Perform convolution between the two given signals 𝑥(𝑡) = 5 cos 𝑡 and ℎ(𝑡) = 2𝑒 −|𝑡| . Verify the same using MATLAB.

How to perform convolution.

[Steven Lord]

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Answer 1

[Kautuk Raj]

To perform convolution between the two given signals x(t) = 5cos(t) and h(t) = 2e^(-|t|), we can use the following steps:

1. Define the time range over which to evaluate the signals using the t variable.
2. Define the signals x and h as functions of t.
3. Use the conv function to compute the convolution of x and h.

The MATLAB code to implement these steps:

% Define the time range over which to evaluate the signals
t = -10:0.01:10;
% Define the signals x and h
x = 5*cos(t);
h = 2*exp(-abs(t));
% Compute the convolution of x and h using the conv function
y = conv(x, h, 'same') * 0.01;
% Plot the signals x, h, and y
subplot(3, 1, 1);
plot(t, x);
title('Signal x(t) = 5cos(t)');
xlabel('Time (s)');
ylabel('Amplitude');
subplot(3, 1, 2);
plot(t, h);
title('Signal h(t) = 2e^{-|t|}');
xlabel('Time (s)');
ylabel('Amplitude');
subplot(3, 1, 3);
plot(t, y);
title('Convolution y(t) = x(t) * h(t)');
xlabel('Time (s)');
ylabel('Amplitude');

And this is the output: