The fractional wavelet transform on spaces of type<i>W</i>

Prasad, Akhilesh; Mahato, Ashutosh

doi:10.1080/10652469.2012.685939

Cited by 8 publications

(3 citation statements)

References 6 publications

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“…Similar with previous studies, 3‐5,23,24 now, we recall some definitions for the purpose of this paper.…”

Section: Introductionmentioning

confidence: 86%

“…This work was extended by Pathak and Pandey 3 and studied wavelet transform associated with Fourier transform on the Gelfand‐Shilov spaces of type W . Furthermore, Prasad and Mahato 4,5 developed and studied wavelet transform in terms of fractional Fourier transform on Gelfand‐Shilov spaces of S and W types. Pseudo‐differential operators are the generalizations of partial differential operators, and they play an important role in the study of partial differential equations.…”

Section: Introductionmentioning

confidence: 99%

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Mapping properties of pseudo‐differential operator on the spaces of type Gelfand‐Shilov

Mahato

Pasawan

2021

Math Methods in App Sciences

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“…Similar with previous studies, 3‐5,23,24 now, we recall some definitions for the purpose of this paper.…”

Section: Introductionmentioning

confidence: 86%

Section: Introductionmentioning

confidence: 99%

Mapping properties of pseudo‐differential operator on the spaces of type Gelfand‐Shilov

Mahato

Pasawan

2021

Math Methods in App Sciences

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“…Mendlovic et al. (1997) defined the FRWT as where κ α is the transform kernel, which can take different definitions (Mendlovic et al., 1997; Prasad and Mahato, 2012; Sejdić et al., 2011; Shi et al., 2012). One possible definition is the same definition as the FRFT kernel, which is given by Depending on the kernel and how α is defined, the FRWT can take different meanings.…”

Section: Waveletsmentioning

confidence: 99%

Wavelets as a tool for systems analysis and control

Abuhamdia

Taheri

2015

Journal of Vibration and Control

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This survey presents the broad range of research on using wavelets in the analysis and design of dynamic systems. Though wavelets have been used with all types of systems, the major focus of this survey is mechanical and electromechanical systems in addition to their controls. However, the techniques presented can be applied to any category of dynamic systems such as economic, biological, and social systems. Wavelets can be classified into three different types: orthogonal, biorthogonal, and pseudo, all of which are employed in dynamic systems engineering. Wavelets-based methods for dynamic systems applications can be divided into vibrations analysis and systems and control analysis. Wavelets applications in vibrations extend to oscillatory response solutions and vibrations-based systems identification. Also, their applications in systems and control extend to time–frequency representation and modeling, nonlinear systems linearization and model reduction, and control design and control law computation. There are serious efforts within systems and control theory to establish time–frequency and wavelets-based Frequency Response Functions (FRFs) parallel to the Fourier-based FRFs, which will pave the road for time-varying FRFs. Moreover, the natural similarity of wavelets to the representation of neural networks allows them to slip into neural-networks-based and fuzzy-neural-networks-based controllers. Additionally, wavelets have been considered for applications in feedforward and feedback control loops for computation, analysis, and synthesis of control laws.

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