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prony - Prony method for filter design

Syntax

[Num,Den] = prony(impulse_resp,num_ord,denom_ord)

Description

[Num,Den] = prony(impulse_resp,num_ord,denom_ord) returns the numerator Num and denominator Den coefficients for a causal rational system function with impulse response impulse_resp. The system function has numerator order num_ord and denominator order denom_ord. The lengths of Num and Den are num_ord+1 and denom_ord+1. If the length of impulse_resp is less than the largest order (num_ord or denom_ord), impulse_resp is padded with zeros. Enter 0 in num_ord for an all-pole system function. For an all-zero system function, enter a 0 for denom_ord.

Definitions

The system function is the z-transform of the impulse response h[n]:

A rational system function is a ratio of polynomials in z^-1. By convention the numerator polynomial is B(z) and the denominator is A(z). The following equation describes a causal rational system function of numerator order num_ord q and denominator order denom_ord p :

where a[0]=1.

Examples

Fit IIR model to an impulse response of lowpass filter:

d=fdesign.lowpass('Nb,Na,F3dB',4,4,0.2);
% Butterworth filter design
Hd=design(d,'butter');
% Obtain impulse response
impulse_resp=filter(Hd,[1 zeros(1,31)]);
% Find system function of order 4
denom_order=4; num_order=4;
[Num,Den]=prony(impulse_resp,num_order,denom_order);
% Compare impulse response with input
subplot(211); 
stem(impz(Num,Den,length(impulse_resp)));
title('Impulse Response with Prony Design');
subplot(212);
stem(impulse_resp); title('Input Impulse Response');

Fit FIR model to an impulse response of highpass filter:

d=fdesign.highpass('N,F3dB',10,0.8);
Hd=design(d,'maxflat');
% Impulse response
impulse_resp=filter(Hd,[1 zeros(1,31)]);
% Find all-zero system function of order 10
num_order=10; denom_order=0;
[Num,Den]=prony(impulse_resp,num_order,denom_order);
% compare Num to Hd.Numerator