Time-Frequency analysis using Bayesian Regularized Neural Network Model

Abstract

During the last twenty years there has been spectacular growth in the volume of research on studying and processing the signals with time–dependant spectral content. For such signals we need techniques that can show the variation in the frequency of the signal over time. Although some of the methods may not result in a proper distribution, these techniqes are generally known as time–frequency distributions (TFDs) (1, Boashash 2003). The TFDs are two–dimensional (2–D) functions which provide simultaneously, the temporal and spectral information and thus are used to analyze the non–stationary signals. By distributing the signal energy over the time–frequency (TF) plane, the TFDs provide the analyst with information unavailable from the signal’s time or frequency domain representation alone. This includes the number of components present in the signal, the time durations and frequency bands over which these components are defined, the components’ relative amplitudes, phase information, and the instantaneous frequency (IF) laws that components follow in the TF plane. There has been a great surge of activity in the past few years in the TF signal processing domain. The pioneering work in this area is performed by (2, Claasen & Mecklenbrauker 1980), (3, Janse & Kaizer 1983), and (4, Boashash 1978). They provided the initial impetus, demonstrated useful methods for implementation and developed ideas uniquely suited to the situation. Also, they innovatively and efficiently made use of the similarities and differences of signal processing fundamentals with quantum mechanics. Claasen and Mecklenbrauker devised many new ideas, procedures and developed a comprehensive approach for the study of joint TFDs. However Boashash is believed to be the first researcher, who used various TFDs for real world problems. He developed a number of new methods and particularly realized that a distribution may not behave properly in all respects or interpretations, but it could still be used if a particular property such as the IF is well defined. The research presented in (6, Flandrin & Escudie 1980) transcribed directly some of the early quantum mechanical results, particularly the work on the general class of distributions, into signal analysis. The work in (3, Janse & Kaizer 1983) developed innovative theoretical and practical techniques for the use of TFDs and introduced new methodologies remarkable in their scope. Historically the spectrogram has been the most widely used tool for the analysis of time– varying spectra. The spectrogram is expressed mathematically as the magnitude–square of the short–time Fourier transform (STFT) of the signal, given by 24