A Combination of Linear and Quadratic Time- Frequency Techniques for Time-Varying Signals

Abstract

Majority of the time-frequency representations (TFRs) make some kind of compromise between auto-component’s resolution and cross-terms suppression during the analysis of time varying signals. Linear TFRs offer no cross-terms but have low resolution of auto-components. Quadratic TFRs offer better resolutions of auto- components but have cross-terms. The proposed research focuses on TFRs that can combine the advantages of both linear and quadratic TFRs. In the first part of this research, a modified form of Gabor Wigner Transform (GWT) has been proposed by using adaptive thresholding in Gabor Transform (GT) and Wigner Distribution (WD). The proposed GWT combines the advantages of both GT and WD and provides a powerful analysis tool for analyzing multi-component signals. This technique is however not very efficient for multi-component signals having large abrupt amplitude variation in its auto-components. In multi-component signal analysis where GWT fails to extract auto- components, the combination of signal processing techniques such as fractional Fourier transform (FRFT) and image processing techniques such as image thresholding and segmentation have proven their potential to extract auto- components. In the second part of this research, an algorithm is proposed for an effective representation in time-frequency domain called Modified Fractional GWT that combines the strengths of GWT, image segmentation and FRFT. This representation maintains the resolution of auto-components besides recognizing FRFT, a powerful tool for signal analysis. Performance analysis of proposed fractional GWT reveals that it provides solution of cross-terms of WD and worst resolution faced by linear TFRs. In the third part of this work, a novel algorithm for effective representation of multi-component signals in time-frequency domain is proposed. The scheme not only suppresses the cross terms but also ensures that all the auto-components even very weak ones are properly shown in time-frequency domain. The scheme also results in much localized time frequency representation (TFR). The algorithm uses the strengths of GWT and linear time-varying (LTV) filtering in time domain to design a filter in time-frequency domain that suppresses cross terms and enhances auto components through an iterative approach. Performance analysis of proposed algorithm reveals viithat it provides concentrated and high resolution auto-components which are desirable for a TFR. The TFRs are used to separate and extract signal’s auto-components which are buried in noise and are used to estimate the instantaneous frequency of a multi- component signal in low SNR scenarios. The modified GWT can be used for detection, identification and classification of power quality disturbances (such as voltage sag, voltage swell, transients and harmonics). The LTV based GWT and modified fractional GWT can be extended for IF estimation of auto-components of EEG Seizure.