Time–Frequency Analysis in Rn

Vesa Vuojamo; Ville Turunen; Heikki Orelma

doi:10.1007/s00041-021-09894-3

Time–Frequency Analysis in Rⁿ

Vesa Vuojamo^*, Ville Turunen, Heikki Orelma

^*Corresponding author for this work

Tampere University

Research output: Contribution to journal › Article › Scientific › peer-review

10 Citations (Scopus)

132 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 language	English
Article number	6
Pages (from-to)	1-38
Number of pages	38
Journal	Journal of Fourier Analysis and Applications
Volume	28
Issue number	1
DOIs	https://doi.org/10.1007/s00041-021-09894-3
Publication status	Published - Feb 2021
MoE publication type	A1 Journal article-refereed

Keywords

Cohen class
Quadratic time–frequency transforms
Time–frequency analysis

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Time–Frequency Analysis in RnFinal published version, 616 KBLicence: CC BY

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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.",

keywords = "Cohen class, Quadratic time–frequency transforms, Time–frequency analysis",

author = "Vesa Vuojamo and Ville Turunen and Heikki Orelma",

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AB - 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.

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ER -

Time–Frequency Analysis in Rⁿ

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Keywords

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