Product of continuous fractional wave packet transforms

2019 ◽  
Vol 17 (04) ◽  
pp. 1950021
Author(s):  
Akhilesh Prasad ◽  
Praveen Kumar ◽  
Tanuj Kumar
Keyword(s):  
Fourier Transform ◽  
Wave Packet ◽  
Inversion Formula ◽  
Fractional Fourier Transform

In this paper, we investigated the fractional Fourier transform (FrFT) of the continuous fractional wave packet transform and studied some properties of continuous fractional wave packet transform. The product of continuous fractional wave packet transforms (CFrWPTs) is defined. Parseval’s relation and an inversion formula for product of CFrWPT are obtained. An example is also given.

scholarly journals Cauchy representation of fractional Fourier transform for Boehmians

2018 ◽  
Vol 38 (1) ◽  
pp. 55-65
Author(s):  
Abhishek Singh ◽  
P. K. Banerji
Keyword(s):  
Fourier Transform ◽  
Inversion Formula ◽  
Fractional Fourier Transform ◽  
Lizorkin Space

Results relating to fractional Fourier transform and their properties in the Lizorkin space are employed in this paper to investigate the Cauchy representation of fractional Fourier transform for integrable Boehmians. An inversion formula for the fractional Fourier transform is addressed. The conclusion remark of the paper spells the initiation for the present investigation.

Logarithmic uncertainty principle, convolution theorem related to continuous fractional wavelet transform and its properties on a generalized Sobolev space

2017 ◽  
Vol 15 (05) ◽  
pp. 1750050 ◽  
Author(s):  
Mawardi Bahri ◽  
Ryuichi Ashino
Keyword(s):  
Fourier Transform ◽  
Wavelet Transform ◽  
Sobolev Space ◽  
Inversion Formula ◽  
Uncertainty Relation ◽  
Fractional Fourier Transform ◽  
Convolution Theorem ◽  
Inner Product ◽  
Fractional Wavelet Transform ◽  
Product Relation

The continuous fractional wavelet transform (CFrWT) is a nontrivial generalization of the classical wavelet transform (WT) in the fractional Fourier transform (FrFT) domain. Firstly, the Riemann–Lebesgue lemma for the FrFT is derived, and secondly, the CFrWT in terms of the FrFT is introduced. Based on the CFrWT, a different proof of the inner product relation and the inversion formula of the CFrWT are provided. Thereafter, a logarithmic uncertainty relation for the CFrWT is investigated and the convolution theorem related to the CFrWT is established using the convolution of the FrFT. The CFrWT on a generalized Sobolev space is introduced and its important properties are presented.

A New Study of Shape and Size-dependent Properties of Nanocrystals Utilizing the Fractional Fourier Transform

2020 ◽  
Vol 5 (2) ◽  
pp. 165-174
Author(s):  
Aeshah Salem
Keyword(s):  
Fourier Transform ◽  
Infrared Spectroscopy ◽  
Fourier Transform Infrared Spectroscopy ◽  
Surface Area ◽  
Fractional Fourier Transform ◽  
Fourier Transform Infrared ◽  
Chemical Dynamics ◽  
Znse Nanoparticles ◽  
Size Dependent ◽  
Shape And Size

Background: Possessions of components, described by their shape and size (S&S), are certainly attractive and has formed the foundation of the developing field of nanoscience. Methods: Here, we study the S&S reliant on electronic construction and possession of nanocrystals by semiconductors and metals to explain this feature. We formerly considered the chemical dynamics of mineral nanocrystals that are arranged according to the S&S not only for the big surface area, but also as a consequence of the considerably diverse electronic construction of the nanocrystals. Results: The S&S of models, approved by using the Fractional Fourier Transform Infrared Spectroscopy (FFTIR), indicate the construction of CdSe and ZnSe nanoparticles. Conclusion: In order to study the historical behavior of the nanomaterial in terms of S&S and estimate further results, the FFTIR was used to solve this project.

Computer-generated hologram of asymmetry fractional Fourier transform

2005 ◽  
Author(s):  
Zhaoxuan Sheng ◽  
Hongxia Wang ◽  
Junfa He ◽  
Youjie Zhou ◽  
Jun Wang ◽  
...  
Keyword(s):  
Fourier Transform ◽  
Fractional Fourier Transform ◽  
Computer Generated Hologram
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