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# yulewalk() - Signal Processing

### Syntax

### Example

### Output / Return Value

### Limitations

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### Reference

yulewalk designs recursive IIR digital filters using a least-squares fit to a specified frequency response.[b,a] = yulewalk(n,f,m) returns row vectors, b and a, containing the n+1 coefficients of the order n IIR filter whose frequency-magnitude characteristics approximately match those given in vectors f and m:f is a vector of frequency points, specified in the range between 0 and 1, where 1 corresponds to half the sample frequency (the Nyquist frequency). The first point of f must be 0 and the last point 1. All intermediate points must be in increasing order. Duplicate frequency points are allowed, corresponding to steps in the frequency response.m is a vector containing the desired magnitude response at the points specified in f.f and m must be the same length.plot(f,m) displays the filter shape.The output filter coefficients are ordered in descending powers of z.B(z)A(z)=b(1)+b(2)z−1+⋯+b(n+1)z−na(1)+a(2)z−1+⋯+a(n+1)z−nWhen specifying the frequency response, avoid excessively sharp transitions from passband to stopband. You may need to experiment with the slope of the transition region to get the best filter design.

[b,a] = yulewalk(n,f,m)

Yule-Walker Design of Lowpass FilterOpen This Example Design an 8th-order lowpass filter with normalized cutoff frequency 0.6. Plot its frequency response and overlay the response of the corresponding ideal filter. f = [0 0.6 0.6 1]; m = [1 1 0 0]; [b,a] = yulewalk(8,f,m); [h,w] = freqz(b,a,128); plot(w/pi,abs(h),f,m,'--') xlabel 'Radian frequency (\omega/\pi)', ylabel Magnitude legend('Yule-Walker','Ideal'), legend boxoff