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In mathematics, the discrete Fourier transform (DFT) converts a finite sequence of equally-spaced samples of a function into an equivalent-length sequence of equally-spaced samples of the discrete-time Fourier transform (DTFT), which is a complex-valued function of frequency.
after Fourierâs work that the signals did not have to be continuous in the time domain but. could instead be discrete data points. This led to the inception of the discrete-time. Fourier series and the discrete-time Fourier transform [2]. Four different Fourier representations exist: 1. Fourier series (FS) 2. Fourier transform (FT) 3. Discrete-time Fourier series (DTFS) 4. Discrete-time Fourier transform (DTFT) The discrete-time Fourier series that this chapter will primarily focus on is often referred to as the discrete Fourier transform, or DFT. This terminology is not to be confused with the discrete-time Fourier transform. The factor that determines whether to use a series or a transform is periodicity in