Parametric Adaptive Time-Frequency Representation And Its Applications For Non-Stationary Signals

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...