Local and global aspects of product quantization

The design of digital filters involves the consideration of various factors to achieve a satisfactory result. The complexity of implementation, sensitivity of the transfer function with respect to coefficient quantization (c.q.), and product quantization (p.q.) has an impact on the final design. The noise model is often used to model the resulting nonlinear system with p.q. The application of the noise model in a cascade of lower order sections is discussed. The effect of correlation of samples between stages is considered. It is found that the effect of the stages in the cascade form on each other implies that the total noise power is no longer given by the sum of each individual stage. A modification to the noise model is consequently presented which can accommodate these intra-stage dependencies. An application of the intra-stage noise model shows that the noise power of the direct form structure and the cascade form structure, with the same transfer functions, is the same. A specific choice of the direct form coefficients results in a uniform pole distribution. It is concluded on the basis of the intra-stage noise model that the ordering of cascade sections is unimportant. The noise model can, however, still not explain phenomena with low amplitude input signals, such as limit cycles. It is known that different filter structures exhibit different behaviour under these conditions. The advantage of a variable wordlength structure is demonstrated