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prony
Prony's method for time domain IIR filter design.
[b,a] = prony(h,nb,na)Prony's method is an algorithm for finding an IIR filter with a prescribed time domain impulse response. It has applications in filter design, exponential signal modeling, and system identification (parametric modeling).
[b,a] = prony(h,nb,na)
finds a filter with numerator order nb, denominator order na, and the time domain impulse response in h. prony returns the filter coefficients in row vectors b and a, of length nb + 1 and na + 1, respectively. The filter coefficients are in descending powers of z:
Recover the coefficients of a Butterworth filter from its impulse response:
[b,a] = butter(4,0.2) b = 0.0048 0.0193 0.0289 0.0193 0.0048 a = 1.0000 -2.3695 2.3140 -1.0547 0.1874 h = filter(b,a,[1 zeros(1,25)]); [bb,aa] = prony(h,4,4) bb = 0.0048 0.0193 0.0289 0.0193 0.0048 ab = 1.0000 -2.3695 2.3140 -1.0547 0.1874
prony implements the method described in reference [1]. This method uses a variation of the covariance method of AR modeling to find the denominator coefficients a and then finds the numerator coefficients b for which the impulse response of the output filter matches exactly the first nb + 1 samples of x. The filter is not necessarily stable, but potentially can recover the coefficients exactly if the data sequence is truly an autoregressive moving average (ARMA) process of the correct order.