impulse

Impulse response for rational objects

Syntax

[response,tout] = impulse(h,ts,n)

Description

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

Examples

Impulse Response of Data Stored in File

Create a sparameters object from a file and use rfparam to extract the $S_{21}$parameters.

S = sparameters('passive.s2p');
S21 = rfparam(S,2,1);

Fit a $S_{21}$ data by using a rational object.

freq = S.Frequencies;
fit_data = rational(freq,S21)

fit_data = 
  rational with properties:

      NumPorts: 1
      NumPoles: 8
         Poles: [8×1 double]
      Residues: [1×1×8 double]
    DirectTerm: 0
         ErrDB: -40.8419

Calculate the impulse response using the impulse method and plot the results.

[resp,t] = impulse(fit_data,1e-12,1e3);
plot(t,resp);
xlabel('Time (s)');
ylabel('Amplitude (V)');
title('Impulse Response of S21');

Impulse Response of S-Parameters Object

Perform rational fitting on a S-parameters object to create a rational function.

S = sparameters("passive.s2p");
fit = rational(S);

Compute the impulse response using the impulse method.

[resp,t] = impulse(fit,1e-12,1e2)

resp=2×2 cell array
    {100×1 double}    {100×1 double}
    {100×1 double}    {100×1 double}

t=2×2 cell array
    {100×1 double}    {100×1 double}
    {100×1 double}    {100×1 double}

Plot the results of the S21 data.

plot(t{2,1},resp{2,1})
xlabel('Time (s)');
ylabel('Amplitude (V)');
title('Impulse Response of S21');

Input Arguments

h — Rational function object

rational object | rationalfit object

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

Data Types: double
Complex Number Support: Yes

ts — Sample time of computed impulse response

positive scalar integer

Sample time of the computed impulse response, specified as a positive scalar integer in seconds.

Data Types: double

n — Number of samples

positive scalar integer

Number of samples in the impulse response, specified as a positive scalar integer.

Data Types: double

Output Arguments

response — Computed impulse response

real vector

Computed impulse response, returned as an n element real vector of impulse response values.

tout — 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 response in seconds.

Data Types: double

More About

Impulse Response And Time Samples Equation

RF Toolbox™ uses the following equation to for the impulse response:

$$resp={\displaystyle \sum _{k=1}^M{C}_k{e}^{A_k(t-Delay)}u(t-Delay)+D\delta (t-Delay)}$$

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.

The vector of time samples of the impulse response, t, is computed from the inputs as t = [0,ts,2*ts,...,(n-1)*ts]

Version History

Introduced in R2006b