Plot the time-domain response of a swept frequency signal

Hello, I am currently trying to plot the response of a swept-frequncy cosinusoidal signal and lsim this swept-frequency signal using a transfer function.

Ie; suppose I generate the following input swept frequency signal of the form:

y = chirp(t,f0,t1,f1)

And if i generate a continuous time transfer function of the format:

sys = tf(numerator,denominator)

Can i use lsim and plot the output of all signals within the swept-band?

output=lsim(sys,y,t)

The end goal of mine is to have all of these overlayed signals' eye diagrams be plotted.

I want to then do:

eyediagram(output, %numsamples/trace);

Is this good framework to follow or do you all suggest something else that may work better?

Regards

Answer 1

[Paras Gupta]

Hi Rohan,

I understand that you want to plot time-domain response of multiple signals using eye diagrams in a swept frequency band. The approach followed by you is valid and can be run for multiple signals by:

• Using for loops
• Passing a signals matrix as input to the ‘lsim’ function

An example code that uses for loops is given below:

% Define the swept-band parameters
t = 0:0.01:10;     % Time vector
f0 = 1;            % Initial frequency
t1 = 10;           % End time
f1 = 10;           % Final frequency
numFreqs = 10;     % Number of frequencies in the swept-band

% Generate the swept-band signals
frequencies = linspace(f0, f1, numFreqs);   % Frequency range
signals = zeros(length(t), numFreqs);      % Matrix to store the signals

for i = 1:numFreqs
    signals(:, i) = chirp(t, f0, t1, frequencies(i));
end

% Define the transfer functions for each input channel
numerator = 1;           % Numerator coefficients
denominator = [1, 1, 1];   % Denominator coefficients
sys = tf(numerator, denominator);  % Define the transfer function for the current signal

% Simulate the response for each signal in the swept-band
outputs = zeros(length(t), numFreqs);  % Matrix to store the outputs

for i = 1:numFreqs
    outputs(:, i) = lsim(sys, signals(:, i), t);
end

% Plot the output of all signals within the swept-band
figure;
hold on;
for i = 1:numFreqs
    plot(t, outputs(:, i));
end
hold off;
xlabel('Time');
ylabel('Output Signal');
title('Response of the System for Swept-Band Signals');

% Generate the eye diagram for a specific signal
signalIndex = 3;          % Index of the signal to generate the eye diagram
numsamples = 100;         % Number of samples per trace
eyediagram(outputs(:, signalIndex), numsamples);
xlabel('Time');
ylabel('Amplitude');
title('Eye Diagram of a Swept-Band Signal');

More information on using the signals matrix as an argument to the ‘lsim’ function can be found in the documentation below under section 'Plot Simulated Response of MIMO System'.

• https://in.mathworks.com/help/control/ref/dynamicsystem.lsim.html

Hope this helps.

[Rohan Gulur]

This is aweome Paras,

Eye Diagram looks really clean in this.

Thank you.