Methods For Minimax Design Of IIR Digital Filters With Reduced Group-delay Error

With the rapid development of computers and microelectronics, theories and algorithms ofdigital signal processing as well as the implementation means for digital signal processingalgorithms have been widely used in diverse application areas. Digital filtering is an importantfunction of digital signal processing, and how to design digital filters satisfying the requirements offiltering is then a basic problem in practical applications.This thesis mainly considers the minimax design of infinite impulse response (IIR) digitalfilters with reduced group-delay error. In order to obtain IIR digital filters with reduced group-delayerror, the minimax design methods in this thesis do not impose constraints on the group delay errordirectly. Instead, a phase error constraint is imposed on the filter resulting in a phase errorconstrained minimax design problem. A sequential constrained least-squares method is used toconvert the phase error constrained minimax design problem into a sequence of constrainedleast-squares (CLS) sub-problems, and then combined with a Levy-Sanathanan-Koerner (L-SK)strategy and a Taylor series expansion to deal with the non-convexities of the cost functions andfrequency-response error constraints and the nonlinearities of the phase error constraints of thesub-problems to convert each sub-problem into a sequence of quadratic programming (QP)problems with circular and linear constraints.After a briefly introduction to some basic concepts of IIR digital filters and their designs andreviewing the advantages and disadvantages of the existing methods for the minimax design of IIRdigital filters, this thesis presents two improved algorithms for the minimax design of IIR digitalfilters with reduced group delay error. The main works of this thesis include the following threeaspects:1. A review on a sequential constrained least-squares (SCLS) method for the minimax designof IIR digital filters and a phase-error upper-bound function method for the reduction ofgroup-delay error. The SCLS method converts the minimax design of an IIR digital filter into asequence of CLS sub-problems to increase the possibility of obtaining better filters. In thephase-error upper-bound function method, the group-delay error is controlled by the appropriatelychosen, say, a sigmoid phase-error upper-bound function, which is especially effective to reduce themaximum group-delay error near the passband edges.2. Propose an SCLS method for the minimax design of IIR digital filters with phase errorsconstrained by a sigmoid upper-bound function to effectively reduce the maximum group-delayerrors of the filters. Specifically, a phase-error constraint is introduced to the minimax design problem, and then use an SCLS method, the L-SK strategy and a first-order Taylor series expansionto convert the non-convex phaseerror constrained minimax design problem into a series of QPproblems with circular and linear constraints. Design examples demonstrate that the proposedmethod has obtained much smaller group-delay error than existing methods under appropriatelychosen sigmoid phase-error upper-bound functions.3. Propose an iterative procedure for automatic updating of the phase-error upper-boundfunction to reduce the maximum group-delay error of the designed minimax IIR digital filters. Theabove mentioned sigmoid phase-error upper-bound function method can effectively reduce themaximum group-delay error, but the parameters of the sigmoid function should be chosen manuallyby the user. In this thesis, the iterative procedure for reducing the group-delay error of finiteimpulse responses (FIR) filters in their design is applied to the minimax design of IIR digital filters,which extends the application of the phase-error upper-bound function method for reducing thegroup-delay error. Very good results have been obtained by the proposed method.