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# timeresp

Time response for rational function object

## Syntax

[y,t] = timeresp(h,u,ts)

## Description

[y,t] = timeresp(h,u,ts) computes the output signal, y, that the rational function object, h, produces in response to the given input signal, u.

The input h is the handle of a rational function object returned by rationalfit. ts is a positive scalar value that specifies the sample time of the input signal.

The output y is the output signal. RF Toolbox™ software computes the value of the signal at the time samples in the vector t using the following equation.

$Y\left(n\right)=sum\left(C.*X\left(n-Delay/ts\right)\right)+D*U\left(n-Delay/ts\right)$

where

$\begin{array}{l}X\left(n+1\right)=F*X\left(n\right)+G*U\left(n\right)\\ X\left(1\right)=0\\ F=\mathrm{exp}\left(A*ts\right)\\ G=\left(F-1\right)./A\end{array}$

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

## Examples

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

```% Define the input signal
SampleTime = 2e-11;
OverSamplingFactor = 25;
TotalSampleNumber = 2^12;
InputTime = double((1:TotalSampleNumber)')*SampleTime;
InputSignal = sign(randn(1, ...
ceil(TotalSampleNumber/OverSamplingFactor)));
InputSignal = repmat(InputSignal, [OverSamplingFactor, 1]);
InputSignal = InputSignal(:);

% Create a rational function object
freq=orig_data.Freq;
data=orig_data.S_Parameters(2,1,:);
fit_data=rationalfit(freq,data);

% Compute the time response
[y,t]=timeresp(fit_data,InputSignal,SampleTime);

```