T IME –F REQUENCY A NALYSIS U SING N EURAL N ETWORKS

Abstract

The thesis is divided in three parts. In the rst part, it explores and discusses the diversity of concepts and motivations for obtaining good resolution and highly concentrated time–frequency distributions (TFDs) for the research community. The description of the methods used for TFDs' objective assessment is provided later in this part. In the second part, a novel multi–processes ANN based framework to obtain highly concentrated TFDs is proposed. The propose method utilizes a localised Bayesian regularised neural network model (BRNNM) to obtain the energy concentration along the instantaneous frequencies (IFs) of individual components in the multicomponent signals without assuming any prior knowledge. The spectrogram and pre–processed Wigner–Ville distribution (WD) of the signals with known IF laws are used as the train- ing set for the BRNNM. These distributions, taken as two–dimensional (2–D) image matrices, are vectorized and clustered according to the elbow criterion. Each cluster contains the pairs of the input and target vectors from the spectrograms and highly concentrated pre–processed WD respectively. For each cluster, the pairs of vectors are used to train the multiple ANNs under the Bayesian framework of David Mackay. The best trained network for each cluster is selected based on network error criterion. In the test phase, the test TFDs of unknown signals, after vectorization and clustering, are processed through these specialized ANNs. After post–processing, the resultingTFDs are found to exhibit improved resolution and concentration along the individual components then the initial blurred estimates. The third part presents the discussion on the experimental results obtained by the proposed technique. Moreover the framework is extended to include the various objec- tive methods of assessment to evaluate the performance of de–blurred TFDs obtained through the proposed technique. The selected methods not only allow quantifying the quality of TFDs instead of relying solely on visual inspection of their plots, but also help in drawing comparison of the proposed technique with the other existing tech- niques found in literature for the purpose. In particular the computation regularities show the effectiveness of the objective criteria in quantifying the TFDs' concentration and resolution information.