Problem with Square() for high frequenzies

Kshitij Singh answered . 2025-03-24 20:10:31

To help you with the issue of analyzing aliasing for a 20kHz frequency using an ideal square wave, let's consider some factors that could be affecting your script:

1. Sampling Rate: Ensure that your sampling rate is significantly higher than 20kHz to avoid aliasing. A common practice is to use a sampling rate at least 10 times higher than the signal frequency.

2. Nyquist Theorem: According to the Nyquist theorem, the sampling rate should be at least twice the highest frequency present in the signal. For a 20kHz signal, you should have a sampling rate of at least 40kHz.

3. FFT Resolution: The resolution of the FFT depends on the number of points in the FFT. Ensure you have a sufficient number of points to achieve the desired frequency resolution.

Here's an example script that addresses these considerations for a 20kHz square wave:

% Define parameters
Fs = 200000; % Sampling frequency (200 kHz)
T = 1/Fs;    % Sampling period
L = 10000;   % Length of signal
t = (0:L-1)*T; % Time vector

% Define the square wave signal (20 kHz)
f = 20000; % Frequency of the square wave (20 kHz)
signal = square(2*pi*f*t);

% Perform FFT
Y = fft(signal);

% Compute the two-sided spectrum and then the single-sided spectrum
P2 = abs(Y/L);
P1 = P2(1:L/2+1);
P1(2:end-1) = 2*P1(2:end-1);

% Define frequency domain
f = Fs*(0:(L/2))/L;

% Plot the single-sided amplitude spectrum
figure;
plot(f, P1)
title('Single-Sided Amplitude Spectrum of Square Wave')
xlabel('f (Hz)')
ylabel('|P1(f)|')
xlim([0 50000]); % Limit x-axis to 50 kHz for better visualization

In this script:

• Sampling Frequency (Fs): Set to 200 kHz to ensure a high enough sampling rate to avoid aliasing.

• Square Wave Frequency (f): Set to 20 kHz.

• FFT Calculation: Performed to analyze the frequency content of the square wave.

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