Recursive digital filter design
[b,a] = yulewalk(n,f,m)
yulewalk designs recursive IIR digital filters
using a least-squares fit to a specified frequency response.
[b,a] = yulewalk(n,f,m) returns
n+1 coefficients of the order
filter whose frequency-magnitude characteristics approximately match
those given in vectors
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
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
be the same length.
plot(f,m) displays the filter shape.
The output filter coefficients are ordered in descending powers of z.
When 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.
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
yulewalk performs a least-squares fit in
the time domain. It computes the denominator coefficients using modified
Yule-Walker equations, with correlation coefficients computed by inverse
Fourier transformation of the specified frequency response. To compute
yulewalk takes the following steps:
Computes a numerator polynomial corresponding to an additive decomposition of the power frequency response.
Evaluates the complete frequency response corresponding to the numerator and denominator polynomials.
Uses a spectral factorization technique to obtain the impulse response of the filter.
Obtains the numerator polynomial by a least-squares fit to this impulse response.
 Friedlander, B., and Boaz Porat. "The Modified Yule-Walker Method of ARMA Spectral Estimation." IEEE® Transactions on Aerospace Electronic Systems. Vol. AES-20, Number 2, 1984, pp. 158–173.