Time–Frequency Analysis in Rn

Vesa Vuojamo*, Ville Turunen, Heikki Orelma

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

1 Citation (Scopus)
17 Downloads (Pure)

Abstract

A time–frequency transform is a sesquilinear mapping from a suitable family of test functions to functions on the time–frequency plane. The goal is to quantify the energy present in the signal at any given time and frequency. The transform is further specified by imposing conditions such as those stemming from basic transformations of signals and those which an energy density should satisfy. We present a systematic study on how properties of a time–frequency transform are reflected in the associated evaluation at time–frequency origin, integral kernel and quantization and discuss some examples of time–frequency transforms.

Original languageEnglish
Article number6
Pages (from-to)1-38
Number of pages38
JournalJournal of Fourier Analysis and Applications
Volume28
Issue number1
DOIs
Publication statusPublished - Feb 2021
MoE publication typeA1 Journal article-refereed

Keywords

  • Cohen class
  • Quadratic time–frequency transforms
  • Time–frequency analysis

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