Explicit and Progressive Solution Method for Wigner-Ville Distribution of Prolate Spheroidal Wave Functions Signal

WANG Hongxing; ZHAO Leyuan; LU Faping; LIU Chuanhui; KANG Jiafang

doi:10.11999/JEIT210820

Volume 44 Issue 10

Oct. 2022

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Article Navigation > Journal of Electronics & Information Technology > 2022 > 44(10): 3574-3582

WANG Hongxing, ZHAO Leyuan, LU Faping, LIU Chuanhui, KANG Jiafang. Explicit and Progressive Solution Method for Wigner-Ville Distribution of Prolate Spheroidal Wave Functions Signal[J]. Journal of Electronics & Information Technology, 2022, 44(10): 3574-3582. doi: 10.11999/JEIT210820

Citation:

WANG Hongxing, ZHAO Leyuan, LU Faping, LIU Chuanhui, KANG Jiafang. Explicit and Progressive Solution Method for Wigner-Ville Distribution of Prolate Spheroidal Wave Functions Signal[J]. Journal of Electronics & Information Technology, 2022, 44(10): 3574-3582. doi: 10.11999/JEIT210820

Citation:

WANG Hongxing, ZHAO Leyuan, LU Faping, LIU Chuanhui, KANG Jiafang. Explicit and Progressive Solution Method for Wigner-Ville Distribution of Prolate Spheroidal Wave Functions Signal[J]. Journal of Electronics & Information Technology, 2022, 44(10): 3574-3582. doi: 10.11999/JEIT210820

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Explicit and Progressive Solution Method for Wigner-Ville Distribution of Prolate Spheroidal Wave Functions Signal

doi: 10.11999/JEIT210820

WANG Hongxing^{1, 2},
ZHAO Leyuan^{1, 2
,
,},
LU Faping^{1, 3},
LIU Chuanhui^{1, 2},
KANG Jiafang^{1, 2}

1.
Naval Aviation University, Yantai 264001, China
2.
Key Laboratory on Signal & Information Processing of Shandong Province, Yantai 264001, China
3.
Unit 91206 of the PLA, Qingdao 266000, China

Funds: The National Natural Science Foundation of China (61701518), The Special Foundation Project of Taishan Scholar of Shandong Province (ts20081130)

Received Date: 2021-08-12
Accepted Date: 2022-01-05
Rev Recd Date: 2022-01-03

Available Online: 2022-01-27

Publish Date: 2022-10-19

Abstract

Abstract

Considering the problems of the existing time-frequency analysis of Prolate Spheroidal Wave Functions (PSWFs) signals without explicit expressions, uncontrollable numerical simulation errors, and lack of symmetry in the time-frequency distribution results, Legendre polynomials and Wigner- Ville Distribution (WVD) are introduced in this paper, and an explicit and progressive solution method for PSWFs signal WVD is proposed. According to the error requirements, this method generates the Legendre polynomial WVD self-terms and cross-terms of the required order, and then multiplies them with the corresponding WVD-Legendre coefficients and superimposes linearly them to obtain the explicit and progressive expression of the PSWFs signal WVD. Theoretical and numerical simulation results show that the proposed method can produce an explicit and progressive expression of the PSWFs signal WVD that meets the error requirements, and can effectively maintain the original time-domain and frequency-domain symmetry of the signal. In addition, in the case of the same number of sampling points, compared with the PSWFs signal WVD based on the numerical solution, the PSWFs signal WVD obtained by the proposed method has a higher frequency domain resolution.
- Prolate Spheroidal Wave Functions (PSWFs),
- Time-frequency analysis,
- Wigner-Ville Distribution (WVD),
- Explicitly progressive

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References(21)

References

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