Block Digital Filter Implementation Techniques and Transform Domain Processing

This dissertation is concerned with block implementation techniques of digital filters and their application to transform domain processing. Block implementation of digital filters is useful for high throughput filtering due to inherent parallelism. Furthermore, more accurate computation is possible through proper allocation of computation resources in the block transform domain when input data are correlated. The performance improvement is closely related to block transform coding gain of the input signal. By extending scalar linear constant coefficient difference equation (LCCDE) to block LCCDE, we have shown various block filter structure implementation techniques, and investigated their finite precision coefficient quantization effects. Particularly, block lattice implementation of IIR and FIR filters is of interest due to their good numerical properties. In order to derive the block lattice structures, we have used block lossless bounded real (BLBR) functions; in the block IIR lattice implementation, a BLBR function derived from the denominator of the block transfer function is used, which parallels the Gray-Markel lattice for the scalar case, and in the block FIR lattice implementation, the block version of power complementary pair polynomials is derived and utilized. It has been demonstrated that these block lattice filter structures have better finite coefficient quantization characteristics than those of any other block filter structures. The block filter structures are directly applied to transform domain filtering without any modification of the block filter structures. The matrix coefficients only need to be changed to the transform domain coefficients. It has been shown that nonuniform coefficient quantization in the transform domain filtering improves the accuracy of filtering for finite given computational resources (for example, number of transistors in the VLSI implementation).