Efficient and accurate multiparameter analysis of linear digital filters using a multivariable feedback representation

The fundamental property of bilinearity is exploited, to develop a unifying concept, for the analysis of the effects of large-scale changes in the coefficients of a digital filter. This makes use of a multivariable feedback representation of the filter. The transfer matrix of this multivariable system has the inherent property that, it can be directly evaluated for all possible coefficient vectors, from its value for a given coefficient vector. Based on this concept, computationally efficient and numerically reliable algorithms are derived for performing two tasks: (i) to evaluate accurately the complex frequency transfer function for arbitrary values of the network coefficients, and (ii) to compute feasible values of the coefficients for which the magnitude and phase of the frequency response satisfy prescribed bounds. These can be used in existing computer-aided filter design and optimization tools to improve their quality and efficiency as well as to develop new optimization techniques. An application of these algorithms to the discrete coefficient optimization problem for a PCM low-pass filter is illustrated. It is also shown that the proposed techniques are .superior to existing methods of symbolic analysis, repeated network analyses, and Taylor approximations.