C. Charalambous

Bio: C. Charalambous is an academic researcher from University of Waterloo. The author has contributed to research in topics: Adaptive filter & Nonlinear programming. The author has an hindex of 2, co-authored 2 publications receiving 66 citations.

Optimization of recursive digital filters with finite word lengths

Abstract: The application of the "branch and bound" technique for nonlinear discrete optimization, due to Dakin, to the problem of finding the coefficients of a recursive digital filter with prescribed number of bits, to meet arbitrary response specifications of the magnitude characteristic, is investigated. Due to the fact that the objective function is nonlinear and the stability constraints are linear with respect to the parameter, the recent algorithm for nonlinear programming due to Best and Ritter is used. Based on the ideas presented, a general computer program has been developed. Numerical experience with the present approach is also presented.

Minimax optimization of recursive digital filters using recent minimax results

Abstract: The purpose of this paper is to use some recent work by the author on nonlinear minimax optimization to derive an efficient algorithm for the minimax optimization problem. This is followed by the application of the algorithm to the problem of choosing the coefficients of a recursive digital filter to meet arbitrary design specifications on the magnitude or the group delay characteristics.

Discrete coefficient FIR digital filter design based upon an LMS criteria

Abstract: An efficient method optimizing (in the least square response error sense) the remaining unquantized coefficients of a FIR linear phase digital filter when one or more of the filter coefficients takes on discrete values is introduced. By incorporating this optimization method into a tree search algorithm and employing a suitable branching policy, an efficient algorithm for the design of high-order discrete coefficient FIR filters is produced. This approach can also be used to design FIR filters on a minimax basis. The minimax criterion is approximated by adjusting the least squares weighting. Results show that the least square criteria is capable of designing filters of order well beyond other approaches by a factor of three for the same computer time. The discrete coefficient spaces discussed include the evenly distributed finite wordlength space as well as the nonuniformly distributed powers-of-two space.

Design of optimal finite wordlength FIR digital filters using integer programming techniques

Abstract: The application of a general-purpose integer-programming computer program to the design of optimal finite wordlength FIR digital filters is described. Examples of two optimal low-pass FIR finite wordlength filters are given and the results are compared with the results obtained by rounding the infinite wordlength coefficients. An analysis of the approach based on the results of more than 50 design cases is presented and the problem of optimal wordlength choice is discussed.

Optimal design of IIR digital filters with robust stability using conic-quadratic-programming updates

Abstract: In this paper, minimax design of infinite-impulse-response (IIR) filters with prescribed stability margin is formulated as a conic quadratic programming (CQP) problem. CQP is known as a class of well-structured convex programming problems for which efficient interior-point solvers are available. By considering factorized denominators, the proposed formulation incorporates a set of linear constraints that are sufficient and near necessary for the IIR filter to have a prescribed stability margin. A second-order cone condition on the magnitude of each update that ensures the validity of a key linear approximation used in the design is also included in the formulation and eliminates a line-search step. Collectively, these features lead to improved designs relative to several established methods. The paper then moves on to extend the proposed design methodology to quadrantally symmetric two-dimensional (2-D) digital filters. Simulation results for both one-dimensional (1-D) and 2-D cases are presented to illustrate the new design algorithms and demonstrate their performance in comparison with several existing methods.

Design of two-dimensional FIR digital filters by using the singular-value decomposition

Abstract: Singular-value decomposition (SVD) is applied to the design of two-dimensional (2-D) FIR (finite-impulse-response) digital filters. It is shown that three realizations are possible, namely, a direct realization, a modified version of direct realization, and a realization based on the combined application of SV and LU decomposition. Each of the realizations consists of a parallel arrangement of cascaded pairs of 1-D filters; hence extensive parallel processing and pipelining can be applied. The 1-D FIR filters can be designed using standard methods, and linear-phase causal 2-D filters that are suitable for real-time or quasi-real-time applications can also be designed. The three realizations are compared, and it is shown that the realization based on combined SV and LU decomposition leads to the lowest approximation error and involves the smallest number of multiplications. SVD, the McClellan transformation, and 2-D window design methods are used to design a bandpass and a fan filter, and the results are compared. >

Roundoff noise bounds derived from coefficient sensitivities for digital filters

Abstract: The sensitivities of the transfer function of a digital filter with respect to its coefficients are utilized to derive lower bounds on the roundoff noise output in the cases of L_{\infty} and L_{\infty} scaling for fixed-point arithmetic. General bounds are produced which apply to any filter structure if rounding is performed after multiplication and the filter has already been scaled. For the parallel and cascade forms, alternate bounds are derived which apply to rounding after multiplication or summation and which do not require prior scaling. The alternate bounds arethus independent (or nearly so) of pairing, ordering, and transposition. Examples are presented which show that the bounds are reasonably tight.