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A fast matrix iterative technique for the WLS design of 2-D quadrantally symmetic FIR filters 总被引:2,自引:1,他引:1
High computational complexity is a major problem encountered in the optimal design of two-dimensional (2-D) finite impulse response (FIR) filters. In this paper, we present an iterative matrix solution with very low complexity to the weighted least square (WLS) design of 2-D quadrantally symmetric FIR filters with two-valued weighting functions. Firstly, a necessary and sufficient condition for the WLS design of 2-D quadrantally symmetric filters with general nonnegative weighting functions is obtained. Then, based on this optimality condition, a novel iterative algorithm is derived for the WLS design problem with a two-valued weighting function. Because the filter parameters are arranged in their natural 2-D form and the transition band is not sampled, the computation amount of the proposed algorithm is reduced significantly, especially for high-order filters. The exponential convergence of the algorithm is established, and its computational complexity is estimated. Design examples demonstrating the convergence rate and solution accuracy of the algorithm, as well as the relation between the iteration number of the algorithm and the size and transition-band width of the filter are given. 相似文献
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In this paper we present a new and numerically efficient technique for designing 2-D linear phase octagonally symmetric digital filters using Schur decomposition method (SDM) and the diagonal symmetry of the 2-D impulse response specifications. This technique is based on two steps. First, the 2-D impulse response matrix is decomposed into a parallel realization of k sections, each comprising two cascaded linear phase SISO 1-D FIR digital filters. It is shown that using the symmetry property of the 2-D impulse response matrix and the fact that the left and right eigenspaces obtained by SDM are transpose of each other, the design problem of two 1-D digital filters is reduced to the design problem of only one 1-D digital filter in each section. 相似文献
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A quadratic programming (QP) approach for determining the coefficients of the McClellan transform is presented for the design of 2-D FIR digital filters. Three features of the proposed method are as follows. First, the transform parameters are determined by minimising the integration of the squared errors along the desired contour. Second, a set of linear constraints are incorporated into the QP formulation such that the conventional scaling problem of the transform can be avoided. Third, the optimal cutoff frequencies of a 1-D prototype filter are obtained directly from the QP solution. Several design examples, including fan filters, elliptic filters, diamond filters and bandpass filters, are illustrated to demonstrate the effectiveness of the QP method 相似文献
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A Hopfield-type neural network for the design of 2-D FIR filters is proposed. The network is contrived to have an energy function that coincides with the sum-squared error of the approximation problem at hand and by ensuring that the energy is a monotonic decreasing function of time, the approximation problem can be solved. Two solutions are obtained. In the first the 2-D FIR filter is designed on the basis of a specified amplitude response and in the second a filter that has specified maximum passband and stopband errors is designed. The network has been simulated with HSPICE and design examples are included to show that this is an efficient way of solving the approximation problem for 2-D FIR filters. The neural network has high potential for implementation in analog VLSI and can, as a consequence, be used in real-time applications. 相似文献
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A new derivation is presented for the least squares solution of the design problem of two-dimensional (2-D) finite impulse response (FIR) filters by minimizing the Frobenius norm of the difference between the matrices of the ideal and actual frequency responses sampled at the points of a frequency grid. The mathematical approach is based on the singular value decomposition (SVD) of two complex transformation matrices. Interestingly, the designed filter is proved to be zero-phase if the ideal filter is so without assuming any kind of symmetry 相似文献
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In this investigation, subfilters are cascaded in the design of a 2-D narrow transition band FIR digital filter with double
transformations, a transformation from wide transition band subfilter into 1-D narrow transition band filter and a McClellan
transformation from 1-D filter into 2-D filter. The traditional method for designing a 2-D FIR digital filter with a narrow
transition band yields very high orders. The difficulty of the design and implementation will increase with orders exponentially.
Numerous identical low-order subfilters are cascaded together to simplify the design of a high-order 2-D filter compared to
traditional design method. A powerful genetic algorithm (GA) is presented to determine the best coefficients of the McClellan
transformation. It can be used to design any contours of arbitrary shape for mapping 1-D to 2-D FIR filters very effectively.
A generalized McClellan transformation is presented, and can be used to design 2-D complex FIR filters. Various numerical
design examples are presented to demonstrate the usefulness and effectiveness of the presented approach.
