Programming for Mathematical Applications
The Fast Fourier Transform (FFT) is an efficient algorithm to compute the discrete Fourier transform (DFT) and its inverse, transforming a sequence of complex numbers into its frequency components. It dramatically reduces the computation time required to analyze signals, making it a vital tool in various fields, including engineering and physics, where it is used to study waveforms and signal processing. The FFT exploits symmetries in the DFT computation to achieve this efficiency, transforming operations that could take hundreds or thousands of calculations into just a few.
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