The Fourier Transform may be applied to a general class of functions. For special classes of functions, other Fourier analysis techniques have been developed to simplify analysis and provide additional insight. These include the Fourier Series (FS) and the Discrete Fourier Transform (DFT) and the the Discrete Time Discrete Fourier Transform (DTFT). The Fourier Series is applicable to continuous periodic signals, the DTFT is appliciable to discrete signals, and the while the DFT is applicable to discrete periodic signals. The Fast Fourier Transform (FFT) is an efficient numerical implementation of the DFT. The following table summarizes the applicability of each form of the Fourier Transform.
