rectangular signal, 2V amplitude and duration of 1ms, how to present the amplitude spectrum

rectangular signal, 2V amplitude and duration of 1ms, how to present the amplitude spectrum

Answer 1

[Hari]

Hi,

I understand that you want to present the amplitude spectrum of a rectangular signal with a 2V amplitude and a duration of 1 ms.

I assume you want to do this using the Fourier Transform.

In order to present the amplitude spectrum of the rectangular signal, you can follow the below steps:

Generate the Rectangular Signal:

Create a rectangular pulse with a specified amplitude and duration.

fs = 10000; % Sampling frequency in Hz
t = 0:1/fs:1-1/fs; % Time vector for 1 second
rect_signal = 2 * (t < 0.001); % 2V amplitude, 1ms duration

Compute the Fourier Transform:

Use the “fft” function to transform the rectangular signal into the frequency domain.

Y = fft(rect_signal);
L = length(rect_signal);
P2 = abs(Y/L); % Two-sided spectrum
P1 = P2(1:L/2+1); % Single-sided spectrum
P1(2:end-1) = 2*P1(2:end-1);

Define the Frequency Domain:

Create a frequency vector for plotting.

f_axis = fs*(0:(L/2))/L;

Plot the Amplitude Spectrum:

Visualize the single-sided amplitude spectrum.

plot(f_axis, P1);
title('Single-Sided Amplitude Spectrum of Rectangular Signal');
xlabel('Frequency (Hz)');
ylabel('|P1(f)|');

Analyze the Spectrum:

Note that the spectrum will display sinc-like characteristics due to the Fourier Transform of a rectangular pulse.

Refer to the documentation of “fft” function to know more about its usage:

• https://www.mathworks.com/help/matlab/ref/fft.html

Hope this helps!