Numerical performance and optimal synthesis of block digital filters

The speed restriction inherent to the recursive nature of Infinite Impulse Response (IIR) filter algorithms could be overcome by modifying the algorithms by look-ahead computations, which resulted in several pipelined and block structures. Recent developments in scaled VLSI technologies provide a way to achieve high performance by exploiting the concurrencies in these structures. By modifying algorithms, we do not change the input-output characteristics, but we do change the numerical performance under finite precision implementations. In this dissertation, numerical performance of canonic and non-canonic block structures is explored first, and then optimal block filter synthesis is considered based on the joint consideration with implementation complexity. Only fixed point arithmetic is considered.;Besides the primary advantage of high throughput in the block structures, side effects of reduced roundoff noise and improved limit cycle behavior were also noticed and were studied for state space structures. The equally important coefficient quantization effects, though, have barely been investigated so far. Contrary to the general belief that Coefficient Quantization Noise (CQN) in block structures would decrease much like the roundoff noise, some narrowband Direct Form (DF)-derived block filters behave much worse than their underlying Single Input Single Output (SISO) filter under coefficient quantization. Variation of coefficient values in the feedback matrix A of state space block filters are studied, and analytical expressions as a function of block size are obtained for DF-derived, Normal Form (NF), and Minimum Roundoff Noise Form (MRNF). This reveals that DF-derived block filters may have large coefficient values, which deteriorates block filter performance under quantization. NF and MRNF structures behave much better than DF-derived block filters, but their average output CQN increases almost linearly with block size. An analytical expression for the average output noise power in canonic and non-canonic state space block structure is derived by statistical analysis method. Based on the CQN analysis for canonic structures, a new row quantization method is proposed to improve the filter performance for a large block size. Numerical examples are shown which demonstrates the results of the analyses. For a very high throughput IIR filter, canonic block structures have the practical limit that their complexity per output point linearly increases in block size. Recently proposed non-canonic DF and state space structures achieve the constant complexity, but their numerical performance has not been explored or has been misunderstood. Roundoff noise of these non-canonic structures is analyzed. It is shown that their internal pipelined structures generate more roundoff noise than canonic structures, and thus nullify the gain obtained from the blocking algorithm. Finally, results from the numerical performance analysis are used to optimize canonic and non-canonic state-space structures for minimum total noise.