You are here : matlabSignal Processingprony

# prony() - Signal Processing

```[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.```

### Syntax

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

### Example

```Filter Responses via Prony's MethodOpen This Example
Fit a 4th-order IIR model to the impulse response of a lowpass filter. Plot the original and Prony-designed impulse responses.
d = designfilt('lowpassiir','NumeratorOrder',4,'DenominatorOrder',4, ...
'HalfPowerFrequency',0.2,'DesignMethod','butter');

impulse_resp = filter(d,[1 zeros(1,31)]);
denom_order = 4;
num_order = 4;
[Num,Den] = prony(impulse_resp,num_order,denom_order);

subplot(2,1,1)
stem(impz(Num,Den,length(impulse_resp)))
title 'Impulse Response with Prony Design'

subplot(2,1,2)
stem(impulse_resp)
title 'Input Impulse Response'

Fit a 10th-order FIR model to the impulse response of a highpass filter. Plot the original and Prony-designed frequency responses.d = designfilt('highpassfir', 'FilterOrder', 10, 'CutoffFrequency', .8);

impulse_resp = filter(d,[1 zeros(1,31)]);
num_order = 10;
denom_order = 0;
[Num,Den] = prony(impulse_resp,num_order,denom_order);

fvt = fvtool(Num,Den,d);
legend(fvt,'Prony','Original')```