Mathematics
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Browsing Mathematics by Author "Dr. "Mohammad Othman" Omran"
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- ItemOn Singular Value Decomposition of Rectangular Matrices(2009) Sheren Najeh Issa Odeh; Dr. "Mohammad Othman" OmranThe singular value decomposition of matrices stands as one of the most important concepts in mathematics, because of its variety of applications in mathematics, statistics, biology and many other areas of science. In this thesis, we present the singular value decomposition and its relation to the spectral decomposition . We also investigate the singular value decomposition of a matrix together with some of its applications. Some of these applications include the Moore-Penrose psuedoinverse, the effective rank of matrices and image compression.
- ItemOn Z-transform and Its Applications(2015) Asma Belal Fadel; Dr. "Mohammad Othman" OmranIn this thesis we study Z-transform (the two-sided Z-transform), the one-sided Z-transform and the two-dimensional Z-transform with their properties, their inverses and some examples on them. We also present the relation between Z-transform and Laplace transform and between Z-transform and Fourier transform. Some applications of Z-transform including solutions of some kinds of linear difference equations, analysis of linear shift-invariant systems, implementation of FIR and IIR filters and design of IIR filters from analog filters are discussed. Chirp Z-transform algorithm is also presented with two applications: enhancement in poles and high resolution and narrow band frequency analysis