Ruijie Zhao

A fast design algorithm for elliptic-error and phase-error constrained LS 2-D FIR filters

Two-dimensional (2-D) nonlinear-phase finite impulse response (FIR) filters have found many applications in signal processing and communication systems. This paper considers the elliptic-error and phase-error constrained least-squares design of 2-D nonlinear-phase FIR filters, and develops a matrix-based algorithm to solve the design problem directly for the filter’s coefficient matrix rather than vectorizing it first as in the conventional methods. The matrix-based algorithm makes the design to consume much less design time than existing algorithms. Design examples and comparisons with existing methods demonstrate the effectiveness and high efficiency of the proposed design method.

A matrix iterative algorithm for the WLS design of variable fractional delay FIR filters

The design of variable fractional delay (VFD) FIR filters in the weighted least squares (WLS) sense is investigated in this paper. Unlike most methods in the literature where separable weighting functions are used, we consider the more general case with an arbitrary nonnegative weighting function. To solve this problem more efficiently, the WLS design of VFD FIR filters is formulated using matrix notation, and its optimality condition is established as a matrix equation. Then, a matrix iterative algorithm is presented to solve this matrix equation, leading to a great saving in computations and memory space compared to existing methods. Finally, an example is provided to show the good performance of the proposed algorithm.

Weighted least squares design of 2-D FIR filters using a matrix-based generalized conjugate gradient method

Abstract One of the important issues in the weighted least-squares (WLS) design of two-dimensional (2-D) finite impulse response (FIR) filters is the computational complexity of the design algorithms. This paper presents a matrix formulation of the design problem and derives a matrix-based generalized conjugate gradient (GCG) algorithm. By defining a linear operator acting on the coefficient matrix of the filter, the optimality condition of the design problem is expressed as a linear operator equation. By proving the boundedness, self-adjointness and positive-definiteness of the linear operator in the Hilbert space of the coefficient matrix, a GCG algorithm designated for the Hilbert matrix space is used to solve the linear operator equation. The convergence of the proposed algorithm in finite steps is established and its high computational efficiency is demonstrated by design examples and comparison with some existing methods.

An Alternating Variable Technique for the Constrained Minimax Design of Frequency-Response-Masking Filters

The frequency-response-masking (FRM) technique is one of the most efficient approaches to the design of narrow transition band FIR filters. The constrained minimax design of linear-phase FRM FIR filters in the frequency domain is considered in this paper. The corresponding optimization problem is a nonconvex one. To deal with the nonconvex design problem and improve the FRM filter performance, we propose an algorithm to alternately optimize different subsets of the design variables by fixing the remaining ones. In this way, the nonconvex optimization problem is converted into a series of linear programming subproblems defined on different frequency bands, which are then solved alternately and iteratively. Moreover, the new algorithm converges to a better FRM filter than those obtained by several competitive methods and is flexible to incorporate linear constraints in the design. Several design examples are provided to demonstrate the advantages of the proposed algorithm.

Almost minimax design of FIR filter using an IRLS algorithm without matrix inversion

An iterative reweighted least squares (IRLS) algorithm is presented in this paper for the minimax design of FIR filters. In the algorithm, the resulted subproblems generated by the weighted least squares (WLS) are solved by using the conjugate gradient (CG) method instead of the time-consuming matrix inversion method. An almost minimax solution for filter design is consequently obtained. This solution is found to be very efficient compared with most existing algorithms. Moreover, the filtering solution is flexible enough for extension towards a broad range of filter designs, including constrained filters. Two design examples are given and the comparison with other existing algorithms shows the excellent performance of the proposed algorithm.

A matrix-based algorithm for the CLS design of centrally symmetric 2-D FIR filters

An efficient algorithm is presented in this paper for the constrained least-squares design of centrally symmetric two-dimensional (2-D) finite impulse response filters. The problem is basically a quadratic programming with positive-definite quadratic cost and linear constraint functions. This paper formulates both the cost and constraint functions in terms of two coefficient matrices of small size and then presents an efficient algorithm to solve the quadratic programming directly for the two coefficient matrices rather than vectorizing it first as in conventional methods. Design example and comparisons demonstrate the effectiveness and high efficiency of the proposed algorithm.

WLS design of centro-symmetric 2-D FIR filters using matrix iterative algorithm

The weighted least squares (WLS) design problem of two-dimensional (2-D) FIR filters with centro-symmetric response is considered in this paper. Its optimality condition is given and expressed as a pair of matrix equations, which involves two matrix variables, i.e., the coefficients of filters to be determined. Then, based on the optimality condition, a matrix iterative algorithm is developed to solve the design problem and its convergence is established using linear operator theory. Because the coefficients of filters are in their natural matrix forms in the algorithm, great savings in computations and memory space required are achieved. Finally, a design example and comparisons with existing methods are provided to illustrate the effectiveness and efficiency of the proposed algorithm.

A matrix-based constrained minimax design of 2-D FIR filters with reduced group delay error

Conventional algorithms for phase-error constrained minimax (PCMM) designs of two-dimensional (2-D) FIR filters vectorize the filters impulse response coefficient. Recently, an efficient algorithm exploiting the matrix nature of the impulse response is proposed for the constrained least-squares (CLS) design of 2-D nonlinear-phase FIR filters. This paper devotes to transform the PCMM design into the same form as the CLS design. A 2-D sigmoid function is introduced to constrain the phase error, resulting in 2-D FIR filters with much smaller maximum group delay error than that obtained under corresponding constant phase-error constraints. Design example and comparisons demonstrate the effectiveness and high efficiency of the proposed method.