The Hopping Discrete Fourier Transform [sp Tips&Tricks]

The discrete Fourier transform (DFT) produces a Fourier representation for finite-duration data sequences. In addition to its theoretical importance, the DFT plays a key role in the implementation of a variety of digital signal-?processing algorithms. Several algorithms including the fast Fourier transform (FFT) and the Goertzel algorithm have been introduced for the fast implementation of the DFT [1], [2].