timeresp

Time response for rational objects

Syntax

[y,t,xf] = timeresp(h,inputsignal,ts)

[y,t,xf] = timeresp(h,inputsignal,ts,xo)

Description

[y,t,xf] = timeresp(h,inputsignal,ts) computes the time response y, sample time t of y, and final states of the system xf. The function calculates the time response for a rational, rfmodel.rational, or rationalfit object h, using the time-varying input signal inputsignal at the specified sample time ts.

[y,t,xf] = timeresp(h,inputsignal,ts,xo) computes the time response using xo as the initial states of a system.

Examples

Time Response of Rational Object

Compute Time Response with Single Input Signal

Define an input signal.

SampleTime = 2e-11;
OverSamplingFactor = 25;
TotalSampleNumber = 2^12;
InputSignal = sign(randn(1, ...
              ceil(TotalSampleNumber/OverSamplingFactor)));
InputSignal = repmat(InputSignal, [OverSamplingFactor, 1]);
InputSignal = InputSignal(:);

Create a rational function object.

S = sparameters('default.s2p');
s21 = rfparam(S,2,1);
datafreq = S.Frequencies;
fit_data = rationalfit(datafreq,s21,'Tolerance',-32);

Compute the time response with initial states set to 0.

[y,t,xf]=timeresp(fit_data,InputSignal,SampleTime);

Compute Time Response with Segmented Input Signals

Segment the input signal into two parts.

Compute the time response of the first half of the input signal segment.

[y2(1:2000,1),t21,xf2]=timeresp(fit_data,InputSignal(1:2000),SampleTime);

Use the final states of the first half of the input signal segment xf2 as the initial states to compute the time response of the second half of the input signal segment.

[y2(2001:4100,1),t22,xf2]=timeresp(fit_data,InputSignal(2001:4100),SampleTime,xf2);

Plot Time Responses

Plot the time responses of the single and segmented input signals.

plot(t,y,':',t,y2,'--')
legend({'Single Input Signal','Multiple or Segmented Input Signals'}) 

Input Arguments

inputsignal — Time-varying input signal

real finite vector

Time-varying input signal, specified as a real finite vector.

Data Types: double

h — Rational function object

rationalfit object | rfmodel.rational object | rational object

Rational function object, specified as a rationalfit, rfmodel.rational, or a rational object.

Data Types: double
Complex Number Support: Yes

ts — Sample time of input signal

positive scalar integer

Sample time of the input signal, specified as a positive scalar integer in seconds.

Data Types: double

xo — Initial states of system

0 (default) | real or complex column vector

Initial states of the system, specified as a real or complex column vector of length L, where L is equal to length(h.ComplexPoles/2)+length(h.RealPoles).

Data Types: double

Output Arguments

y — Time-varying output signal

real finite vector

Time-varying output signal, returned as a real finite vector.

Data Types: double

t — Sample time of output signal

nonnegative vector

Sample time of the output signal, returned as a nonnegative vector of time values with discrete step size ts corresponding to the data in y in seconds.

Data Types: double

xf — Final states of system

real or complex column vector

Final states of the system that the function uses in computing the last value of the y, returned as a real or complex column vector of length L, where L is equal to length(h.ComplexPoles/2)+length(h.RealPoles).

Data Types: double

More About

Output Signal Equation

timeresp function uses a variant of this equation to calculate the output signal.

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

where

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

A — Complex vector of poles of the rational function

C — Complex vector of residues of the rational function

D — Scalar value specifying direct feedthrough

Delay — Delay time properties of the rational function object h. For more information, see rationalfit function.

Version History

Introduced in R2007a

R2022b: Compute time response of rational objects with initial states

To compute the time response of rational objects with the initial states, use xo as one of the input arguments to this function.