Analysis and design of optimum block matrix filters with prescribed system constraints

Date of Award




Degree Name

Doctor of Philosophy (Ph.D.)

First Committee Member

Claude S. Lindquist - Committee Chair


Single-input single-output (SISO) finite impulse response (FIR) digital block matrix filters implement convolution for time-domain processing of real signals with samples implemented in vector form. Often, these block matrix filters are subject to the following system constraints resulting from limitations in system capability: (1) Matrix Structure constraint--the a priori requirements on the interrelationships between the elements of the block filter matrix. (2) Speed-Memory constraint--the a priori system memory or computational speed requirements that can be met by setting certain element values of the block filter matrix to zero to exploit sparseness. (3) Relative Performance Bias constraint--the a priori bound on allowable performance deterioration of the block matrix filter subject to the matrix structure and speed-memory constraints. A constrained block matrix filter is termed realizable if it meets all the prescribed system constraints and optimum if it is realizable and minimizes the relative performance bias constraint.This dissertation introduces the R scEALIZABILITY T scHEOREM and the R scEALIZABILITY A scLGORITHM, encompassing the main theory for the realizability and synthesis of optimum constrained block matrix digital filters based on the supremum norm of the relative performance bias and the well-proven methods of linear programming. It is shown that the proposed convergent iterative R scEALIZABILITY A scLGORITHM determines and obtains the optimum block matrix filter subject to the prescribed system constraints. In addition, the R scEALIZABILITY T scHEOREM is extended to a variety of performance bias considerations. Simulations are submitted and discussed in support of the theory.


Engineering, Electronics and Electrical

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