相似文献
Shian-Tang Tzeng (Corresponding author)Email: |
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It is shown that the singular-value decomposition (SVD) of the sampled amplitude response of a two-dimensional (2-D) digital filter possesses a special structure: every singular vector is either mirror-image symmetric or antisymmetric with respect to its midpoint. Consequently, the SVD can be applied along with 1-D finite impulse response (FIR) techniques for the design of linear-phase 2-D filters with arbitrary prescribed amplitude responses which are symmetrical with respect to the origin of the (ωΨω2) plane. The balanced approximation method is applied to linear-phase 2-D FIR filters of the type that may be obtained by using the SVD method. The method leads to economical and computationally efficient filters, usually infinite impulse response filters, which have prescribed amplitude responses and whose phase responses are approximately linear 相似文献
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Xiaoying Hong Xiaoping Lai Ruijie Zhao 《Multidimensional Systems and Signal Processing》2016,27(2):477-491
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. 相似文献
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本文研究了二维线性相位实系数FIR数字滤波器的最小二乘设计问题,导出了滤波器系数的闭式解。运用给出的计算公式可方便地计算滤波器的系数,而不必对矩阵进行数值求逆运算也不需要复杂的优化过程.设计实例表明本文给出的方法程序简单、计算时间极短. 相似文献
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Eigenfilter approach for the design of variable fractional delay FIR and all-pass filters 总被引:1,自引:0,他引:1
An eigenfilter approach is presented for designing 1-D and 2-D variable fractional delay FIR and all-pass filters. First, the coefficients of filters are expressed as a polynomial of the fractional delay parameter. Then, the optimal polynomial coefficients are obtained from the elements of the eigenvector corresponding to the minimum eigenvalue of a real, symmetric and positive definite matrix. Finally, several design examples of 1-D and 2-D variable fractional delay FIR and all-pass filters are used to illustrate the effectiveness of the eigenfilter approach. 相似文献
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二维零相位FIR数字滤波器设计的闭式最小二乘解 总被引:1,自引:0,他引:1
本文二维零相位FIR数字滤波器的解析最小二乘设计技术。通过建立频域误差差函数的矩阵形式,并运用与设计问题有关的矩阵的一些性质,得到了滤波器系数的闭式解,使得由给定的频响指标可直接计算滤波器系数,而不必对矩阵进行数值示逆,也不需要基于迭代运算的优化过程。文中给出了滤波器实例,其结果证实了该设计方法的简便性与有效性。 相似文献
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Two-Dimensional Farrow Structure and the Design of Variable Fractional-Delay 2-D FIR Digital Filters
《IEEE transactions on circuits and systems. I, Regular papers》2009,56(2):395-404
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This paper solves the weighted least mean square (WLMS) design of two-dimensional (2-D) finite impulse response (FIR) filters with general half plane symmetric frequency responses and nonnegative weighting functions. The optimal solution is characterized by a pair of coupled integral equations, and the existence and uniqueness of the WLMS solution for 2-D FIR filter design are established. Two efficient numerical algorithms using a 2-D fast Fourier transform (FFT) are proposed to solve the WLMS solution. One is based on the contraction mapping and fix point theorem characterizing the coupled integral equation; the other uses conjugate gradient techniques, which guarantees finite convergence. The associated computational complexity is analyzed and compared with existing algorithms. Examples are used to illustrate the effectiveness of the proposed design algorithms. The selection of weighting functions to improve the minimax performance of the filter is also discussed 相似文献
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《IEEE transactions on circuits and systems. I, Regular papers》2009,56(3):574-582
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This paper presents a method for designing finite impulse response (FIR) filters for samples of a 2-D signal, e.g., an image, and its gradient. The filters, which are called blended filters, are decomposable in three filters, each separable in 1-D filters on subsets of the data set. Optimality in the minimum mean square error sense (MMSE) of blended filtering is shown for signals with separable autocorrelation function. Relations between correlation functions for signals and their gradients are derived. Blended filters may be composed from FIR Wiener filters using these relations. Simple blended filters are developed and applied to the problem of gray value image reconstruction from bilevel (scanned) clustered-dot halftone images, which is an application useful in the graphic arts. Reconstruction results are given, showing that reconstruction with higher resolution than the halftone grid is achievable with blended filters. 相似文献
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Efficient 2-D based algorithms for WLS designs of 2-D FIR filters with arbitrary weighting functions
The impulse response coefficients of a two-dimensional (2-D) finite impulse response (FIR) filter naturally constitute a matrix. It has been shown by several researchers that, two-dimension (2-D) based algorithms that retain the natural matrix form of the 2-D filter’s coefficients are computationally much more efficient than the conventional one-dimension (1-D) based algorithms that rearrange the coefficient matrix into a vector. In this paper, two 2-D based algorithms are presented for the weighted least squares (WLS) design of quadrantally symmetric 2-D FIR filters with arbitrary weighting functions. Both algorithms are based on matrix iterative techniques with guaranteed convergence, and they solve the WLS design problems accurately and efficiently. The convergence rate, solution accuracy and design time of these proposed algorithms are demonstrated and compared with existing algorithms through two design examples. 相似文献