Linear Phase Recursive Digital Filters Research Articles

Improved Design Method for Nearly Linear-Phase IIR Filters Using Constrained Optimization

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.

Design Methodology for Nearly Linear-Phase Recursive Digital Filters by Constrained Optimization

A methodology for the design of recursive digital filters having nearly linear phase response is proposed. The underlying design method is of the direct type whereby the filter is designed as a single unit. The design problem is formulated as a cascade of filter sections where each section is represented by a biquadratic transfer function either in the conventional polynomial form or in the polar form. The design problem is then solved using a constrained Newton's method whereby constraints are used to assure the stability of the filter, to control the step size in order to achieve fast convergence, and to eliminate a real-axis pole-migration problem that often interferes with the design process. Several design examples demonstrate that when compared with filters designed using existing state-of-the-art methods, the proposed methodology yields filters having reduced order and/or improved performance.

A systematic technique for designing approximately linear phase recursive digital filters

A systematic method is introduced for designing approximately linear phase low-pass recursive digital filters. The filter structures under consideration are the conventional cascade form realization and the parallel connection of two allpass filters (lattice wave digital filters). Given the amplitude specifications, the filter parameters as well as the slope of the linear phase response are optimized in such a way that the maximum phase deviation from this linear phase is minimized in the passband. The filters are designed such that either the maximum amplitude value in the transition hand is less than or equal to the passband maximum or the amplitude response is monotonically decreasing in this band. The design scheme consists of two basic steps. The first step involves finding, in a simpler manner, a good suboptimum filter. In the second step, this filter is then used as an initial filter for further optimization that is carried out by the second algorithm of Dutta and Vidyasagar. Several examples are included illustrating the efficiency of the proposed design scheme. They also show the superiority of the resulting recursive filters over their linear phase finite-impulse response equivalents, especially in narrow-band cases.

Design of variable 2-D linear phase recursive digital filters with guaranteed stability

This paper proposes a new technique for designing variable two-dimensional (2-D) linear phase recursive digital filters, the stability of which is always guaranteed. The method finds each variable filter coefficient as a multidimensional (M-D) polynomial of a few parameters. The parameters specify different frequency responses, thus they are called the spectral parameters. In applying the resulting variable filters, substituting different spectral parameter values into the M-D polynomials will obtain different filter coefficients and, thus, different frequency responses. To guarantee the stability, we first perform denominator coefficient transformations such that they satisfy the stability conditions. Then, both denominator and numerator coefficients are determined as M-D polynomials.

The design of 2-D approximately linear phase filters using a direct approach

A novel approach to the design of approximately linear phase recursive digital filters was recently described. The technique exploited a property of allpass transfer functions which allowed the creation of a set of linear simultaneous equations in the filter coefficients which could then be solved in the least-squares sense. This paper extends the design method to 2-D and multi-D filters. These filters find application in many areas including image processing, image coding, filter banks and seismic data processing. Several problems arise which are not present in the 1-D design and the paper looks at ways to overcome them. In addition, there is discussion on the stability issue. Several examples including circularly, elliptically and diamond symmetric lowpass filters and a fan filter are presented. Comparison is made between the proposed technique and those of Gu and Swamy (1994) and Toyoshima et al. (1990).

On approximated linear-phase recursive digital filters

The recursive forms to approximate the causal linear-phase IIR digital filters are studied. Actual causal linear-phase IIR digital filters have been proposed (Clements and Pease 1989); however, the lack of rational expressions of the considered systems render them unrealizable. As a consequence, applications for this kind of filter do not exist. In this paper, based on the Pade approximation and the eigenfilter design, the approximations of linear-phase recursive representations of the filters are proposed for practical applications. Experimental results show good approximation on phase linearity. Finally, the magnitude response is designed to meet the specifications in the passband of the low-pass filter.

An efficient algorithm for the design of circular symmetric linear phase recursive digital filters with separable denominator transfer function

A method for generating 1-variable Hurwitz Polynomial using properties of Positive Definite Matrices is presented. Also, a two-step approach for the design of separable denominator zero-phase numerator 2-D filters with constant group-delay specifications is given. An illustrative example shows the effectiveness of the proposed technique.

Economic linear-phase recursive digital filters

This letter describes the design by z plane methods of an attractive class of recursive digital filters. The computational economy achieved by recursive operation is further enhanced by the use of integer weighting coefficients, making the filters particularly suitable for online processing of sampled-data signals.