基于分数阶Fourier变换的时频分布

上海大学学报(自然科学版)

基于分数阶Fourier变换的时频分布

陈俊丽，万旺根，黄炳，谢寥沙

上海大学通信与信息工程学院，上海 200072

收稿日期:2007-03-13 修回日期:1900-01-01 出版日期:2007-08-20 发布日期:2007-08-20
通讯作者: 陈俊丽

Time-Frequency Distribution of the Fractional Fourier Transform

CHEN Jun-li, WAN Wang-gen, HUANG Bing, XIE Liao-sha

School of Communication and Information Engineering, Shanghai University, Shanghai 200072, China

Received:2007-03-13 Revised:1900-01-01 Online:2007-08-20 Published:2007-08-20
Contact: CHEN Jun-li

摘要/Abstract

摘要： 分数阶Fourier变换是对经典Fourier变换的推广.根据信号瞬时相关函数、点谱相关函数、Wigner分布和模糊函数这4种信号表示方法之间的Fourier变换关系，基于二维分数阶Fourier变换，给出一种新的分数阶时频分布，它表征了信号的局部时间/频偏和局部频率/时延特性，进一步讨论该分布函数的主要性质.最后给出它在线性调频（chirp）信号检测中应用的仿真结果.

关键词: Wigner分布, 分数阶Fourier, 模糊函数, 时频分析

Abstract: Fractional Fourier transform can be considered as generalization of the Fourier transform. Four basic quadratic signal representations, i.e., signal correlation function, spectral correlation function, Wigner distribution, and ambiguity function, can be interpreted with Fourier transform. A new timefrequency distribution function based on 2D fractional Fourier transform is presented. The distributions have partial time/frequency-lag and partial frequency/time-lag characteristics of signals. Main properties of the distribution function are discussed. Simulations show that the described distribution can detect chirp signal.

Key words: ambiguity function
, fractional Fourier transform, Wigner distribution, timefrequency analysis

中图分类号:

TN911.72

陈俊丽;万旺根;黄炳;谢寥沙. 基于分数阶Fourier变换的时频分布[J]. 上海大学学报(自然科学版).

CHEN Jun-li;WAN Wang-gen;HUANG Bing;XIE Liao-sha. Time-Frequency Distribution of the Fractional Fourier Transform
[J]. Journal of Shanghai University（Natural Science Edition）.

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[2]	邱志易,郑国莘,刘雅君,卢佳欣. 超窄带甚小线性调频信号的小波分析[J]. 上海大学学报(自然科学版), 2012, 18(2): 132-138.