Some Applications of S-Transform and its Modifications in Signal and Image Processing

Abstract

Signal analysis generally involves the usage of time-frequency analysis tools. Fourier transform was able to decompose a periodic signal into multiple sine/cosine signals. This led to the development of many transforms which decomposed the signal using various basis functions. Disadvantages associated with Fourier transform paved the way to introduction of other transforms like short-term Fourier transform. S-transform is a time-frequency analysis tool which has close association with Fourier transform. Unlike the short-term Fourier transform (where the window width was kept constant), the S-transform provided a Gaussian window whose standard deviation was frequency dependent. Thus, the S-transform offered improved frequency resolution at high frequencies and good time resolution at lower frequencies. The focus of this thesis is on the suitable modification as well as different applications of S-transform. We have applied S-transform and its variations on varieties of one and twodimensional signals. In addition to proposing a modification of S-transform (which uses a kernel having compact support), we have: 1. Analysed the changes in the phase of an EEG signal, using the conventional S-transform, to identify the eye-blink artifacts. EEG electrodes are used to record signals on the scalp. Due to propagation delay, a phase difference exists between the signal captured by different electrodes. This phase information is used to determine the eye-blink artifacts in the EEG signal . 2. Performed wind speed prediction, using artificial neural network and a modified form of the S-transform (CBST). Experimental results show that this method lowers the prediction errors. To achieve this, we have used CBST to decompose the wind-speed into sub-series. We have performed “one-step-ahead” prediction on the subseries using artificial neural network with backpropagation algorithm. The sub-series predictions are recombined to obtain the wind-speed prediction. 3. Despeckled SAR images using discrete orthonormal S-transform (DOST).We have made use of shock filter, in addition to two-dimensional DOST to remove the speckles in the image. An edge enhancement algorithm is used to enhance the details at the edges. This ensures that the homogenous regions of the SAR image are smooth while retaining the details in the heterogenous regions.