scholarly journals Time-frequency estimates for pseudodifferential operators

2007 ◽  
pp. 13-22 ◽  
Author(s):  
Árpád Bényi ◽  
Kasso A. Okoudjou
Keyword(s):  
Pseudodifferential Operators ◽  
Time Frequency

scholarly journals Subexponential decay and regularity estimates for eigenfunctions of localization operators

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Federico Bastianoni ◽  
Nenad Teofanov
Keyword(s):  
Pseudodifferential Operators ◽  
Modulation Space ◽  
Modulation Spaces ◽  
Weight Functions ◽  
Auxiliary Result ◽  
Localization Operators ◽  
Time Frequency ◽  
Continuity Properties ◽  
Regularity Properties ◽  
Time Frequency Localization

AbstractWe consider time-frequency localization operators $$A_a^{\varphi _1,\varphi _2}$$ A a φ 1 , φ 2 with symbols a in the wide weighted modulation space $$ M^\infty _{w}({\mathbb {R}^{2d}})$$ M w ∞ ( R 2 d ) , and windows $$ \varphi _1, \varphi _2 $$ φ 1 , φ 2 in the Gelfand–Shilov space $$\mathcal {S}^{\left( 1\right) }(\mathbb {R}^d)$$ S 1 ( R d ) . If the weights under consideration are of ultra-rapid growth, we prove that the eigenfunctions of $$A_a^{\varphi _1,\varphi _2}$$ A a φ 1 , φ 2 have appropriate subexponential decay in phase space, i.e. that they belong to the Gelfand–Shilov space $$ \mathcal {S}^{(\gamma )} (\mathbb {R^{d}}) $$ S ( γ ) ( R d ) , where the parameter $$\gamma \ge 1 $$ γ ≥ 1 is related to the growth of the considered weight. An important role is played by $$\tau $$ τ -pseudodifferential operators $$Op_{\tau } (\sigma )$$ O p τ ( σ ) . In that direction we show convenient continuity properties of $$Op_{\tau } (\sigma )$$ O p τ ( σ ) when acting on weighted modulation spaces. Furthermore, we prove subexponential decay and regularity properties of the eigenfunctions of $$Op_{\tau } (\sigma )$$ O p τ ( σ ) when the symbol $$\sigma $$ σ belongs to a modulation space with appropriately chosen weight functions. As an auxiliary result we also prove new convolution relations for (quasi-)Banach weighted modulation spaces.

scholarly journals Time-frequency analysis of Born–Jordan pseudodifferential operators

2017 ◽  
Vol 272 (2) ◽  
pp. 577-598 ◽  
Author(s):  
Elena Cordero ◽  
Maurice de Gosson ◽  
Fabio Nicola
Keyword(s):  
Frequency Analysis ◽  
Pseudodifferential Operators ◽  
Time Frequency Analysis ◽  
Time Frequency

scholarly journals On the local well-posedness of the nonlinear heat equation associated to the fractional Hermite operator in modulation spaces

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Elena Cordero
Keyword(s):  
Cauchy Problem ◽  
Heat Equation ◽  
Frequency Analysis ◽  
Pseudodifferential Operators ◽  
Local Solvability ◽  
Modulation Spaces ◽  
Nonlinear Heat Equation ◽  
Well Posedness ◽  
Hermite Operator ◽  
Time Frequency

AbstractIn this note we consider the nonlinear heat equation associated to the fractional Hermite operator $$H^\beta =(-\Delta +|x|^2)^\beta $$ H β = ( - Δ + | x | 2 ) β , $$0<\beta \le 1$$ 0 < β ≤ 1 . We show the local solvability of the related Cauchy problem in the framework of modulation spaces. The result is obtained by combining tools from microlocal and time-frequency analysis. As a byproduct, we compute the Gabor matrix of pseudodifferential operators with symbols in the Hörmander class $$S^m_{0,0}$$ S 0 , 0 m , $$m\in \mathbb {R}$$ m ∈ R .

A Fault Detection Approach Based on Sound Signal Analysis for Equipment Monitoring

2020 ◽  
pp. 129-139
Author(s):  
Weihai Sun ◽  
Lemei Han
Keyword(s):  
Fault Detection ◽  
Signal Analysis ◽  
Energy Analysis ◽  
Detection Method ◽  
Sound Signal ◽  
Practical Significance ◽  
Time Frequency ◽  
Detection Approach ◽  
Machine Fault ◽  
Learning Data

Machine fault detection has great practical significance. Compared with the detection method that requires external sensors, the detection of machine fault by sound signal does not need to destroy its structure. The current popular audio-based fault detection often needs a lot of learning data and complex learning process, and needs the support of known fault database. The fault detection method based on audio proposed in this paper only needs to ensure that the machine works normally in the first second. Through the correlation coefficient calculation, energy analysis, EMD and other methods to carry out time-frequency analysis of the subsequent collected sound signals, we can detect whether the machine has fault.

Time-Frequency Analysis of Partial Discharge Phenomena in SF6 gas using Wavelet Transform

1997 ◽  
Vol 117 (3) ◽  
pp. 338-345 ◽  
Author(s):  
Masatake Kawada ◽  
Masakazu Wada ◽  
Zen-Ichiro Kawasaki ◽  
Kenji Matsu-ura ◽  
Makoto Kawasaki
Keyword(s):  
Wavelet Transform ◽  
Frequency Analysis ◽  
Partial Discharge ◽  
Time Frequency Analysis ◽  
Time Frequency

Time-Frequency Channel Parameterization with Application to Multi-Mode Receivers

2009 ◽  
Vol E92-B (12) ◽  
pp. 3717-3725
Author(s):  
Thomas HUNZIKER ◽  
Ziyang JU ◽  
Dirk DAHLHAUS
Keyword(s):  
Frequency Channel ◽  
Time Frequency ◽  
Multi Mode
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