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Presenter: Abdussalam Omar
Supervisor:

Date: Wed, February 26, 2025
Time: 11:00:00 - 00:00:00
Place: EOW 430

ABSTRACT

Abstract

This seminar presents design algorithms for nearly linear-phase one-dimensional (1-D) and two-dimensional (2-D) infinite impulse response (IIR) digital filters. Optimization techniques as well as model order reduction (MOR) filter design methods are considered in this study.

For 1-D, finite impulse response (FIR) filters can achieve perfectly linear phase which makes them important in applications such as the field of audio signal processing where a flat delay characteristic may be desired. However, in most applications a perfectly linear phase response is not required and filters that have nearly linear phase response are quite acceptable. In such cases, IIR filters are more attractive than FIR filters. The design of IIR filters is more challenging than that of FIR filters because it results in a highly nonlinear objective function that requires sophisticated optimization methods. The 1-D optimization method proposed here solves the problem of approximating specified magnitude and linear-phase responses simultaneously.

Since IIR filters can be designed to have nearly linear phase response in the passband, their passband group delay is usually considerably smaller than the delay of linear phase FIR filters with equivalent magnitude responses. Meeting a required minimum stopband attenuation or a minimum deviation from the desired magnitude and phase responses in the passbands are common design constraints that can be handled by

the proposed optimization method for 1-D IIR filter. Also, an important constraint in the design of IIR filters is the prescription of a maximum pole radius, which allows to guarantee the stability margin and low coefficient selectivity for the obtained filter for finite-precision implementations. These design specifications are consistent with the constraints which often arise in practical filter design problems. In this work, an optimization method for solving this constrained 1-D IIR design problem is

presented.

The above optimization method used for designing 1-D IIR filters is extended to 2-D separable-denominator IIR digital filters with nearly linear phase in the passband. During the development of the proposed design techniques for 2-D digital filters, a special emphasis has been placed on their computational efficiency and a method for the design of 2-D IIR digital filters based on a balanced realization (BR) model order

reduction technique is proposed. In this method, the initial design is a linear phase 2-D FIR filter realized in a 2-D state space model, which leads to a stable 2-D separable-denominator IIR filter with nearly linear phase in the passband. The model reduction method is based on structured controllability Ps and structured observability Qs gramians. The use of these gramians ensures that the resulting 2-D IIR filter is a 2-D stable filter. Furthermore, the obtained nearly linear-phase 2-D IIR filter is more economical and computationally more efficient than the original 2-D FIR filter. Numerical examples using MATLAB show that the proposed method provides a good compromise between the filter selectivity and computational complexity when

compared to existing techniques, making the results of this work directly applicable to many practical applications.