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See the recommended documentation of this function

Ajuda Scilab >> Processamento de Sinais > remez

# 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)`

### Arguments

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 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.f` written 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);```