【作者】 马世伟；

【导师】 曹家麟；

【作者基本信息】 上海大学 ， 控制理论与控制工程， 2000， 博士

【摘要】 时频分析理论和技术是信号处理中的一个研究热点，它对自然界和工程实践中经常遇到的时变非平稳信号提供了有效的分析和处理手段。本文在研究了典型的时频表示方法，以及时频分析中基函数的时频结构特征的基础上，提出了时频分析中基函数的参数化描述的概念和实现方法，以及参数自适应信号分解方法和参数自适应时频分布(PAD)。设计了高效数值算法，分别从时域和频域实现了具有四个参数的频率切变高斯基和时间切变高斯基信号分解，并就它们的特性以及在去噪和瞬时频率估计等方面的应用进行了探索和研究。 本文第一章介绍了非平稳信号与时频分析的基本概念和主要数学工具，概述了国内外研究和应用现状，阐明了本文研究的目的和特殊意义。 第二章介绍了短时傅立叶变换(STFT)、Gabor扩展和小波变换等线性时频表示方法，以及Wigner-Ville分布(WVD)和Cohen类等二次型时频表示方法，研究了它们之间的关系和各自的优缺点。STFT简单易实现，但其窗效应使得时频分辨率较低。WVD有较高的分辨率，但对于多分量信号，交叉项干扰严重。研究了加性白噪声环境下有用信号时频表示的估计问题，理论分析和仿真实验表明：有噪信号的STFT和小波变换都可以无偏地估计原信号的相应时频表示；其WVD以及伪WVD都不能用来估计原信号的WVD；其平滑的伪WVD可以对原信2000年上海大学博士学位论文号的WvD做有偏估计，估计偏差和方差都与窗函数有关，实际应用中需要在时间或频率平滑窗的长度与估计偏差和方差之间作一些折衷。 第三章提出了参数化基函数的描述方法，即通过对单窗函数施加时移、频移、尺度、时间切变、频率切变和旋转等算子，可以得到具有各种不同时频特性的基函数模型，以匹配现实中存在的复杂非平稳信号。利用参数化基函数，我们可以在一个统一的框架下定义更为一般的多参数信号线性变换，以及多参数时频分布函数。 第四章提出了基于信号分解的参数自适应时频表示方法。它将信号分解到完备基函数集上，能够随着被分析信号的局部时频特征自适应地调节基函数的参数，从而避免了窗效应，可以较大地提高时频分辨率。分解所得参数包含了信号局部时频结构的信息，可以用于进一步的信号处理。相应的队D满足实值性、时移不变性、频移不变性和能量守恒关系，且对于多分量信号没有交叉项干扰，从而可以给出信号时频分布的清晰图像。实验结果表明该方法对于典型的非平稳信号，如线性调频信号以及宽带和窄带信号，都可以给出同时具有较高时间分辨率和频率分辨率的时频分析，其分析效果优于STFT谱图、尺度图、wvD等方法，并进一步发展了已有的自适应时频表示方法。 在本文第五章和第六章中，分别构造了频率切变高斯基函数和时间切变高斯基函数集合，它们分别由对不同时频位置的尺度高斯函数乘线性调频因子和与线性调频因子的卷积而产生。设计了一个高效的数值算法，采用类似于多尺度分析的模拟变焦距过程，将四维参数(尺度一频率切变一时移一频移，或尺度-时间切变一频移一时移)的估计间题降低为各一维参数的估计，从 非平稳信号的参数自适应时频表示及其应用的研究而可以分别在时域和频域快速实现基于这两类基函数的参数自适应信号分解，以及相应的正值队D。实验结果表明所提算法有较快的收敛速度，且有较强的抗白噪声干扰能力，因而有利于低信噪比下信号的检测、分析和综合。这些方法有望对于信号中的线性调频成分和频率散射成分进行分析。 第七章研究了参数自适应时频表示的几个典型应用。实验结果表明:它对地震信号、鸟声和语音信号等典型的非平稳信号均能够给出准确的时变频谱;可以通过对分解所得参数的取舍进行去噪和滤波，去噪效果和小波变换去噪的效果相当，但该方法比小波变换去噪方法要简单;队D可以用于峰值检测的瞬时频率估计，对于像线性调频一类的信号能给出较好的估计结果，在较低信噪比的情况下，估计误差小于WVD、STFT、相位差分法和极大似然估计法，和平滑的伪WVD接近。 需要进一步解决的问题和研究方向主要有更为高效的自适应分解参数估计数值算法，非对称基函数和其他参数模型，以及参数自适应时频表示的实际应用的研究。更多还原

