Cheng-Han Chan

An iterative method for the design of variable fractional-order FIR differintegrators

In the paper, a new method is proposed for the design of variable fractional-order (VFO) FIR differintegrators. Comparing with the existing methods, the elements of relevant matrices can be determined just by the given specification, which makes the method easier. An iterative technique is also incorporated to adjust the weighting function, such that the peak absolute error of variable frequency response can be reduced drastically. Several design examples, including a VFO differintegrator, two VFO differentiators and a VFO integrator, are presented to demonstrate the effectiveness and flexibility of the proposed method.

Minimax phase error design of allpass variable fractional-delay digital filters by iterative weighted least-squares method

In this paper, an iterative weighted least-squares (LS) method is proposed for the design of allpass variable fractional-delay (VFD) digital filters, so that the maximum absolute phase error can be minimized. Meanwhile, it is found that the range of variable parameter will affect overall performance of the designed filter, which will be analyzed and discussed in this paper through several examples designed by least-squares and iterative weighted least-squares methods. And the stability of the designed filters and the effectiveness of the proposed iterative method are also revealed by these presented examples.

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.

Iterative design of variable fractional-order IIR differintegrators

In this paper, the variable fractional-order (VFO) differintegrator is designed based on IIR-typed Farrow structure. The stability of the designed VFO IIR differintegrator is achieved by incorporating a constrained function into the objective error function. But the minimization of the original objective error function is a highly nonlinear problem, so an iterative quadratic method is proposed to overcome it. Comparing with the design based on FIR-typed Farrow structure, several designed examples, including a VFO differintegrator, a pure VFO differentiator and a pure VFO integrator, are presented to demonstrate the effectiveness of the proposed method.

A new structure for the design of wideband variable fractional-order FIR differentiators

In this paper, a new structure is proposed for the design of wideband variable fractional-order (VFO) FIR differentiators. Part of subfilters in the conventional structure are replaced by the cascade of a prefilter and the modified subfilters, such that the performance of the designed system can be improved as well as the computational cost can be reduced. 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 Method for Least-Squares and Minimax Group-Delay Error Design of Allpass Variable Fractional-Delay Digital Filters

A double-loop iterative method is proposed to design allpass variable fractional-delay (VFD) digital filters basing on the minimization of root-mean-squared group-delay error. In the inner loop, an iterative quadratic optimization is proposed to replace the original nonlinear optimization for the minimization of root-mean-squared group-delay error, while an iterative weighting-updated technique is applied in the outer loop to further reduce the maximum group-delay error. Several examples will be presented to demonstrate the effectiveness and good convergence of the proposed method.

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.

Design of complex coefficient variable fractional-delay allpass digital filters by eigenfilter approach

In this paper, the technique of eigenfilter approach is applied to the design of complex coefficient variable fractional-delay (VFD) allpass digital filters. The objective error function is formulated into a quadratic form aTQa where a is a coefficient vector and Q is a real, symmetric and positive-definite matrix. By Rayleigh principle, the eigenvector corresponding to the smallest eigenvalue of Q minimizes the error function, and is the desired solution. Several examples are presented to demonstrate the effectiveness of the proposed method.