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Fourier Transform Definition, Visualisation & MATLAB Code (Steve Blog Ref)

Definitions of Fourier Transform: The time domain (or spatial domain for image processing) and the frequency domain are both continuous, infinite domains. There is no explicit or implied periodicity in either domain. This is the one I call the  Fourier transform . The time domain is continuous and the time-domain functions are periodic. The frequency domain is discrete. I call this the Fourier series . The time domain is discrete and infinite, and the frequency domain is continuous. In the frequency domain the transform is periodic. This is the  discrete-time Fourier transform  (DTFT). The time domain and the frequency domain are both discrete and finite. Although finite, the time and frequency domains are both implicitly periodic. This form is the  discrete Fourier transform  (DFT). Fourier Visualization: Here is the first example, the input image contains the single sinusoidal pattern, while doing 2D Discrete Fourier Transform it can b...