Local Price uncertainty principle and time-frequency localization operators for the Hankel–Stockwell transform

2020 ◽  
Vol 18 (06) ◽  
pp. 2050050
Author(s):  
Nadia Ben Hamadi ◽  
Zineb Hafirassou
Keyword(s):  
Uncertainty Principle ◽  
Price Uncertainty ◽  
Localization Operators ◽  
Von Neumann ◽  
Time Frequency ◽  
Neumann Class ◽  
Time Frequency Localization ◽  
Stockwell Transform

For the Hankel–Stockwell transform, the Price uncertainty principle is proved, we define the Localization operators and we study their boundedness and compactness. We also show that these operators belong to the so-called Schatten–von Neumann class.

scholarly journals Sampling time-frequency localized functions and constructing localized time-frequency frames

2016 ◽  
Vol 28 (5) ◽  
pp. 854-876 ◽  
Author(s):  
G. A. M. VELASCO ◽  
M. DÖRFLER
Keyword(s):  
Region Of Interest ◽  
Main Tool ◽  
Sampling Time ◽  
Frequency Content ◽  
Gabor System ◽  
Localization Operators ◽  
Time Frequency ◽  
Compact Region ◽  
Time Frequency Localization ◽  
Finite Linear

We study functions whose time-frequency content are concentrated in a compact region in phase space using time-frequency localization operators as a main tool. We obtain approximation inequalities for such functions using a finite linear combination of eigenfunctions of these operators, as well as a local Gabor system covering the region of interest. These would allow the construction of modified time-frequency dictionaries concentrated in the region.

scholarly journals Localization Operators and an Uncertainty Principle for the Discrete Short Time Fourier Transform

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Carmen Fernández ◽  
Antonio Galbis ◽  
Josep Martínez
Keyword(s):  
Fourier Transform ◽  
Uncertainty Principle ◽  
Extremal Functions ◽  
Short Time Fourier Transform ◽  
Localization Operators ◽  
Time Frequency ◽  
Short Time ◽  
Frequency Basis ◽  
Discrete Setting

Localization operators in the discrete setting are used to obtain information on a signalffrom the knowledge on the support of its short time Fourier transform. In particular, the extremal functions of the uncertainty principle for the discrete short time Fourier transform are characterized and their connection with functions that generate a time-frequency basis is studied.

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