多项式Chirplet变换在瞬时频率估计中的应用

发布时间：2018-03-12 14:57

本文选题：时频分析　切入点：多项式Chirplet变换　出处：《西安电子科技大学》2014年硕士论文　论文类型：学位论文

【摘要】：瞬时频率是时频模式中的一种基本的参数,在调频信号中作为一个重要的角色,它已经出现在雷达、检测、语音等各个领域并获得广泛的应用。研究瞬时频率估计的方法以及相应的参数估计在信号的时频分析中具有重要的实用价值,而且时频分布作为非平稳信号的度量工具,它可以充分地展现出信号频率随着时间变化的规律,以及能够在时频分布中观测到信号能量集中的程度。本文首要讲述了瞬时频率的基础研究背景以及相应各个概念产生的缘由,进而定义了瞬时频率普遍运用的概念。其次又介绍了在时频分析中常用的时频分析方法：首先着重介绍了短时傅里叶变换以及Wigner-Ville分布,然而这两种方法都存在各自的缺陷,并不能达到本文期望的效果,即在得到高度信号能量以及聚集性的同时,估计的信号瞬时频率更接近理论值。并由此引出了不同于以往的参数化时频分析方法,其中详细介绍了线性调频小波变换和多项式线性调频小波变换的算法实现,并着重阐述了参数的选择对参数化时频分析方法的重要性。线性调频小波变换的方法引入频率旋转算子和平移算子的概念,以及通过一个额外的用线性调频率参数描绘核函数来处理线性调频信号。进而通过扩展其频率平移算子与旋转算子,以及改变其核函数,最终主要介绍本文重点研究的针对非线性调频信号的多项式Chirplet变换的基本原理。本文主要研究的对象是参数化时频分析方法——多项式Chirplet变换在瞬时频率估计及参数估计中的应用,该方法的核心是将多项式核函数来替代线性调频小波变换中的线性核函数,非常适合非平稳非线性调频信号的处理。为了保证时频分析的质量,本文提出了一种基于目标信号的迭代算法自适应选择多项式Chirplet变换参数。该算法利用雷尼熵来终止迭代,计算出每次迭代中时频表示的雷尼熵,当后一次迭代的雷尼熵大于前一次迭代,或雷尼熵一直减小到不明显变化时终止迭代。此外,该算法中还运用到多项式拟合的方法去更好的匹配理论值,可以更好的估计瞬时频率以及参数。最后,本文通过不同的目标信号来进行仿真试验,通过观察和数据分析,以及在加噪的情况下与其对比的试验手段,证明了本文算法的有效性。在与其它估计方法对比,本文方法的实验效果较为理想。
[Abstract]:Instantaneous frequency is a basic parameter in time-frequency mode. As an important role in FM signal, it has already appeared in radar, detection, The methods of instantaneous frequency estimation and the corresponding parameter estimation have important practical value in time-frequency analysis of signals, and time-frequency distribution is used as a measurement tool for non-stationary signals. It can fully show the variation of signal frequency over time. And the degree of signal energy concentration can be observed in time-frequency distribution. This paper mainly describes the basic research background of instantaneous frequency and the origin of the corresponding concepts. Then the concept of universal use of instantaneous frequency is defined. Secondly, the time-frequency analysis methods commonly used in time-frequency analysis are introduced. First, the short-time Fourier transform and Wigner-Ville distribution are introduced emphatically. However, each of these two methods has their own defects. It can not reach the desired effect in this paper, that is, the estimated instantaneous frequency of the signal is closer to the theoretical value, and the parameterized time-frequency analysis method is different from the previous method. The algorithms of LFM wavelet transform and polynomial LFM wavelet transform are introduced in detail. The importance of parameter selection to parameterized time-frequency analysis is emphasized. The concepts of frequency rotation operator and translation operator are introduced into the method of linear frequency modulation wavelet transform. And the LFM signal is processed by an extra description of the kernel function with linear frequency modulation parameters, and then by extending its frequency translation operator and rotation operator, and changing its kernel function, Finally, the basic principle of polynomial Chirplet transform for nonlinear frequency modulation signal is introduced. The main object of this paper is the parametric time-frequency analysis method-polynomial Chirplet transform in instantaneous frequency estimation and parameter. Applications in number estimation, The core of this method is to replace the linear kernel function in the linear frequency modulation wavelet transform with polynomial kernel function, which is very suitable for the processing of nonstationary nonlinear frequency modulation signals. In this paper, an iterative algorithm based on target signal is proposed to adaptively select polynomial Chirplet transform parameters. In this algorithm, Rayney entropy is used to terminate the iteration, and the Rayney entropy of time-frequency representation in each iteration is calculated. When the reni entropy of the last iteration is larger than that of the previous iteration, or if the Rayney entropy decreases until the change is not obvious, the iteration is terminated. In addition, the polynomial fitting method is used in the algorithm to better match the theoretical values. The instantaneous frequency and parameters can be better estimated. Finally, this paper carries out simulation experiments through different target signals, through observation and data analysis, as well as the test means compared with them in the case of adding noise. The effectiveness of the proposed method is proved. Compared with other estimation methods, the experimental results of this method are satisfactory.
【学位授予单位】：西安电子科技大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：TN911.23

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