【Abstract】 The researches on the time-frequency (TF) analysis (TFA) are hot now in signal processing. They provide effective tools for dealing with the non-stationary signals that are often encountered in natures and engineering practices.In this dissertation, starting with the discussions on some typical methods of the TF representation (TFR) and the properties of their localized basis, a novel idea of the parametric descriptions for the basis in the TFA is proposed. Further, a new TFR method, we name it the parametric adaptive TFR, which includes a method of parametric adaptive signal decomposition and a related parametric adaptive TF distribution (TFD), is derived. An effective numerical algorithm is presented, which implemented a frequency-sheared Gaussian functions based parametric adaptive TFR in time domain, and a time-sheared one in frequency domain, respectively. The characteristics of the new method and its applications in the de-noising and the estimation of signal’s instantaneous frequency (IF) are studied.In chapter one, the fundamental concepts about the TFA, the non-stationary signals and some of the key mathematical tools used in the TFA are introduced. The worldwide developments in this field are summarized. The purposes and the significance of the works in this dissertation are indicated.In chapter two, the linear and the quadratic TFR methods, as well as the relationships among them are introduced. Their defects, such as the window effects and the lower TF resolutions in short time Fouriertransform (STFT) and the cross-term interference in Wigner-Ville distribution (WVD) are discussed. The noise influence on the TFA is analyzed. The theoretic analyses and the simulations show that it is the STFT and the wavelet transform, but the WVD and the pseudo WVD, of the noisy signal are non-biased estimators to the corresponding TFR of the clean signal. However, the smoothed pseudo WVD of the noisy signal is a biased estimator to the WVD of the clean signal. For the bias and variance of the estimation by using smoothed pseudo WVD depend on both the time smoothing window and the frequency one, we must make a trade-off between the lengths of the windows and the bias or the variance.In chapter three, the method for building the parametric basis is given. In terms of this method, one can construct various basis models with different TF properties to match the signals in real world, via imposing some operators such as translation, modulation, dilation, shearing and rotation on a window function. Based on the parametric basis models, one can define more general multi-parameter linear signal transforms and multi-parameter TFD, under a unifying framework.In chapter four, the method of the parametric adaptive TFR is derived. The related parametric adaptive TFD is real-valued, translating and modulating invariable, energy conservative and free of cross-term interference for multi-component signals. So, it can give a clear picture of the signal’s energy distribution in the TF plane. Because the parameters of the basis automatically match the signal’s local natures during the adaptive decomposition, which expands the analyzed signal onto a complete set of the parametric basis, the window effects are avoided and the TF resolutions are improved with the proposed method. In addition, the parameters of the basis obtained from the adaptivedecomposition contain all of the information about the signal’s TF natures and can be easily used for the further signal processing. The simulation results indicate that the proposed method is effective in analyzing non-stationary signals, such as the chirps, with the performances better than that of the spectrogram, WVD, scalogram, etc. It also extends the existing adaptive TFR methods.In chapter five and six, the set of the frequency-sheared Gaussian bases and that of the time-sheared one are constructed respectively. The frequency-sheared one is obtained through the dilated Gaussian functions modulated with linear chirps in the TF plane, but the time-sheared one through the更多还原