👉 The Fast Fourier Transform (FFT) is an efficient algorithm for computing the Discrete Fourier Transform (DFT), a mathematical operation that decomposes a function or signal into its constituent frequencies. While the DFT directly computes the frequency components of a signal, it requires \(O(N^2)\) operations, where \(N\) is the number of data points. The FFT reduces this complexity to \(O(N \log N)\) by exploiting the periodicity and symmetry properties of the DFT, effectively breaking down the transformation into smaller, more manageable subproblems. This makes it significantly faster and more practical for large datasets, widely used in fields like signal processing, image analysis, and data compression.
