Signal representation and data coding for multi-dimensional signals have recently received considerable attention due to their importance to several modern technologies. Many useful contributions have been reported that employ wavelets and transform methods. For signal representation, it is always desired that a signal be represented using minimum number of parameters. The transform efficiency and ease of its implementation are to a large extent mutually incompatible. If a stationary process is not periodic, then the coefficients of its Fourier expansion are not uncorrelated. With the exception of periodic signals the expansion of such a process as a superposition of exponentials, particularly in the study of linear systems, needs no elaboration. In this research, stationary and non-periodic signals are represented using approximate trigonometric expansions. These expansions have a user-defined parameter which can be used for making the transformation a signal decomposition tool. It is shown that fast implementation of these expansions is possible using wavelets. These approximate trigonometric expansions are applied to multidimensional signals in a constrained environment where dominant coefficients of the expansion are retained and insignificant ones are set to zero. The signal is then reconstructed using these limited set of coefficients, thus leading to compression. Sample results for representing multidimensional signals are given to illustrate the efficiency of the proposed method. It is verified that for a given number of coefficients, the proposed technique yields higher signal to noise ratio than conventional techniques employing the discrete cosine transform technique.
Doctor of Philosophy (Ph.D.)
College of Engineering
Electrical and Computer Engineering
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Length of Campus-only Access
Doctoral Dissertation (Open Access)
Dissertations, Academic -- Engineering; Engineering -- Dissertations, Academic
Memon, Qurban A., "Approximate trigonometric expansions with applications to signal decomposition and coding" (1996). Retrospective Theses and Dissertations. 3014.