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This book contains the proceedings of an international conference held in Cairo, Egypt (January 1994). This glorious ancient city was the gathering place for mathematicians and engineers to exchange ideas and to discuss new research trends. Mathematics and engineering discoveries, such as wavelets, multiresolution analysis, and subband coding schemes, caused rapid advancements in signal processing, necessitating an interdisciplinary approach. Contributors to this conference demonstrated that some traditional areas of mathematical analysis - sampling theory, approximation theory, and orthogonal polynomials - have proven extremely useful in solving various signal processing problems.This book features P. L. Butzer on...""Mathematics in Egypt and Its Connections with the Court School of Charlemagne"".With several articles discussing the most recent advances and new trends in mathematical analysis and signal processing, this book emphasizes interactions between mathematics and electrical engineering.