# impulse

Impulse response for rational function object

 Note:   impulse may be removed in a future release. Use timeresp instead.

## Syntax

[resp,t] = impulse(h,ts,n)

## Description

[resp,t] = impulse(h,ts,n) computes the impulse response, resp, of the rational function object, h, over the time period specified by ts and n.

 Note:   While you can compute the output response for a rational function object by computing the impulse response of the object and then convolving that response with the input signal, this approach is not recommended. Instead, you should use the timeresp method to perform this computation because it generally gives a more accurate output signal for a given input signal.

The input h is the handle of a rational function object. ts is a positive scalar value that specifies the sample time of the computed impulse response, and n is a positive integer that specifies the total number of samples in the response.

The vector of time samples of the impulse response, t, is computed from the inputs as t = [0,ts,2*ts,...,(n-1)*ts]. The impulse response, resp, is an n-element vector of impulse response values corresponding to these times. It is computed using the analytical form of the rational function

$resp=\sum _{k=1}^{M}{C}_{k}{e}^{{A}_{k}\left(t-Delay\right)}u\left(t-Delay\right)+D\delta \left(t-Delay\right)$

where

• A, C, D, and Delay are properties of the rational function object, h.

• M is the number of poles in the rational function object.

## Examples

The following example shows you how to compute the impulse response of the data stored in the file default.s2p by fitting a rational function object to the data and using the impulse method to compute the impulse response of the object.

freq=orig_data.Freq;
data=orig_data.S_Parameters(2,1,:);
fit_data=rationalfit(freq,data)

[resp,t]=impulse(fit_data,1e-12,1e4);

plot(t,resp);