A Fast Algorithm for Fractional Fourier Transform with Zooming-in Ability

2008 ◽  
Author(s):  
Xinghao Zhao ◽  
Ran Tao ◽  
Yue Wang
Keyword(s):  
Fourier Transform ◽  
Fast Algorithm ◽  
Fractional Fourier Transform

scholarly journals Discrete Pseudo-Fractional Fourier Transform and Its Fast Algorithm

Electronics ◽  
2021 ◽  
Vol 10 (17) ◽  
pp. 2145
Author(s):  
Dorota Majorkowska-Mech ◽  
Aleksandr Cariow
Keyword(s):  
Fourier Transform ◽  
Fast Algorithm ◽  
Fourier Transforms ◽  
Fractional Fourier Transform ◽  
Composite Number ◽  
Fractional Fourier Transforms ◽  
Fractional Transform

In this article, we introduce a new discrete fractional transform for data sequences whose size is a composite number. The main kernels of the introduced transform are small-size discrete fractional Fourier transforms. Since the introduced transformation is not, in the generally known sense, a classical discrete fractional transform, we call it discrete pseudo-fractional Fourier transform. We also provide a generalization of this new transform, which depends on many fractional parameters. A fast algorithm for computing the introduced transform is developed and described.

Rotation Distortion Invariant Image Recognition Based on Fractional Correlation

2012 ◽  
Vol 220-223 ◽  
pp. 2899-2902
Author(s):  
Hong Xia Wang ◽  
Pan Shi Li ◽  
Zhan Rong Zhou ◽  
You Zhang Zhu
Keyword(s):  
Fourier Transform ◽  
Numerical Calculation ◽  
Fractional Order ◽  
Image Recognition ◽  
Fast Algorithm ◽  
Fractional Fourier Transform ◽  
Correlation Peak

In this paper, a fast algorithm for fractional Fourier transform was proposed based on the theory of fractional Fourier transform, the fast numerical calculation of the fractional Fourier transform and fractional correlation was realized using MATLAB language. The characteristics of rotation distortion invariant image recognition based on fractional correlation were analyzed and compared with the traditional correlation. The results show that the quality of the fractional correlation peak is obviously improved. When fractional order P = 0.7, the fractional correlator can realize rotation distortion invariant image recognition within the scope of 15°.

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.

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