Sensitivity Analysis of the Equivalent Direct Form of IIR Digital Filters

Abstract

The authors are developing a new paradigm for the synthesis of recursive digital filters with finite word length. Within the framework of this paradigm, the stage of structural synthesis does not distort the results of functional synthesis, on which zeros and poles are calculated. Zeros and poles are calculated considering the finite word length, taking into account their algebraic-numerical nature. This approach reduces the importance of considering the sensitivity of different structures, because the structure is generated considering the calculated zeros and poles. However, analytical expressions for solving the problem of functional synthesis directly in the s-plane are now obtained only for algebraic numbers of the second degree. For higher degrees, an indirect approach based on the transition from the sampled z-plane to the coefficient space is used. Instead of zeros and poles, the quantized coefficients of the so-called equivalent direct form are calculated. To reduce the dimension of the problem of finding the corresponding coefficients, it is necessary to develop effective algorithms. For these purposes, the analysis of the module of the normalized absolute sensitivity of the transfer function is considered in the paper.