Yun-Da Huang

Design of Variable Two-Dimensional FIR Digital Filters by McClellan Transformation

In this paper, the technique of McClellan transformation is applied to design variable 2-D FIR digital filters. Compared with the conventional transformation, the 2-D transformation subfilter and the 1-D prototype filter are designed such that their frequency characteristics are adjustable. Moreover, they are tunable by the same variable parameter, so the variable characteristics of 1-D prototype filters are coincident with those of 2-D subfilters. Several examples, including variable fan filters, variable circularly symmetric filters, and variable elliptically symmetric filters with arbitrary orientation, are presented to demonstrate the effectiveness and the flexibility of the presented method.

Minimax Design of Variable Fractional-Delay FIR Digital Filters by Iterative Weighted Least-Squares Approach

In this letter, an iterative weighted least-squares (LS) approach is proposed for the design of variable fractional-delay (VFD) finite impulse response (FIR) digital filters in minimax sense. For deriving the elements of relevant matrices, there is no need for numerical integration or closed-form formulation and they obey given specifications. Comparing with the existing method, the proposed method does not lead to a misleading problem, and the performance of convergence is also better. Especially, it is found that the used LS weighting function is only dependent on the frequency, not on the tunable parameter, which makes it easier for the minimax design of VFD FIR digital filters.

A New Criterion for the Design of Variable Fractional-Delay FIR Digital Filters

Conventionally, variable fractional-delay finite-impulse-response digital filters are generally designed by minimizing the root-mean-square error of variable frequency response. In this paper, a new criterion concerning the minimization of the root-mean-square error of variable group-delay response is proposed. However, minimization is a highly nonlinear problem, so an iterative method is proposed in this paper to overcome it. To further reduce the maximum absolute group-delay error in the least squares design, an iterative weighting-updated technique is also proposed, which constitutes the outer loop of the overall iterative process while the iteration stated earlier makes up the inner loop. Several design examples will be presented to demonstrate the effectiveness of the proposed method.

Two-Dimensional Farrow Structure and the Design of Variable Fractional-Delay 2-D FIR Digital Filters

In this paper, a 2-D Farrow structure is proposed and used to implement variable fractional-delay (VFD) 2-D FIR digital filters. Compared with the existing literature, the desired response of a VFD 2-D digital filter is analyzed in detail, and it is found that there are four types of 2-D symmetric/antisymmetric sequences that need to be used for the design of VFD 2-D FIR digital filters. Moreover, due to the orthogonality among the approach functions, the four types of 2-D sequences can be determined independently, such that the dimension for each computation can be reduced drastically. For simplicity, only the designs of even-even- and odd-odd-order VFD 2-D filters are presented in this paper, and the other cases can be achieved in the same manner. To reveal the coefficient characteristics, the symmetric/antisymmetric properties of filter coefficients and the relationships between coefficients are all tabulated. Also, design examples such as nonseparable circularly symmetric low-pass VFD filters are presented to demonstrate the effectiveness of the proposed method.

An iterative approach for minimax design of multidimensional quadrature mirror filters

In this paper, a nest of iterative techniques is proposed for the minimax design of quadrature mirror filter (QMF) banks. The method can be generalized such that multidimensional QMF banks can be designed by the proposed algorithm. For a given weighting function, an iterative method is used to minimize the objective error function in the inner iterations. To further reduce the peak error of overall magnitude response, an iterative weighting-updated technique is adopted in the outer iterations. Comparing with the existing works concern the design of perfect-reconstruction QMF banks, only one of the filters is needed to be designed under the cost of magnitude distortion, but the system complexity can be reduced drastically. Several examples, including design of 2-D and 3-D QMF banks, will be presented to demonstrate the effectiveness of the proposed method.

Least-Squares Design of Variable Maximally Linear FIR Differentiators

In this correspondence, the design of variable maximally linear (VML) FIR differentiators by least-squares method is proposed. The VML differentiator is designed such that its maximally flat frequency is adjustable. The used transfer function is formulated in a variable frame, and the Farrow structure can be applied for the implementation of VML FIR differentiators. For comparison, the non-variable optimal design of maximally linear FIR differentiators is also proposed. The experiments show that the variable design indeed possesses the flat characteristics as the independent optimal design.

3-D FIR Cone-Shaped Filter Design by a Nest of McClellan Transformations and Its Variable Design

In this paper, the technique of a nest of McClellan transformations is proposed for the design of 3-D FIR cone-shaped filters. First, a transformation subfilter for fan-type mapping is found. Then the cosine term of a frequency variable of the above transformation subfilter is replaced by an embedded transformation subfilter which possesses circular contours. The technique stated above is also extended to design 3-D FIR variable cone-shaped filters such that the inclination of the cone-shaped filters can be adjusted online. Moreover, an efficient structure is proposed for the implementation of the designed filters. Several examples will be presented to demonstrate the effectiveness of the proposed method.

Improved Methods for the Design of Variable Fractional-Delay IIR Digital Filters

In this paper, both methods of magnitude-oriented design and delay-oriented design for variable fractional-delay (VFD) infinite impulse response (IIR) filters are proposed. In the former, the objective error function is formed by including root-mean-square error function of variable frequency response and the stability error constrained function, such that the designed filters are stable. As for the second part of this paper, it is desirable to minimize the root-mean-square error of variable group-delay response while the magnitude response and stability can be preserved. Hence, except those stated above, the root-mean-square error function of variable group-delay response is further included in the objective error function. However, these induced problems are highly nonlinear, so iterative methods are proposed to overcome them. Several design examples are presented to demonstrate the features of these design methods, including concerns among VFD finite impulse response (FIR) filters, VFD allpass filters and VFD IIR filters as well as the designed results of both methods.

A new structure and design method for variable fractional-delay 2-D FIR digital filters

In this paper, a new structure and design method are proposed for variable fractional-delay (VFD) 2-D FIR digital filters. Basing on the Taylor series expansion of the desired frequency response, a prefilter–subfilter cascaded structure can be derived. For the 1-D differentiating prefilters and the 2-D quadrantally symmetric subfilters, they can be designed simply by the least-squares method. Design examples show that the required number of independent coefficients of the proposed system is much less than that of the existing structure while the performance of the designed VFD 2-D filters is still better under the cost of larger delays.

An Improved method for the design of variable fractional-delay IIR digital filters

In this paper, an improved method is proposed for the design of variable fractional-delay (VFD) IIR digital filters. The objective error function is constituted directly by the root-mean-squared error function of variable frequency response and the stability constrained function, so that the root-mean-squared error of variable frequency response can be minimized while the designed VFD IIR filter is stable. Several design examples will be presented to demonstrate the effectiveness of the proposed method.