On spectral interference of the short-time Fourier transform and its nonlinear variations
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866917206198059008 |
|---|---|
| author | Chand, Shrikant Nolen, James Wu, Hau-Tieng |
| author_facet | Chand, Shrikant Nolen, James Wu, Hau-Tieng |
| contents | Spectral interference, the frequency counterpart of the beating phenomenon in the time domain, can severely distort time-frequency representations (TFRs) in physical applications. We study this phenomenon for the short-time Fourier transform (STFT) with a Gaussian window and for nonlinear refinements based on the reassignment method, with an emphasis on the synchrosqueezing transform (SST). Working with a two-component harmonic model, we quantify when STFT can (and cannot) resolve two nearby frequencies: a sharp transition occurs at a critical gap that scales inversely to kernel bandwidth and depends explicitly on the amplitude ratio. Below this threshold, the spectrogram ridges undergo bifurcation and form repeating time-frequency bubbles, which we describe asymptotically and, in the balanced-amplitude case, approximate closely by ellipses. We then analyze the STFT phase, showing a canonical winding behavior, and relate the complex-valued SST reassignment map to a holomorphic structure via the Bargmann transform. In the two-component setting the reassignment rule admits an explicit Mobius-geometry description, sending frequency lines to circular arcs in the complex plane. Finally, viewing SST and reassignment through a measure mapping perspective, we derive small-kernel asymptotics that explain when reassignment sharpens energy and when it produces distorted or misleading TFRs; we also introduce a generalized synchrosqueezing framework that isolates the role of STFT weighting and clarifies how alternative choices can mitigate interference in certain regimes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_10910 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On spectral interference of the short-time Fourier transform and its nonlinear variations Chand, Shrikant Nolen, James Wu, Hau-Tieng Classical Analysis and ODEs Numerical Analysis Spectral interference, the frequency counterpart of the beating phenomenon in the time domain, can severely distort time-frequency representations (TFRs) in physical applications. We study this phenomenon for the short-time Fourier transform (STFT) with a Gaussian window and for nonlinear refinements based on the reassignment method, with an emphasis on the synchrosqueezing transform (SST). Working with a two-component harmonic model, we quantify when STFT can (and cannot) resolve two nearby frequencies: a sharp transition occurs at a critical gap that scales inversely to kernel bandwidth and depends explicitly on the amplitude ratio. Below this threshold, the spectrogram ridges undergo bifurcation and form repeating time-frequency bubbles, which we describe asymptotically and, in the balanced-amplitude case, approximate closely by ellipses. We then analyze the STFT phase, showing a canonical winding behavior, and relate the complex-valued SST reassignment map to a holomorphic structure via the Bargmann transform. In the two-component setting the reassignment rule admits an explicit Mobius-geometry description, sending frequency lines to circular arcs in the complex plane. Finally, viewing SST and reassignment through a measure mapping perspective, we derive small-kernel asymptotics that explain when reassignment sharpens energy and when it produces distorted or misleading TFRs; we also introduce a generalized synchrosqueezing framework that isolates the role of STFT weighting and clarifies how alternative choices can mitigate interference in certain regimes. |
| title | On spectral interference of the short-time Fourier transform and its nonlinear variations |
| topic | Classical Analysis and ODEs Numerical Analysis |
| url | https://arxiv.org/abs/2601.10910 |