Sliding DFT

In digital signal processing, the sliding discrete Fourier transform (sliding DFT or SDFT) is a recursive algorithm for computing a sequence of discrete Fourier transforms on overlapping data windows. Successive windows differ by only one sample, so the transform for the new window can be obtained by updating the transform of the previous window rather than recomputing it from scratch.

The sliding DFT is useful in applications that require a new spectral estimate for every input sample, especially when only a subset of DFT frequency bins are needed. In these cases, the sliding DFT can require fewer computations than repeatedly evaluating a complete DFT or FFT. The sliding DFT's recursive structure is closely related to resonator based DFT methods such as the Goertzel algorithm.