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Most of the signals in practice are time-domain signals in their raw format. Time amplitude representation is not always the best representation of the signal for most signal processing related applications. Fourier analysis has a serious drawback that in transforming to the frequency domain, time information is lost. This drawback isn't very important if the signal is a stationary signal. However, most interesting signals are non-stationary (ECG, EMG, EEG etc.) and thus Fourier analysis is not suited to detecting transitory characteristics. The traditional Fourier transform only provides the spectral information of a signal and thus it is not suitable for the analysis of non-stationary signals and hence a more suitable technique has been applied for the study. The main goal of the book is to develop the compression algorithms based upon the various one transform techniques available and from there to develop a new two dimensional Transform technique which will give better results as compared to the previous one dimensional signal compression technique without loss of any signal information.