S Transform: Time Frequency Analysis & Filtering

Abstract

The S transform, a hybrid of the Short Time Fourier Transform and Wavelet transform, has a time frequency resolution which is far from ideal. This thesis proposes a modified S transform, which offers better time frequency resolution compared to the original S transform. The improvement is achieved through the introduction of a new scaling rule for the Gaussian window used in S transform. The S transform analysis of financial time series revealed the presence of business cycles, which could help forecasting economic booms and recessions. A noisy time series, with both signal and noise varying in frequency and in time, presents special challenges for improving the signal to noise ratio. The modified S-transform time-frequency representation is used to filter a synthetic time series in a two step filtering process. The filter method appears robust within a wide range of background noise levels. The new filtering approach developed was successfully applied for the identification of Post Glacial rebound in Eastern Canada.