DEVELOPMENT OF SIGNAL PROCESSING TECHNIQUES FOR ENHANCEMENT OF ENERGY CONCENTRATION IN TIME-FREQUENCY REPRESENTATION OF S-TRANSFORM

Abstract

The motivation behind the time-frequency analysis (TFA) is rooted in classical Fourier analysis. In contrast to Fourier transform (FT), time-frequency transforms analyze signals in both time and frequency domain simultaneously and provide time-frequency representation (TFR). The conventional methods for TFA can be categorized into two groups. The first group includes linear time-frequency transforms which attempt to make FT time dependent. The second group includes quadratic TFA techniques. Short time Fourier transform (STFT), wavelet transform (WT) and S-transform (ST) are some well-known transforms listed under the first category whereas Wigner-Ville distribution and Cohen class of distribution are listed under the later. ST is an advancement of the STFT and CWT. It has direct relationship with FT, and retains the absolutely referenced phase property of STFT. It provides frequency invariant amplitude response along with multi-resolution analysis. These properties of ST have led to its wide usage in various fields such as geophysics, power system engineering, biomedical engineering, biometric, etc. The conventional ST uses a Gaussian window whose width varies as inversely proportional to the frequency. The long taper of the Gaussian window and the scaling criterion provide very large window width for lower frequencies, and very short window width for higher frequencies, and hence leads to unnecessary deterioration in time and frequency resolution at lower and higher frequencies, respectively. In the first objective of this dissertation, two variants of ST, namely time-limited ST (TST) and band-limited ST (BST) are proposed. TST and BST are based on optimally concentrated discrete time-limited and band-limited windows of finite length. The proposed TST has ability to precisely localize the signals in time domain while maximizing the energy concentration in frequency domain. The proposed BST has ability to precisely localize the signals in given band while maximizing the energy concentration in time domain. The second objective focuses on maximally achievable trade-off between time and frequency domain energy concentrations for discrete time finite length sequences. The problem of simultaneous maximization of time and frequency domain energy concentrations is formulated as the maximization of weighted linear combination of desired concentration measures in time and frequency domains. A novel optimal window with finite support (OWFS) is proposed based on discrete time continuous frequency scenario. The proposed OWFS is extended to design an adaptive TFA method for reducing the instantaneous frequency (IF) estimation error in case of multi-component signals in noisy environment. For discrete time discrete frequency scenario, a novel optimally concentrated discrete window (OCDW) is proposed. OCDW is designed by solving a constraint optimization problem of maximization of the product of time and frequency domain energy concentrations in given time and frequency intervals. Further, it is extended to design an OCDW based ST (OST) for multi-resolution analysis. A new scaling criterion is also proposed for OST which prevents unnecessary deterioration in frequency resolution at higher frequencies, and time resolution at lower frequencies. In the third objective, an asymmetrical modified Kaiser window (AMKW) based ST is proposed for sharp detection of event’s onset. The multi-resolution analysis and frequency dependent asymmetry are obtained by modifying the parameter of first order Bessel function of Kaiser window. The proposed scheme leads to sharp detection of events in front direction while having minimum degradation in backward direction. This scheme also results in minimum degradation in frequency resolution as compared to other existing TFA techniques for event detection. In the fourth objective of this dissertation, the reassignment method (RM) and synchrosqueezing transform (SST) are deployed on the TFR of OST, and further investigated for detecting multiple power quality disturbances. It is found that the OST combined with RM and SST provides better visualization as compared to other counterparts of ST. Further, a product-ST is proposed for better visualization by multiplying the TFRs of TST and BST. The concepts of RM and SST are incorporated in the product-ST, and the resulting TFR is found to provide better visualization and frequency detection accuracy as compared to its OST counterpart. In this dissertation, different techniques are proposed to enhance the energy concentration in the ST. The performances of these techniques are demonstrated using synthetic and real world examples from power system engineering, biomedical engineering and geoscience.