A certain family of fractional wavelet transformations

Srivástava, H. M.; Khatterwani, Komal; Upadhyay, Subrahamanyam

doi:10.1002/mma.5570

Cited by 22 publications

(18 citation statements)

References 17 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…If scale and position are varied very smoothly then the transform is called continuous wavelet transform (CWT). The CWT of signal

f \in L^{2} false(ℝ false)

with respect to

ϕ \in L^{2} false(ℝ false)

is defined as 8–13

\begin{matrix} ((), W_{ϕ} f) false(b, c false) & = \int_{- \infty}^{\infty} f false(x false) \overset{ϕ_{b, c} false(x false)}{true} d x \\ = false(f * {scriptD}_{- c} ϕ false) false(b false) . \end{matrix}

…”

Section: Introductionmentioning

confidence: 99%

“…Since translation, dilation, and convolution operators have been defined for various integral transforms, using these operators and following the above notion, many authors defined wavelets and wavelet transforms in terms of fractional Fourier transform 12,14,15 and studied their theory and properties. In addition, some more wavelet transforms have also been established for positive half line by using the transforms of special functions, namely, the Bessel wavelet transform, 16–18 Laguerre wavelet transform, 19 Mehler–Fock wavelet transform, 20 and Kontorovich–Lebedev wavelet transform, 21 and discussed their properties and applications.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Wavelet transforms associated with the index Whittaker transform

Prasad

Maan

Verma

2021

Math Methods in App Sciences

View full text Add to dashboard Cite

The continuous wavelet transform (CWT) associated with the index Whittaker transform is defined and discussed using its convolution theory. Existence theorem and reconstruction formula for CWT are obtained. Moreover, composition of CWT is discussed, and its Plancherel's and Parseval's relations are also derived. Further, the discrete version of this wavelet transform and its reconstruction formula are given. Furthermore, certain properties of the discrete Whittaker wavelet transform are discussed.

show abstract

“…If scale and position are varied very smoothly then the transform is called continuous wavelet transform (CWT). The CWT of signal

f \in L^{2} false(ℝ false)

with respect to

ϕ \in L^{2} false(ℝ false)

is defined as 8–13

\begin{matrix} ((), W_{ϕ} f) false(b, c false) & = \int_{- \infty}^{\infty} f false(x false) \overset{ϕ_{b, c} false(x false)}{true} d x \\ = false(f * {scriptD}_{- c} ϕ false) false(b false) . \end{matrix}

…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Wavelet transforms associated with the index Whittaker transform

Prasad

Maan

Verma

2021

Math Methods in App Sciences

View full text Add to dashboard Cite

show abstract

“…During the last decade or so, the operational matrices of integration based on Haar wavelets, Legendre wavelets, Chebyshev wavelets, CAS wavelets, Bernoulli wavelets, Gegenbauer wavelets, fractional wavelets, wavelet frames, and the spline wavelets have been developed in order to solve a wide variety of differential, integral, and integro-differential equations. [14][15][16][17][18] The Haar wavelets are a specific kind of compactly supported wavelets generated by the combined action of dyadic dilations and integer translations of a rectangular pulse wave, and these wavelets have gained prominence among researchers due to their simple and lucid structure. Moreover, these wavelets can be integrated analytically in arbitrary times and permit straight inclusion of the different types of boundary conditions in the numerical algorithms.…”

Section: Introductionmentioning

confidence: 99%

Generalized wavelet quasilinearization method for solving population growth model of fractional order

Srivástava

Shah

Irfan

2020

Math Methods in App Sciences

Self Cite

View full text Add to dashboard Cite

The primary aim of this study is to introduce and develop a generalized wavelet method together with the quasilinearization technique to solve the Volterra's population growth model of fractional order. Unlike the existing operational matrix methods based on orthogonal functions, we formulate the wavelet operational matrices of general order integration without using the block pulse functions. Consequently, the governing problem is transformed into an equivalent system of algebraic equations, which can be tackled with any classical method. The applicability of the proposed method is demonstrated via an illustrative comparison of the numerical outcomes with those found by other known methods. The experimental outcomes demonstrate that the proposed method is fast, accurate, simple, and computationally reliable.

show abstract

“…Wavelet transforms have fascinated researchers with their versatile applicability across different branches of science and engineering. For more details about wavelet transforms and their applications, the reader is referred to [2][3][4][5].…”

Section: Introductionmentioning

confidence: 99%

A family of convolution-based generalized Stockwell transforms

Srivástava

Shah

Tantary

2020

J. Pseudo-Differ. Oper. Appl.

View full text Add to dashboard Cite

The main purpose of this paper is to introduce a family of convolution-based generalized Stockwell transforms in the context of time-fractional-frequency analysis. The spirit of this article is completely different from two existing studies (see D. P. Xu and K. Guo [Appl. Geophys. 9 (2012) 73-79] and S. K. Singh [J. Pseudo-Differ. Oper. Appl. 4 (2013) 251-265]) in the sense that our approach completely relies on the convolution structure associated with the fractional Fourier transform. We first study all of the fundamental properties of the generalized Stockwell transform, including a relationship between the fractional Wigner distribution and the proposed transform. In the sequel, we introduce both the semi-discrete and discrete counterparts of the proposed transform. We culminate our investigation by establishing some Heisenberg-type inequalities for the generalized Stockwell transform in the fractional Fourier domain.

show abstract

A certain family of fractional wavelet transformations

Cited by 22 publications

References 17 publications

Wavelet transforms associated with the index Whittaker transform

Wavelet transforms associated with the index Whittaker transform

Generalized wavelet quasilinearization method for solving population growth model of fractional order

A family of convolution-based generalized Stockwell transforms

Contact Info

Product

Resources

About