{"ID":2885236,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2508.05380","arxiv_id":"2508.05380","title":"Unifying Common Signal Analyses with Instantaneous Time-Frequency Atoms","abstract":"In previous work, we presented a general framework for instantaneous time-frequency analysis but did not provide any specific details of how to compute a particular instantaneous spectrum (IS). In this work, we use instantaneous time-frequency atoms to obtain an IS associated with common signal analyses: time domain analysis, frequency domain analysis, fractional Fourier transform, synchrosqueezed short-time Fourier transform, and synchrosqueezed short-time fractional Fourier transform. By doing so, we demonstrate how the general framework can be used to unify these analyses and we develop closed-form expressions for the corresponding ISs. This is accomplished by viewing these analyses as decompositions into AM--FM components and recognizing that each uses a specialized (or limiting) form of a quadratic chirplet as a template during analysis. With a two-parameter quadratic chirplet, we can organize these ISs into a 2D continuum with points in the plane corresponding to a decomposition related to one of the signal analyses. Finally, using several example signals, we compute in closed-form the ISs for the various analyses.","short_abstract":"In previous work, we presented a general framework for instantaneous time-frequency analysis but did not provide any specific details of how to compute a particular instantaneous spectrum (IS). In this work, we use instantaneous time-frequency atoms to obtain an IS associated with common signal analyses: time domain an...","url_abs":"https://arxiv.org/abs/2508.05380","url_pdf":"https://arxiv.org/pdf/2508.05380v2","authors":"[\"Steven Sandoval\",\"Phillip L. De Leon\"]","published":"2025-08-07T13:25:22Z","proceeding":"eess.SP","tasks":"[\"eess.SP\"]","methods":"[\"Generative Adversarial Network\"]","has_code":false}