:

  hn(1:nc-1)=an(nc:-1:2)/2;
  hn(nc)=an(1);
  hn(nc+1:2*nc-1)=an(2:nc)/2;

This function is mainly intended to be called by the remezb function.

Bibliography

E.W. Cheney, Introduction to Approximation Theory, McGraw-Hill, 1966

http://en.wikipedia.org/wiki/Remez_algorithm

References

This function is based on the fortran code remez.fwritten by:

James H. Mcclellan, department of electrical engineering and computer science, Massachusetts Institute of Technology, Cambridge, Massachussets. 02139
Thomas W. Parks, department of electrical engineering, Rice university, Houston, Texas 77001
Thomas W. Parks, department of electrical engineering, Rice university, Houston, Texas 77001

Examples

      nc=21;
      ngrid=nc*250;
      fgrid=.5*(0:(ngrid-1))/(ngrid-1);
      mag(1:ngrid/2)=ones(1:ngrid/2);
      mag(ngrid/2+1:ngrid)=0*ones(1:ngrid/2);
      weight=ones(fgrid);
      guess=round(1:ngrid/nc:ngrid);
      guess(nc+1)=ngrid;
      guess(nc+2)=ngrid;
      an=remez(guess,mag,fgrid,weight);