椭圆球面波信号Wigner-Ville分布显式渐近求解方法

王红星; 赵乐源; 陆发平; 刘传辉; 康家方

doi:10.11999/JEIT210820

椭圆球面波信号Wigner-Ville分布显式渐近求解方法

doi: 10.11999/JEIT210820

王红星^{1, 2},
赵乐源^{1, 2, ,},
陆发平^{1, 3},
刘传辉^{1, 2},
康家方^{1, 2}

1.
海军航空大学烟台 264001
2.
山东省信号与信息处理重点实验室烟台 264001
3.
中国人民解放军 91206部队青岛 266000

基金项目: 国家自然科学基金(61701518)，山东省“泰山学者”建设工程专项经费基金(ts20081130)

详细信息

作者简介:
王红星：男，教授，研究方向为现代通信系统、非正弦波通信、无线光通信

赵乐源：男，硕士生，研究方向为现代通信系统、非正弦波通信

陆发平：男，博士，研究方向为现代通信系统、非正弦波通信、多载波调制

刘传辉：男，讲师，研究方向为现代通信新技术、非正弦波通信

康家方：男，讲师，研究方向为现代通信新技术、扩频通信、非正弦波通信

通讯作者:
赵乐源　zhaolyvip@163.com

中图分类号: TN911.3
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出版历程
- 收稿日期: 2021-08-12
- 修回日期: 2022-01-03
- 录用日期: 2022-01-05
- 网络出版日期: 2022-01-27
- 刊出日期: 2022-10-19

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

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)

摘要

摘要: 针对现有的椭圆球面波函数(PSWFs)信号时频分析无显式表达式、数值仿真误差不可控、时频分布结果对称性缺失等问题，该文引入Legendre多项式以及Wigner-Ville分布(WVD)，提出一种PSWFs信号WVD显式渐近求解方法。该方法根据误差要求，生成所需阶数的Legendre多项式WVD自项、交叉项，进而与对应的WVD-Legendre系数相乘后线性叠加，获取PSWFs信号WVD显式渐近表达式。理论及数值仿真结果表明，所提方法能够产生满足误差要求的PSWFs信号WVD显式渐近表达式，且能够有效保持信号原有的时域、频域对称性。此外，在相同采样点数情况下，相对于基于数值解的PSWFs信号WVD，所提方法获得的PSWFs信号WVD频域分辨率更高。
- 椭圆球面波信号 /
- 时频分析 /
- Wigner-Ville分布 /
- 显式渐近
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

HTML全文

图 1 PSWFs信号WVD显式渐近求解方法原理框图

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图 2 PSWFs信号对应的WVD-Legendre系数

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图 3 PSWFs信号MSE

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图 4 0阶PSWFs信号WVD

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表 1 PSWFs信号仿真参数设置

参数符号数值

时间带宽积(rad·s) c 4π: 4π: 64π
符号周期(s) T 2
阶数 n 0～7
采样点数 N 128, 256, 512

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