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Aide Scilab >> Traitement du Signal > remezb

# remezb

Minimax approximation of magnitude response

### Calling Sequence

`[an]=remezb(nc,fg,ds,wt)`

### Arguments

nc

Number of cosine functions

fg

Grid of frequency points in [0,.5)

ds

Desired magnitude on grid `fg`

wt

Weighting function on error on grid `fg`

an

Cosine filter coefficients

### Description

Minimax approximation of a frequency domain magnitude response. The approximation takes the form `h = sum[a(n)*cos(wn)]` for n=0,1,...,nc. An FIR, linear-phase filter can be obtained from the the output of the function 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;```

### Examples

```// Choose the number of cosine functions and create a dense grid
// in [0,.24) and [.26,.5)
nc=21;ngrid=nc*16;
fg=.24*(0:ngrid/2-1)/(ngrid/2-1);
fg(ngrid/2+1:ngrid)=fg(1:ngrid/2)+.26*ones(1:ngrid/2);

// Specify a low pass filter magnitude for the desired response
ds(1:ngrid/2)=ones(1:ngrid/2);
ds(ngrid/2+1:ngrid)=zeros(1:ngrid/2);

// Specify a uniform weighting function
wt=ones(fg);

// Run remezb
an=remezb(nc,fg,ds,wt)

// Make a linear phase FIR filter
hn(1:nc-1)=an(nc:-1:2)/2;
hn(nc)=an(1);
hn(nc+1:2*nc-1)=an(2:nc)/2;

// Plot the filter's magnitude response
plot(.5*(0:255)/256,frmag(hn,256));

// Choose the number of cosine functions and create a dense grid in [0,.5)
nc=21; ngrid=nc*16;
fg=.5*(0:(ngrid-1))/ngrid;

// Specify a triangular shaped magnitude for the desired response
ds(1:ngrid/2)=(0:ngrid/2-1)/(ngrid/2-1);
ds(ngrid/2+1:ngrid)=ds(ngrid/2:-1:1);

// Specify a uniform weighting function
wt=ones(fg);

// Run remezb
an=remezb(nc,fg,ds,wt)

// Make a linear phase FIR filter
hn(1:nc-1)=an(nc:-1:2)/2;
hn(nc)=an(1);
hn(nc+1:2*nc-1)=an(2:nc)/2;

// Plot the filter's magnitude response
plot(.5*(0:255)/256,frmag(hn,256));```

• eqfir — minimax approximation of FIR filter

C. B.