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Fourier Transform
Fourier Transform - Ayush Tripathi The Fourier Transform Developed by Ayush Tripathi Introduction The Fourier Transform is a mathematical tool that decomposes a function (often a function of time, representing a signal) into its constituent frequencies. It's like separating a musical chord into its individual notes. It's a cornerstone of signal processing, image processing, and many areas of physics and engineering. The Core Idea Any function can be represented as a sum (or integral, for continuous functions) of sine and cosine waves of different frequencies and amplitudes. The Fourier Transform tells us what those frequencies and amplitudes are. Continuous Fourier Transform (CFT) For a continuous-time function \( f(t) \), the Fourier Transform, \( F(\omega) \), is defined as: \( ...
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