In mathematics, the discrete Fourier transform (DFT) is one of the specific forms of Fourier analysis. It transforms one function into another, which is called the frequency domain representation, or simply the DFT. Since the input function is a finite sequence of real or complex numbers, the DFT is ideal for processing information stored in computers. In particular, the DFT is widely employed in signal processing and related fields to analyze the frequencies contained in a sampled signal, to solve partial differential equations, and to perform other operations such as convolutions. The DFT can be computed efficiently in practice using a fast Fourier transform (FFT) algorithm.

inverse discrete Fourier transform (IDFT)