New Concepts in Digital Signal Processing

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Adams Recent research has revealed that the minimax and least- squares optimality criteria are inappropriate for many digital signal processing applications. Minimax and least-squares optimization problems are subsets of a more general (and much more important) class of problems which are referred to as peak- constrained least-squares (PCLS) optimization problems. PCLS solutions are needed for many digital signal processing applications, but PCLS research is still in its infancy. The objective of this research is to develop new concepts in digital signal processing that are based on PCLS optimization. Techniques from the theory of mathematical programming are being used as the basis for this research. Three categories of design algorithms are being developed: 1. new multiple exchange algorithms; 2. extensions of conventional quadratic programming algorithms; and 3. extensions of Lawson's algorithm.