On The Analysis Of Deterministic Time-Varying Signals

Some natural signals, as well as signals encountered in engineering applications, such as communications, radar, and sonar, according to Stone-Weierstrass's theorem, can be modeled as polynomial phase signals (PPS's) whitin the finite observation interval. The analysis of this type of nonstationary signals has received considerable attention in the recent signal processing literature. This dissertation takes multicomponent PPS's (mc-PPS) as signal model, and focuses on its analysis and parameters estimation. The main contributions are as follows:1) The Adaptive Gaussian Kernel (AGK), designed for cross terms reduction of multicomponent LFM signals, is improved, and an efficient method for estimating its parameters is also presented. Then based on the features of ambiguity function of a LFM signal, a new adaptive kernel is proposed. Because the width of both the new kernel and the modified AGK are adaptive to signal length, as is expected, the corresponding adative kernel distributions avoid large loss of autoterms energy while obtaining a certain reduction of the crossterms. Then, the methods for estimating multipath time delay are discussed. Simulation results show that AAD-peak estimation method is better than the methods based on Radon-Wigner transform or based on Radon-AAD transform.2) The shortcomings of the existing PHAF-based techniques in providing reliable detection for mc-PPS are analyzed. Then, a novel parameter estimation method based on HAF is proposed. Firstly, given a set of time delay, it gives rise to a set of estimates of phase coefficients based on HAF. Then it produces the final estimate of phase coefficient by means of voting. The new method improves the probability of detection and estimation accuracy while avoiding the issue of threshold selection. So it overcomes the shortcomings of the existing HAF-based or PHAF-based methods. Moreimportantly, the new method is computationally much less demanding, and can be realized in real time. So it is of great significance in engineering applications.3) Depending on different features of phases of the autoterms and the crossterms of the instantaneous correlation function of the signal under analysis, a novel time frequency distribution (TFD) is presented by using the matched phase transform. The novel TFD not only has ideal frequency concentration, but also realizes reduction of most of crossterms (The number of crossterms in the novel TFD is at best equal to, and generally much less than the number of crossterms in WVD). So, compared with the existing multilinear and bilinear time frequency distribution, it has advantages in exposing inner characteristics of signals.4) A two-dimensional matched-phase transform is proposed. For a mc-PPS, the instantaneous frequency rate (IFR) of each signal component will be local maxima in the transform. However their crossterms seldom emerge as local maxima. Additionally, the IFR of each component is a continuous function of time, but local maxima produced by the crossterms have not this property. So one can realize the estimation of IFR of each signal component. Estimation accuracy of IFR is theoretically analyzed and compared with simulation results. The TIFRD (time-IFR distribution constructed in the time-IFR plane) proposed presents a new idea for exploring the inner characteristics of signals under analysis.5) Wavelet transform enjoys multiresolution property that endears it to the signal processing community. However, the result obtained is not very intuitive. The reason why the continuous wavelet transform of a real signal using a real wavelet (referred to as R-CWT) is not intuitive is unveiled. Then it points out that C-scalogram (scalogram of the continuous wavelet transform using a complex wavelet) is intuitive, and characterizes the local spectrum of signal under analysis, and that C-scalogram is also more appropriate for detection and localization of transient phenomena than R-CWT.6) A few of properties that instantaneous frequency should have are presented.Then it points out that if and only if we define instantaneous frequency of mono- and multi-component signals respectively, can we obtain physically acceptable results, and that defining instantaneous frequency of multi-component signal as weighted average of the individual instantaneous frequency is suitable. Finally it also tries to propose the clear definitions of mono- and multi-component signals.