A unified framework for the fractional Fourier transform

1998 ◽  
Vol 46 (12) ◽  
pp. 3206-3219 ◽  
Author(s):  
G. Cariolaro ◽  
T. Erseghe ◽  
P. Kraniauskas ◽  
N. Laurenti
Keyword(s):  
Fourier Transform ◽  
Fractional Fourier Transform ◽  
Unified Framework

scholarly journals Hermite Functions, Lie Groups and Fourier Analysis

Entropy ◽  
2018 ◽  
Vol 20 (11) ◽  
pp. 816 ◽  
Author(s):  
Enrico Celeghini ◽  
Manuel Gadella ◽  
Mariano del Olmo
Keyword(s):  
Fourier Transform ◽  
Fourier Analysis ◽  
Hilbert Spaces ◽  
Fractional Fourier Transform ◽  
Close Relation ◽  
Hermite Functions ◽  
Symmetry Groups ◽  
Laguerre Functions ◽  
Unified Framework ◽  
Hermite And Laguerre Functions

In this paper, we present recent results in harmonic analysis in the real line R and in the half-line R + , which show a closed relation between Hermite and Laguerre functions, respectively, their symmetry groups and Fourier analysis. This can be done in terms of a unified framework based on the use of rigged Hilbert spaces. We find a relation between the universal enveloping algebra of the symmetry groups with the fractional Fourier transform. The results obtained are relevant in quantum mechanics as well as in signal processing as Fourier analysis has a close relation with signal filters. In addition, we introduce some new results concerning a discretized Fourier transform on the circle. We introduce new functions on the circle constructed with the use of Hermite functions with interesting properties under Fourier transformations.

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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