MATLAB: How to intentionally introduce aliasing of signals in Simulink

I want to intentionally create aliasing in my model to see its effects.

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The attached model contains a sine wave source block, a zero-order hold block, and a spectrum scope block. The frequency of the sine wave is 100 Hz, and its sampling time is 1000 Hz. The sampling time of the zero-order hold block is 75 Hz. When you run the model, you will see a spike in the spectrum scope block at 25 Hz, representing a sinusoid with a frequency of 25 Hz. This is because the 100 Hz source sinusoid becomes aliased to a 25 Hz sinusoid.

In general, f_image = f - N*fs, where f_image is the created, aliased frequency, f is the frequency of the original sinusoid, fs is the new sampling frequency, and N is an integer chosen such that f_image lies within [0, fs/2).

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MATLAB: How do i normalise frequency axis after computing fft

If you have a 50 Hz sampling frequency, the Nyquist frequency — in this instance the normalising frequency if you are designing a digital filter — is 25 Hz. So if you want a 15 Hz cutoff for a lowpass filter for instance, the normalised frequency, ‘Wn’ would be:

Fs = 50;                    % Sampling Frequency (Hz)
Fn = Fs/2;                  % Nyquist Frequency (Hz)
Fc = 15;                    % Cutoff Frequency (Hz)
Wn = Fc/Fn;                 % Normalised Cutoff Frequency (Dimensionless)

So Wn = 15/25 = 0.6

EDIT — For fft scaling, the best documentation is in the R2015a fft version. See specifically the code between the first two plot images.

MATLAB: Do I see frequencies which do not exist in the original signal in the output of the FFT function

The behavior observed is due to a phenomenon called aliasing. Aliasing refers to the distortion that occurs when a continuous time signal has frequencies larger than half of the sampling rate. The process of aliasing describes the phenomenon in which components of the signal at high frequencies are mistaken for components at lower frequencies.

To avoid aliasing, ensure that the sampling rate is high enough to avoid any spectral overlap, or use an anti-aliasing filter. In the code, for example, consider "third_frequency" to be 600. Since the sampling frequency, Fs, is 1000, you will notice a component at 1000 – 600 = 400 Hz. If "third_frequency" is 800, you will see a component at 1000 – 800 = 200 Hz.

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MATLAB: How do i normalise frequency axis after computing fft

MATLAB: Do I see frequencies which do not exist in the original signal in the output of the FFT function

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