Fast Fourier Transform
The Fast Fourier Transform (FFT) is an efficient algorithm for computing the Discrete Fourier Transform (DFT) and its inverse, which decomposes a sequence of values into components of different frequencies. It reduces the computational complexity from O(nĀ²) for the naive DFT to O(n log n), making it practical for real-time signal processing and large datasets. FFT is fundamental in digital signal processing, audio analysis, image compression, and scientific computing.
Developers should learn FFT when working with signal processing, audio/video applications, or data analysis involving frequency domain transformations, such as in telecommunications, music software, or scientific simulations. It is essential for implementing features like audio filtering, spectral analysis, image processing (e.g., JPEG compression), and solving partial differential equations efficiently.