yulewalk

Scilab Function
Last update : 25/04/2007

yulewalk - least-square filter design

### Calling Sequence

  `Hz = yulewalk(N,frq,mag)`

### Parameters

- `N` : integer (order of desired filter)
- `frq` : real row vector (non-decreasing order), frequencies.
- `mag` : non negative real row vector (same size as frq), desired magnitudes.
- `Hz` : filter `B(z)/A(z)`

### Description

Hz = yulewalk(N,frq,mag) finds the N-th order iir filter

                      n-1         n-2
          B(z)   b(1)z     + b(2)z    + .... + b(n)
    H(z)= ---- = ---------------------------------
                    n-1       n-2
          A(z)    z   + a(2)z    + .... + a(n)

which matches the magnitude frequency response given by vectors frq and mag. Vectors frq and mag specify the frequency and magnitude of the desired frequency response. The frequencies in frq must be between 0.0 and 1.0, with 1.0 corresponding to half the sample rate. They must be in increasing order and start with 0.0 and end with 1.0.

### Examples

    f=[0,0.4,0.4,0.6,0.6,1];H=[0,0,1,1,0,0];Hz=yulewalk(8,f,H);
    fs=1000;fhz = f*fs/2;
    xbasc(0);xset('window',0);plot2d(fhz',H');
    xtitle('Desired Frequency Response (Magnitude)')
    [frq,repf]=repfreq(Hz,0:0.001:0.5);
    xbasc(1);xset('window',1);plot2d(fs*frq',abs(repf'));
    xtitle('Obtained Frequency Response (Magnitude)')