Wavelet transform and its approach to signal processing

Abstract

newline The Fourier transform decomposes a waveform into sinusoids and thus provides a way to represent a waveform. The Fourier transform has ability to measures spatial frequencies in the image. Signal processing has long been dominated by the Fourier transform but it suffers from major limitation that Fourier transform is not suitable for non stationary signal. So, for this types of signal researchers developed wavelet transform which is real valued extension of Fourier transform. Wavelet transform has capability that it decomposes a signal into a set of basis functions (wavelets). Multi-resolution analysis (MRA) is the result of calculation of wavelet transform separately for different segments of the time domain signal at different frequencies. It is constructed in such manner that the product of time resolution and frequency resolution is constant. Hence, at high frequencies it provides good time resolution and poor frequency resolution whereas at low frequencies provides good frequencies resolution and poor time resolution. Wavelet transform provides better signal representations with less computation time, due to this it is used as an important analysing tool in signal and image processing. The wavelet transform has three main advantages as follows: - newline1)Good time frequency localization newline2) Possibility of time shifting newline3)Flexibility newlineConvolution is a reverse, shift, multiply and integrate technique. By using this technique, Wavelets can be combined with portions of a known signal to extract information from the unknown signal.This thesis provides detailed review of wavelet transform in signal processing and find out the advantages of wavelet transform in various areas. newlineWavelet selection is most important part in signal processing. We have discussed a technique of best wavelet selection for image processing using Set Partitioning in Hierarchical Trees(SPIHT) method. We have compressed signals(one dimensional and two dimensional) by using different aspects of wavelet transform. A method through which