The sliding DFT

@article{Jacobsen2003TheSD,
  title={The sliding DFT},
  author={Eric A. Jacobsen and Richard G. Lyons},
  journal={IEEE Signal Process. Mag.},
  year={2003},
  volume={20},
  pages={74-80}
}
The sliding DFT process for spectrum analysis was presented and shown to be more efficient than the popular Goertzel (1958) algorithm for sample-by-sample DFT bin computations. The sliding DFT provides computational advantages over the traditional DFT or FFT for many applications requiring successive output calculations, especially when only a subset of the DFT output bins are required. Methods for output stabilization as well as time-domain data windowing by means of frequency-domain… 

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