Continuous Linear Wavelet Transform Associated With The Bessel Operator And Its Discretization

2001 ◽  
pp. 285-304
Keyword(s):  
Wavelet Transform ◽  
Bessel Operator ◽  
Continuous Linear

The wavelet transform on spaces of type S

2006 ◽  
Vol 136 (4) ◽  
pp. 837-850 ◽  
Author(s):  
R. S. Pathak ◽  
S. K. Singh
Keyword(s):  
Wavelet Transform ◽  
Continuous Wavelet Transform ◽  
Wavelet Transforms ◽  
The Other ◽  
Continuous Wavelet ◽  
Continuous Linear ◽  
Ultradifferentiable Functions ◽  
Linear Map ◽  
The One

The continuous wavelet transform is studied on certain Gel'fand–Shilov spaces of type S. It is shown that, for wavelets belonging to the one type of S-space defined on R, the wavelet transform is a continuous linear map of the other type of the S-space into a space of the same type (latter type) defined on R × R+. The wavelet transforms of certain ultradifferentiable functions are also investigated.

scholarly journals The pseudodifferential operatorA(x,D)

2004 ◽  
Vol 2004 (8) ◽  
pp. 407-419
Author(s):  
R. S. Pathak ◽  
S. Pathak
Keyword(s):  
Integral Representation ◽  
Pseudodifferential Operator ◽  
Linear Mapping ◽  
Bessel Operator ◽  
Continuous Linear ◽  
Continuous Linear Mapping ◽  
Zemanian Space ◽  
Norm Continuity ◽  
Hankel Convolution ◽  
Symbol Class

The pseudodifferential operator (p.d.o.)A(x,D), associated with the Bessel operatord2/dx2+(1−4μ2)/4x2, is defined. Symbol classHρ,δmis introduced. It is shown that the p.d.o. associated with a symbol belonging to this class is a continuous linear mapping of the Zemanian spaceHμinto itself. An integral representation of p.d.o. is obtained. Using Hankel convolutionLσ,αp-norm continuity of the p.d.o. is proved.

A Quantum Wavelet Uncertainty Principle

2021 ◽  
Vol 6 (1) ◽  
pp. 8
Author(s):  
Sabrine Arfaoui ◽  
Maryam G. Alshehri ◽  
Anouar Ben Ben Mabrouk
Keyword(s):  
Wavelet Transform ◽  
Uncertainty Principle ◽  
Wavelet Function ◽  
Bessel Operator ◽  
Two Parameters

In the present paper, an uncertainty principle is derived in the quantum wavelet framework. Precisely, a new uncertainty principle for the generalized q-Bessel wavelet transform, based on some q-quantum wavelet, is established. A two-parameters extension of the classical Bessel operator is applied to generate a wavelet function which is used for exploring a wavelet uncertainty principle in the q-calculus framework.

Classification of Acceleration Waveforms during Walking by Wavelet Transform

1997 ◽  
Vol 36 (04/05) ◽  
pp. 356-359 ◽  
Author(s):  
M. Sekine ◽  
M. Ogawa ◽  
T. Togawa ◽  
Y. Fukui ◽  
T. Tamura
Keyword(s):  
Wavelet Transform ◽  
Wavelet Analysis ◽  
Center Of Gravity ◽  
Dynamic Responses ◽  
Sequential Data ◽  
Acceleration Signal ◽  
Continuous Dynamic

Abstract:In this study we have attempted to classify the acceleration signal, while walking both at horizontal level, and upstairs and downstairs, using wavelet analysis. The acceleration signal close to the body’s center of gravity was measured while the subjects walked in a corridor and up and down a stairway. The data for four steps were analyzed and the Daubecies 3 wavelet transform was applied to the sequential data. The variables to be discriminated were the waveforms related to levels -4 and -5. The sum of the square values at each step was compared at levels -4 and -5. Downstairs walking could be discriminated from other types of walking, showing the largest value for level -5. Walking at horizontal level was compared with upstairs walking for level -4. It was possible to discriminate the continuous dynamic responses to walking by the wavelet transform.

Adaptive identification methods of nonlinear random electrical signal

2020 ◽  
Vol 64 (1-4) ◽  
pp. 431-438
Author(s):  
Jian Liu ◽  
Lihui Wang ◽  
Zhengqi Tian
Keyword(s):  
Wavelet Transform ◽  
Electric Vehicle ◽  
Signal To Noise Ratio ◽  
Sudden Change ◽  
Electrical Signal ◽  
Signal Recognition ◽  
State Variable ◽  
Signal Characteristics ◽  
The Matrix ◽  
Kalman Filter Algorithm

The nonlinearity of the electric vehicle DC charging equipment and the complexity of the charging environment lead to the complex and changeable DC charging signal of the electric vehicle. It is urgent to study the distortion signal recognition method suitable for the electric vehicle DC charging. Focusing on the characteristics of fundamental and ripple in DC charging signal, the Kalman filter algorithm is used to establish the matrix model, and the state variable method is introduced into the filter algorithm to track the parameter state, and the amplitude and phase of the fundamental waves and each secondary ripple are identified; In view of the time-varying characteristics of the unsteady and abrupt signal in the DC charging signal, the stratification and threshold parameters of the wavelet transform are corrected, and a multi-resolution method is established to identify and separate the unsteady and abrupt signals. Identification method of DC charging distortion signal of electric vehicle based on Kalman/modified wavelet transform is used to decompose and identify the signal characteristics of the whole charging process. Experiment results demonstrate that the algorithm can accurately identify ripple, sudden change and unsteady wave during charging. It has higher signal to noise ratio and lower mean root mean square error.

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