B.K. Das (India)
Wavelet, Signal Flow Graph, Star Graph, Speed Up, Efficiency
Wavelet Transform has attracted much of the research attention for its ability to analyse rapidly changing transient signals. Any application using the Fourier Transform can be formulated using Wavelet Transform. Like Fourier Analysis, Wavelet Analysis deals with expansion of functions in terms of a set of Basis Functions. But unlike Fourier Transform, Wavelet Transform expands the functions in terms of Wavelets, which are generated by translation and dilation of a fixed function called the Mother Wavelet. The wavelets obtained in this way have got special scaling properties. These have got incredible versatility of applications in pattern recognition, transient signal analysis and image processing. The present work deals with the mathematical formulation of Wavelet Transform Algorithm and design of its signal flow graph. The flow graph has been designed keeping in view its application to the parallel processing domain. The mathematical treatment of the Wavelet Transform Algorithm has been carried out for Filter Analysis. The computational complexity has been estimated in single processor environment. The paper has made an attempt to formalise the Wavelet Transform for Parallel Processing Environment. In this paper, the flow graph of the Wavelet Transform has been analysed and modelled on Star Graph Architecture. The decomposition and ordering has been computed for efficient execution of the algorithm. The necessary theory has been developed for mapping the Task Assignment Graph to the Processing Nodes of Star Graph. The general mathematical formulation has been generated for a varying complexity Wavelet with a variable node Star Graph. Various performance parameters like Speedup, Efficiency and Cost Effectiveness have been computed. The results are given as various closed form formulae.
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