Research on sparsity of frequency modulated signal in fractional Fourier transform domain

Wang Shuo; Guo Yong; Yang Lidong

doi:10.12086/oee.2020.190660

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Wang S, Guo Y, Yang L D. Research on sparsity of frequency modulated signal in fractional Fourier transform domain[J]. Opto-Electron Eng, 2020, 47(11): 190660. doi: 10.12086/oee.2020.190660

Citation:

Wang S, Guo Y, Yang L D. Research on sparsity of frequency modulated signal in fractional Fourier transform domain[J]. Opto-Electron Eng, 2020, 47(11): 190660. doi: 10.12086/oee.2020.190660

Research on sparsity of frequency modulated signal in fractional Fourier transform domain

1.
School of Information Engineering, Inner Mongolia University of Science and Technology, Baotou, Inner Mongolia 014010, China
2.
School of Science, Inner Mongolia University of Science and Technology, Baotou, Inner Mongolia 014010, China

Fund Project: Supported by National Natural Science Foundation of China (11801287), Inner Mongolia Natural Science Foundation (2019BS01007), and Inner Mongolia University of Science and Technology Innovation Fund (2019QDL-B39)

More Information

Corresponding author: Guo Yong. E-mail:guo_yong@imust.edu.cn

Received Date 02 November 2019

Revised Date 19 December 2019

Published Date 15 November 2020

Abstract

Abstract

Frequency modulated (FM) signal is extensively applied in sonar, radar, laser and emerging optical cross-research, its sparsity is a common basic issue for the sampling, denoising and compression of FM signal. This paper mainly studies the sparsity of FM signal in the fractional Fourier transform (FRFT) domain, and a maximum singular value method (MSVM) is proposed to estimate the compact FRFT domain of FM signal. This method uses the maximum singular value of amplitude spectrum of FM signal to measure the compact domain, and WOA is used to search the compact domain, which effectively improves the shortcomings of the existing methods. Compared with MNM and MACF, this method gives a sparser representation of FM signal in the FRFT domain, which has less number of significant amplitudes. Finally, the primary application of this method in the FM signal filtering is given.
- frequency modulated signal /
- sparsity /
- fractional Fourier transform /
- singular value decomposition

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References

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Overview

Overview

Overview:Frequency modulated (FM) signal is a typical non-stationary signal, which is widely used in sonar, radar, laser and other traditional fields. In recent years, it has been applied to the new field of optical intersection. Its sparsity is a common basic problem in the FM signal processing. Fractional Fourier transform (FRFT) uses the orthogonal chirp function to decompose signal and is unaffected by the cross terms, and thus is very suitable for analyzing and processing FM signal. Due to the advantages of FRFT in the FM signal processing, FRFT is also applied to explore the sparsity of FM signal. FRFT can represent the signal from any fractional domain between the time domain and the frequency domain. Therefore, there is at least one optimal fractional Fourier transform domain, which makes the FM signal have best sparsity in this optimal domain. This optimal domain is named as compact fractional Fourier transform domain. In the process of finding the compact fractional Fourier transform domain, the measurement and searching of optimal domain are two key points. On the basis of the above advantages, this paper is devoted to studying the sparsity of FM signal in fractional Fourier transform domain, and a sparse representation method of FM signal based on FRFT and singular value decomposition is proposed, called as maximum singular value method (MSVM). On the one hand, the maximum singular value of amplitude spectrum in FRFT domain is taken as the measurement of optimal domain, which makes MSVM has better sparsity and noise robustness. Since singular value decomposition can map high-dimensional data space to a relatively low-dimensional data space, and thus singular value decomposition effectively reduces the dimension of data processing. The larger the singular value of the amplitude spectrum, the better the sparsity of the FM signal in the corresponding fractional Fourier transform domain. Moreover, the singular value decomposition is a kind of decomposition method which can be applied to any matrix, and has a wider applicability. On the other hand, whale optimization algorithm is used to search optimal domain. Whale optimization algorithm is a new heuristic bionic algorithm, which imitates the behavior of humpback whales in searching, seizing and foraging. Because whale optimization algorithm is flexible and has no gradient limitation. It can effectively avoid falling into the local optimum, and effectively improve the shortcomings of the coarse-to-fine grid search and traversal search methods, and is not influenced by the search step size. The quantitative index is the number of significant amplitudes (NSA), the less NSA means better sparsity. By the simulation, compared with MACF and MNM, MSVM has less NSA in the compact fractional Fourier transform domain. It is concluded that the MSVM can give better sparsity of FM signal in the compact fractional Fourier transform domain. In the end, this paper presents the application of MSVM in the filter of linear FM signal, which basically achieves the filtering of noise and the maintenance of signal behavior.