Instantaneous Frequency Estimation Based on the Wigner‐Ville Distribution Associated with Linear Canonical Transform (WDL)

Liu, Lubo; Luo, Maokang; Lai, Li

doi:10.1049/cje.2017.07.009

Cited by 7 publications

(5 citation statements)

References 7 publications

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“…Convolution and correlation theorems for WVD-LCT are obtained in [16]. In [26] authors proposed a new method of instantaneous frequency estimation by associating the WVD with the LCT, which has a higher capacity for anti-noise and a higher estimation accuracy than WVD. Zhang unified LCWD and WVD-LCT [20], and then presented its special cases with less parameters [21,22].…”

Section: Previous Resultsmentioning

confidence: 99%

“…This results in poor performance under a low signal-to-noise ratio for detection and estimation. Recently, for the purpose to improve the performance of LFM signal detection and estimation, several researchers have associated WVD with the FrFT, LCT, and OLCT, respectively [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27]. Results show that such transforms exploit the advantages of both transforms, which is why we call them hybrid transforms.…”

Section: Introductionmentioning

confidence: 99%

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Hybrid Transforms

Urynbassarova¹,

Urynbassarova²

2023

Time Frequency Analysis of Some Generalized Fourier Transforms

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Hybrid transforms are constructed by associating the Wigner-Ville distribution (WVD) with widely-known signal processing tools, such as fractional Fourier transform, linear canonical transform, offset linear canonical transform (OLCT), and their quaternion-valued versions. We call them hybrid transforms because they combine the advantages of both transforms. Compared to classical transforms, they show better results in applications. The WVD associated with the OLCT (WVD-OLCT) is a class of hybrid transform that generalizes most hybrid transforms. This chapter summarizes research on hybrid transforms by reviewing a computationally efficient type of the WVD-OLCT, which has simplicity in marginal properties compared to WVD-OLCT and WVD.

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Section: Previous Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Hybrid Transforms

Urynbassarova¹,

Urynbassarova²

2023

Time Frequency Analysis of Some Generalized Fourier Transforms

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show abstract

“…Since the LCT's fast discrete algorithms were proposed [ 43‐57 ] , a large number of achievements have emerged in its mathematical foundations (convolution theorems [ 5 , 58‐64 ] , sampling theorems [ 60 , 61 , 65‐79 ] , uncertainty principles [ 80‐91 ] , etc. ), theoretical expansions (time‐frequency analysis [ 92‐99 ] , compressed sensing [ 100 ] , phase retrieval [ 101 ] , etc. ), and practical applications (signal denoising [ 22‐24 , 35 , 36 , 40‐42 , 102‐105 ] , image watermarking [ 106 , 107 ] , weak target detection [ 108 , 109 ] , etc.).…”

Section: Preliminariesmentioning

confidence: 99%

Variance‐SNR Based Noise Suppression on Linear Canonical Choi‐Williams Distribution of LFM Signals

ZHANG

2022

Chinese J of Electronics

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By solving the existing expectation‐signal‐to‐noise ratio (expectation‐SNR) based inequality model of the closed‐form instantaneous cross‐correlation function type of Choi‐Williams distribution (CICFCWD), the linear canonical transform (LCT) free parameters selection strategies obtained are usually unsatisfactory. Since the second‐order moment variance outperforms the first‐order moment expectation in accurately characterizing output SNRs, this paper uses the variance analysis technique to improve parameters selection strategies. The CICFCWD's average variance of deterministic signals embedded in additive zero‐mean stationary circular Gaussian noise processes is first obtained. Then the so‐called variance‐SNRs are defined and applied to model a variance‐SNR based inequality. A stronger inequalities system is also formulated by integrating expectation‐SNR and variance‐SNR based inequality models. Finally, a direct application of the system in noisy one‐component and bi‐component linear frequency‐modulated (LFM) signals detection is studied. Analytical algebraic constraints on LCT free parameters newly derived seem more accurate than the existing ones, achieving better noise suppression effects. Our methods have potential applications in optical, radar, communication and medical signal processing.

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“…The frequency of FHSS signal changes randomly with time, which belongs to non-stationary signal, so joint time-frequency analysis (TFA) [4][5][6][7][8] is a common method to analyze FHSS signals, the basic idea of joint time-frequency analysis is to estimate the instantaneous frequency, and then estimate the modulation parameters. Therefore, the estimation accuracy of the instantaneous frequency determines the accuracy of parameters estimation.…”

Section: Introductionmentioning

confidence: 99%

A Novel Parameter Estimation Method of FHSS Signal with Low SNR

Zhu

Dai

et al. 2023

IEEJ Transactions Elec Engng

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A novel parameter estimation method of frequency hopping spread spectrum (FHSS) signal is proposed. The observed signal is divided into multiple segments and forms an observed matrix, performing FFT on the observed matrix with different segment lengths to obtain the corresponding spectrum matrix. By analyzing the convergence characteristics of the spectrum matrix, the estimation of the symbol period is realized, on this basis, the symbol‐frequency distribution is obtained and its projected spectrum in Frequency‐Amplitude plane is further obtained to select the candidate frequencies. The matrix composed of multiple single frequency signals is constructed according to the candidate frequencies and multiplied with the observed matrix under the segment length of symbol period, then the number of symbols per hopping duration is estimated according to the matrix multiplication result, so as to realize the estimation of the hopping duration, and finally the real hopping frequencies and hopping sequence can be found out from the candidate frequencies. Simulation results are presented to indicate that the proposed method has good estimation performance especially under the condition of low SNR. © 2023 Institute of Electrical Engineers of Japan. Published by Wiley Periodicals LLC.

show abstract

Instantaneous Frequency Estimation Based on the Wigner‐Ville Distribution Associated with Linear Canonical Transform (WDL)

Cited by 7 publications

References 7 publications

Hybrid Transforms

Hybrid Transforms

Variance‐SNR Based Noise Suppression on Linear Canonical Choi‐Williams Distribution of LFM Signals

A Novel Parameter Estimation Method of FHSS Signal with Low SNR

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