The Discrete and Fast Fourier Transforms

The Discrete Fourier Transform (DFT) is of central importance in Digital Signal Processing. When implemented using a Fast Fourier Transform (FFT) algorithm, it offers rapid frequency-domain analysis and processing of digital signals, and investigation of digital systems. The development of FFT algorithms from the mid-1960s onwards gave a huge impetus to DSP, making practicable a range of valuable techniques.