In this paper, a new optimization method for the design of nearly linear-phase two-dimensional infinite impulse (2D IIR) digital filters with a separable denominator is proposed. A design framework for 2D IIR digital filters is formulated as a nonlinear constrained optimization problem where the group delay deviation in the passband is minimized under prescribed soft magnitude constraints and hard stability requirements. To achieve this goal, sub-level sets of the group delay deviations are utilized to generate a sequence of filters, from which the one with the best performance is selected. The quality of the obtained filter is evaluated using three quality factors, namely, the passband magnitude quality factor Qh and the group delay deviation quality factor Qτ, while the third one is a new quality factor Qs that assesses the performance in the stopband relative to the minimum filter gain in the passband. The proposed framework is implemented using the interior-point (IP) method in a MATLAB environment, and the experimental results show that filters designed using the proposed method have good magnitude response and low group delay deviation. The performance of the resulting filters is compared with the results of other methods.
In this paper, the design of nearly linear-phase recursive digital filters using a constrained optimization method is investigated. The method is based on existing constrained optimization techniques for nearly linear-phase IIR digital filters, and it is expected to be useful in applications where both magnitude and phase response specifications are required to be satisfied. Starting from an initial filter, the proposed method minimizes the group delay deviation under a set of linear constraints in terms of the magnitude response and filter stability. Improved sampling functions are introduced to the optimization problem, which are used to control the sampling points that are used for approximating the group delay and the rest of the constraints in various frequency bands. By using the proposed sampling functions we get an improved IIR filter response.
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