👉 The math presented here revolves around the concept of a discrete Fourier transform (DFT), a powerful tool in signal processing and analysis that converts a function of time (or space) into a function of frequency. Given a sequence of complex numbers representing a discrete signal, the DFT calculates the amplitude and phase of each frequency component present in that signal. This is achieved through a summation formula involving the signal's values and complex exponentials, effectively decomposing the signal into its constituent frequencies. The result is a frequency domain representation that reveals the signal's spectral content, making it invaluable in applications like audio processing, image analysis, and data compression. The DFT's efficiency is enhanced by the Fast Fourier Transform (FFT) algorithm, which computes the DFT in O(N log N) time complexity, making it feasible to analyze large datasets.
