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Fractal Fract
Special Issues
Fractional Fourier Transform and Its Applications in Signal Analysis
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Fractional Fourier Transform and Its Applications in Signal Analysis

A special issue of Fractal and Fractional (ISSN 2504-3110).

Deadline for manuscript submissions: closed (31 October 2024) | Viewed by 3468

Special Issue Editors

Dr. Yuan-Min Li

E-Mail Website
Guest Editor
School of Mathematics and Statistics, Xidian University, Xi'an 710071, China
Interests: fractional Fourier transform; sparse optimization; cone and stochastic optimization
Prof. Dr. Deyun Wei

E-Mail Website
Guest Editor
School of Mathematics and Statistics, Xidian University, Xi’an 710071, China
Interests: fractional order signal processing theory and method; time-frequency analysis; sampling theory; sparse discrete algorithm; graph signal processing

Special Issue Information

Dear Colleagues,

With the rapid development of the information technology, the research object of signal processing gradually shifts from relatively simple and stable signals to more complex signals such as non-stationary, non-Gaussian, and time-varying. The fractional Fourier transform uses a set of linear frequency modulated orthogonal bases to decompose the signal, which makes it suitable for processing non-stationary signals. Therefore, fractional Fourier transform is highly favored by researchers in signal analysis such as signal separation, signal filtering, signal detection, and signal estimation. With the demand for big data and real-time signal processing, sparse fractional Fourier transform and expansions, as well as fast algorithms, have been developed and widely applied in radar signal processing, spectral sensing, image recognition and fusion, compressed sampling, and sparse representation. With the continuous emergence of large-scale and high-dimensional signals, two-dimensional fractional Fourier transform and its extensions, as well as graph fractional Fourier transform, have been developed. This has also been widely applied in many fields such as two-dimensional digital signal processing, image super-resolution reconstruction, image encryption and watermarking, medical imaging, image compression, image classification, semi supervised learning, and so on.

This Special Issue aims to continue the research on the theory of fractional Fourier transform and related extended theories, discrete and sparse fast algorithms, and their related applications. The topics for invitation submission include (but are not limited to) the following:

  • Mathematical theory of FRFT;
  • Sparse representation and fast algorithm;
  • Sparse fractional Fourier transform and its applications;
  • Graph fractional Fourier transform and its applications;
  • Applications of FRFT in signal processing, information security and other fields;
  • Applications of two-dimensional FRFT in image processing and other fields.

Dr. Yuan-Min Li
Prof. Dr. Deyun Wei
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Fractal and Fractional is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2700 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • fractional Fourier transform
  • linear canonical transform
  • sparse fractional Fourier transform
  • graph fractional Fourier transform
  • fast Fourier transform
  • sampling theory
  • convolution and filtering
  • digital signal processing

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Published Papers (3 papers)

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Research

14 pages, 2145 KiB  
Article
Synchroextracting Transform Based on the Novel Short-Time Fractional Fourier Transform
by Bei Li and Zhuosheng Zhang
Fractal Fract. 2024, 8(12), 736; https://doi.org/10.3390/fractalfract8120736 (registering DOI) - 14 Dec 2024
Viewed by 209
Abstract
As a generalization of the short-time Fourier transform (STFT), the novel short-time fractional Fourier transform (NSTFRFT) has been introduced recently. In order to improve the concentration of the time–frequency representation (TFR) generated by the NSTFRFT, two post-processing time–frequency analysis methods, two synchroextracting transforms [...] Read more.
As a generalization of the short-time Fourier transform (STFT), the novel short-time fractional Fourier transform (NSTFRFT) has been introduced recently. In order to improve the concentration of the time–frequency representation (TFR) generated by the NSTFRFT, two post-processing time–frequency analysis methods, two synchroextracting transforms based on the NSTFRFT with two different fractional Fourier transform (FRFT) angles, are proposed in this paper. One is achieved via an equation where the instantaneous frequency satisfies the condition where the FRFT angle takes π2, and the other one is obtained using the instantaneous frequency estimator in the case that the FRFT angle takes a value related to the chirp rate of the signal. Although the conditions of the two synchroextracting transforms are different, their implementation can be unified into the same algorithm. The proposed synchroextracting transforms supplement existing post-processing time–frequency analysis methods which are based on the NSTFRFT. Experiments are conducted to verify the performance and superiority of the proposed methods. Full article
(This article belongs to the Special Issue Fractional Fourier Transform and Its Applications in Signal Analysis)
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15 pages, 328 KiB  
Article
Sampling Theorems Associated with Offset Linear Canonical Transform by Polar Coordinates
by Hui Zhao and Bing-Zhao Li
Fractal Fract. 2024, 8(10), 559; https://doi.org/10.3390/fractalfract8100559 - 26 Sep 2024
Viewed by 517
Abstract
The sampling theorem for the offset linear canonical transform (OLCT) of bandlimited functions in polar coordinates is an important signal analysis tool in many fields of signal processing and optics. This paper investigates two sampling theorems for interpolating bandlimited and highest frequency bandlimited [...] Read more.
The sampling theorem for the offset linear canonical transform (OLCT) of bandlimited functions in polar coordinates is an important signal analysis tool in many fields of signal processing and optics. This paper investigates two sampling theorems for interpolating bandlimited and highest frequency bandlimited functions in the OLCT and offset linear canonical Hankel transform (OLCHT) domains by polar coordinates. Based on the classical Stark’s interpolation formulas, we derive the sampling theorems for bandlimited functions in the OLCT and OLCHT domains, respectively. The first interpolation formula is concise and applicable. Due to the consistency of the OLCHT order, the second interpolation formula is superior to the first interpolation formula in computational complexity. Full article
(This article belongs to the Special Issue Fractional Fourier Transform and Its Applications in Signal Analysis)
18 pages, 7596 KiB  
Article
A Novel Image Encryption Algorithm Based on Compressive Sensing and a Two-Dimensional Linear Canonical Transform
by Yuan-Min Li, Mingjie Jiang, Deyun Wei and Yang Deng
Fractal Fract. 2024, 8(2), 92; https://doi.org/10.3390/fractalfract8020092 - 31 Jan 2024
Cited by 4 | Viewed by 1553
Abstract
In this paper, we propose a secure image encryption method using compressive sensing (CS) and a two-dimensional linear canonical transform (2D LCT). First, the SHA256 of the source image is used to generate encryption security keys. As a result, the suggested technique is [...] Read more.
In this paper, we propose a secure image encryption method using compressive sensing (CS) and a two-dimensional linear canonical transform (2D LCT). First, the SHA256 of the source image is used to generate encryption security keys. As a result, the suggested technique is able to resist selected plaintext attacks and is highly sensitive to plain images. CS simultaneously encrypts and compresses a plain image. Using a starting value correlated with the sum of the image pixels, the Mersenne Twister (MT) is used to control a measurement matrix in compressive sensing. Then, the scrambled image is permuted by Lorenz’s hyper-chaotic systems and encoded by chaotic and random phase masks in the 2D LCT domain. In this case, chaotic systems increase the output complexity, and the independent parameters of the 2D LCT expand the key space of the suggested technique. Ultimately, diffusion based on addition and modulus operations yields a cipher-text image. Simulations showed that this cryptosystem was able to withstand common attacks and had adequate cryptographic features. Full article
(This article belongs to the Special Issue Fractional Fourier Transform and Its Applications in Signal Analysis)
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