TSM by Resampling STFTs Across TimeIn 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.
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
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.
TSM and S+N+T