Fast algorithm for determination of linear canonical transform and fractional fourier transform

2004 ◽  
Author(s):  
Bryan M. Hennelly ◽  
John T. Sheridan
Keyword(s):  
Fourier Transform ◽  
Fast Algorithm ◽  
Fractional Fourier Transform ◽  
Linear Canonical Transform

Wavelet packets associated with linear canonical transform on spectrum

2021 ◽  
pp. 2150030
Author(s):  
M. Younus Bhat ◽  
Aamir H. Dar
Keyword(s):  
Fourier Transform ◽  
Multiresolution Analysis ◽  
Fourier Transforms ◽  
Fractional Fourier Transform ◽  
Integral Transforms ◽  
Wavelet Packets ◽  
Linear Canonical Transform ◽  
Fresnel Transform ◽  
The Fourier Transform ◽  
Vector Valued

The linear canonical transform (LCT) provides a unified treatment of the generalized Fourier transforms in the sense that it is an embodiment of several well-known integral transforms including the Fourier transform, fractional Fourier transform, Fresnel transform. Using this fascinating property of LCT, we, in this paper, constructed associated wavelet packets. First, we construct wavelet packets corresponding to nonuniform Multiresolution analysis (MRA) associated with LCT and then those corresponding to vector-valued nonuniform MRA associated with LCT. We investigate their various properties by means of LCT.

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.

scholarly journals A modified convolution and product theorem for the linear canonical transform derived by representation transformation in quantum mechanics

2013 ◽  
Vol 23 (3) ◽  
pp. 685-695 ◽  
Author(s):  
Navdeep Goel ◽  
Kulbir Singh
Keyword(s):  
Fourier Transform ◽  
Quantum Mechanics ◽  
Fractional Fourier Transform ◽  
Integral Transform ◽  
Linear Canonical Transform ◽  
Product Theorem ◽  
Special Cases ◽  
Fresnel Transform ◽  
The Fourier Transform ◽  
Representation Transformation

Abstract The Linear Canonical Transform (LCT) is a four parameter class of integral transform which plays an important role in many fields of signal processing. Well-known transforms such as the Fourier Transform (FT), the FRactional Fourier Transform (FRFT), and the FreSnel Transform (FST) can be seen as special cases of the linear canonical transform. Many properties of the LCT are currently known but the extension of FRFTs and FTs still needs more attention. This paper presents a modified convolution and product theorem in the LCT domain derived by a representation transformation in quantum mechanics, which seems a convenient and concise method. It is compared with the existing convolution theorem for the LCT and is found to be a better and befitting proposition. Further, an application of filtering is presented by using the derived results.

scholarly journals Image Watermarking in the Linear Canonical Transform Domain

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Bing-Zhao Li ◽  
Yu-Pu Shi
Keyword(s):  
Signal Processing ◽  
Fourier Transform ◽  
Fractional Fourier Transform ◽  
Image Watermarking ◽  
Transform Domain ◽  
Linear Canonical Transform ◽  
Watermark Embedding ◽  
Simulation Results ◽  
The Fourier Transform ◽  
Signal Processing Methods

The linear canonical transform, which can be looked at the generalization of the fractional Fourier transform and the Fourier transform, has received much interest and proved to be one of the most powerful tools in fractional signal processing community. A novel watermarking method associated with the linear canonical transform is proposed in this paper. Firstly, the watermark embedding and detecting techniques are proposed and discussed based on the discrete linear canonical transform. Then the Lena image has been used to test this watermarking technique. The simulation results demonstrate that the proposed schemes are robust to several signal processing methods, including addition of Gaussian noise and resizing. Furthermore, the sensitivity of the single and double parameters of the linear canonical transform is also discussed, and the results show that the watermark cannot be detected when the parameters of the linear canonical transform used in the detection are not all the same as the parameters used in the embedding progress.

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°.

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