Design of FIR two- dimensional digital filters by successive projections (original) (raw)

Minimax design of two-dimensional FIR digital filters by using an interior-point algorithm

1993 IEEE International Symposium on Circuits and Systems

This paper considers the design of two dimensional (2-D) linear phase FIR digital filters optimal in the minimax sense. A design method based on an &ne-scaling variant of Karmarkar's linear programming algorithm is presented. In the design process, we first formulate the design problem into a linear programming form. To avoid the huge computation load and storage space required by using a standard simplex algorithm, we present a Karmarkar's algorithm based method to solve the design problem. In each iteration of the proposed method, we only need to calculate a weighted least square (WLS) solution. Nearly optimal solutions can be obtained after several iterations. Design examples and comparison are presented to show the effectiveness of the proposed method.

Finite precision design of optimal linear phase 2-D FIR digital filters

1989

An algorithm is proposed for the design of optimal twodimensional finite impulse response (ZD FIR) digital filters with finite wordlength and linear phase. This algorithm associates linear programming and a branch and bound technique for which two strategies are compared. A large number of examples are presented which show the efficiency of the method for the design of ZD FIR filters with different specifications and sizes, up to 9 X 9 in the case of a circularly symmetric contour and up to 13 x 13 for diamond-shaped filters. Two different types of quantization are also considered.

Design of multidimensional FIR digital filters using the symmetrical decomposition technique

IEEE Transactions on Signal Processing, 1994

A technique for the design of multidimensional FIR filters based on symmetrical decomposition is described. Along with this technique, a procedure to decompose a frequency response into symmetrical components is also discussed. It is proved that the design based on symmetrical decomposition technique when the cost function is chosen as the weighted square error yields the same optimal solution as the classical method that does not use the decomposition technique. The 12 norm design is discussed as a special case of weighted 12 norm design. It is also shown that the decomposition technique is advantageous when the weight function satisfies some symmetry properties. Examples are also provided to illustrate the application and the effectiveness of applying the decomposition in the design of 2-D and 3-D FIR filters.

An L2 based method for the design of one dimensional FIR digital filters

1996

FIR filters obtained with the classical L2 method have performance that is very sensitive to the form of the ideal response selected for the transition region. In this paper we propose a means for selecting the unknown part of a compIex ideal response optimally. By selecting a proper L2 criterion and using variational techniques we succeed in minimizing the criterion with respect to the ideal response and thus obtain its corresponding optimum form. The complete solution to the problem can be obtained by solving a simple system of linear equations suggesting a reduced complexity for the proposed method. Using the optimum form of the ideal response we also propose a new suboptimal method for the design of weighted FIR filters. Design examples are presented to illustrate the performance of the proposed method.

DESIGN OF TWO-DIMENSIONAL FIR FILTERS WITH ARBITRARY MAGNITUDE AND PHASE RESPONSES

2003

ABSTRACT The design problem of two-dimensional finite impulse response filters with arbitrary magnitude and phase frequency responses is considered. The optimal generally complex matrix of the impulse response with a rectangular region of support is derived by minimizing the mean squared error between the desired and actual frequency responses.

Design of finite wordlength 2-D linear phase FIR filters using singular value decomposition

1994

In this paper we present an efficient technique for the design of linear phase 2-D FIR filters using SVD method. We show that by appropriately choosing the order of the 1-D subfilters in the parallel legs of the 2-D filter structure, a sizable reduction in the number of multiplier coefficients is achieved. A local search optimization method is then utilized to obtain finite wordlength coefficients.

An Based Method for the Design of 1-D Zero Phase FIR Digital Filters

1997

Finite impulse response (FIR) filters obtained with the classical L 2 method have performance that is very sensitive to the form of the ideal response selected for the transition region. It is known that design requirements do not constraint in any way the ideal response inside this region. Most existing techniques utilize this flexibility. By selecting various classes of functions to describe the undefined part of the ideal response they develop methods that improve the performance of the L2 based filters. In this paper we propose a means for selecting the unknown part of the ideal response optimally. Specifically by using a well-known property of the Fourier approximation theory we introduce a suitable quality measure. The proposed measure is a functional of the ideal response and depends on its actual form inside the transition region. Using variational techniques we succeed in minimizing the introduced criterion with respect to the ideal response and thus obtain its corresponding optimum form. The complete solution to the problem can be obtained by solving a simple system of linear equations suggesting a reduced complexity for the proposed method. An extensive number of design examples show the definite superiority of our method over most existing non min-max design techniques, while the method compares very favorably with min-max optimum methods. Finally we prove that the approximation error function of our filter has the right number of alternating extrema, required by the L 1 criterion, in the passband and stopband. This results in a significant convergence speed up, if our optimum solution is used as an initialization scheme, of the Remez exchange algorithm.

Fast algorithm for least squares 2D linear-phase FIR filter design

International Conference on Acoustics, Speech, and Signal Processing, 2001

In this paper, we develop a new method for weighted least squares 2D linear-phase FIR filter design. It poses the problem of filter design as the problem of projecting the desired frequency response onto the subspace spanned by an appropriate orthonormal basis. We show how to compute the orthonormal basis efficiently in the cases of quadrantallysymmetric filter design and centro-symmetric filter design. The design examples show that the proposed method is faster than a conventional weighted least squares filter design method. Also, the amount of storage required to compute the filter coefficients is greatly reduced.