Design of digital filters with severely quantized coefficients

Two simple techniques are described for the design of recursive digital filters in the cascade configuration, which minimize the coefficient word-length. These are intended for cases where a statistical treatment is not valid because of the coarseness of quantization. The derivation of the discrete set of pole positions for the basic second-order section in the form of a z-plane pole grid is reviewed. This concept is fundamental to both techniques. They have been implemented by means of interactive operation on a small computer, but the more sophisticated technique, which is a form of one-at-a-time optimization, could be organized as a batchprocessed algorithm.