This work contains the proceedings of an international conference held in Cairo (January 1994), where mathematicians and engineers gathered to exchange ideas and to discuss new research trends. Mathematical and engineering discoveries, such as wavelets, multiresolution analysis, and subband coding schemes, caused rapid advancements in signal analysis and 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. 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.