prony (Signal Processing Toolbox)

Prony's method for time domain IIR filter design.

Syntax

[b,a] = prony(h,nb,na)

Description

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:

Example

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

Algorithm

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.

See Also


`butter`	Butterworth analog and digital filter design.
`cheby1`	Chebyshev type I filter design (passband ripple).
`cheby2`	Chebyshev type II filter design (stopband ripple).
`ellip`	Elliptic (Cauer) filter design.
`invfreqz`	Discrete-time filter identification from frequency data.
`levinson`	Levinson-Durbin recursion.
`lpc`	Linear prediction coefficients.
`stmcb`	Linear model using Steiglitz-McBride iteration.

References

[1] Parks, T.W., and C.S. Burrus. Digital Filter Design. New York: John Wiley & Sons, 1987. Pgs. 226-228.

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