### TSM by Resampling STFTs Across Time

In view of Chapter 8, a natural implementation of TSM based on the STFT is as follows:- Perform a short-time Fourier transform (STFT) using hop size . Denote the STFT at frame and bin by , and denote the result of TSM processing by .
- To perform TSM by the factor , advance the ``frame pointer'' by during resynthesis instead of the usual samples.

*interpolating*(across time) the STFT magnitude magnitude spectra of the first. For example, using simple linear interpolation gives

(11.23) |

where the phase is chosen to preserve continuity and/or the amplitude envelope from frame to frame under the overlap-add (more on this below). Generalizing to arbitrary TSM factors , we obtain

(11.24) |

where , and is advanced by each frame-step. In general, TSM methods based on STFT modification are classified as ``vocoder'' type methods (§G.5). Thus, the TSM implementation outlined above may be termed a

*weighted overlap-add (WOLA) phase-vocoder*method.

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Phase Continuation

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TSM and S+N+T