Statistical design of cascade finite wordlength FIR digital filters

This paper addresses the problem of efficiently designing cascade-form FIR digital filters, particularly relevant to applications that require very short wordlength coefficients. A technique based on the statistical mean-squared error criterion is presented to sequentially construct cascade-form filters one stage at a time, accounting for the effects of previous stages in the design specifications for each new stage. The statistical method has the unique ability to incorporate filter structure and parameter quantization into the approximation phase of the design process without requiring vast amounts of computer time characteristic of discrete optimization problems. Updating of design specifications is accomplished with FFTs and efficient Toeplitz matrix inversions, while coefficients are quantized by either simple coefficient rounding or, optionally, by very low-order local search methods in the latter design stages.