Jong-Jy Shyu

A new approach to the design of discrete coefficient FIR digital filters

In this correspondence, the iterative Lagrange multiplier approach is proposed for designing discrete coefficient FIR digital filters. The method associates the conventional Lagrange multiplier approach and a tree search algorithm. For each branch of the tree, the Lagrange multiplier approach is used to optimize the remaining unquantized coefficients of the designed FIR filter in the least-squares sense when one or more of the coefficients takes on discrete values. Design examples, including general low-pass filters and Nyquist filters, are presented to demonstrate the effectiveness of the method. Also, the method can be extended to design discrete coefficient 2-D FIR filters. >

Design of two-dimensional FIR digital filters by McClellan transformation and least-squares contour mapping

Abstract A new method for searching the coefficients of the McClellan transformation is proposed for designing 2-D FIR digital filters in this paper. It can design arbitrary shape transformation contours to map from 1-D prototypes to 2-D FIR filters very effectively. Certain conditions are composed such that the scaling problem of the transformation can be avoided. Also, a new generalized McClellan transformation is presented, so it can be applied to design 2-D filters with complex coefficients. Several examples including fan filters with arbitrary inclination, elliptically symmetric filters with arbitrary orientation, and full-plane complex filters are presented, which demonstrates the effectiveness of this method.

Symmetric properties of 2-D sequences and their applications for designing linear-phase 2-D FIR digital filters

Abstract Besides the design of quadrantally symmetric linear-phase 2-D filters, various linear-phase 2-D filter designs are proposed in this paper. We will start from the discussion of the symmetric properties of 2-D sequences to disclose their applications for designing linear-phase 2-D FIR digital filters. It is shown that there are 16 types of cases to be considered according to the symmetry/antisymmetry of 2-D sequences in both directions and their filter lengths (even or odd). The corresponding types of amplitude responses are tabulated into a complete table if these 2-D sequences are used to realize 2-D FIR filters. Also, the definition of quadrantal-plane, half-plane and full-plane filters are described along with numerical examples designed by the eigenfilter approach.

Design of IIR multiband filters using IIR all-pass filters

Abstract An efficient method is proposed to design IIR all-pass filters for synthesizing general multiband filters which are of low sensitivity. The method is based on minimizing a quadratic measure of the error derived from the phase design of certain filter. The problem of stability is of no concern, and the performance of the obtained filter is comparable to that of the existing methods. Moreover, the solution is obtained directly with no need for iteration.

General form for designing two-dimensional quadrantally symmetric linear-phase FIR digital filters by analytical least-squares method

Abstract The analytical least-squares method has been generalized and extended for designing 16 types of two-dimensional FIR filters with quadrantally symmetric or antisymmetric frequency responses. By means of a closed-form transformation matrix, this fast design method can determine the filters coefficients very effectively without a recourse to an iterative optimization technique or matrix inversion. Design examples are presented to illustrate the simplicity and efficiency of the proposed method.

Lagrange multiplier approach to the design of two-dimensional FIR digital filters for sampling structure conversion

The 1D Lagrange multiplier approach is extended for the design of 2D FIR digital filters with magnitude or derivative constraints. The method is based on minimizing the integrated square error for the frequency response over the passband and stopband while imposing magnitude or derivative constraints. The technique is used to design the interpolation and decimation filters for the sampling structure conversion. Numerical design examples are presented to demonstrate the effectiveness of the approach. >

Complex Lagrange multiplier approach to the design of arbitrary complex coefficient FIR digital filters

Abstract The Lagrange multiplier approach has been widely used to design maximally flat, real coefficients FIR digital filters and differentiators. This paper extends this approach to design arbitrary complex coefficient FIR digital filters with arbitrary frequency response or derivative constraints. The method can easily be extended to design arbitrary two-dimensional complex FIR digital filters with arbitrary frequency response or derivative constraints, too. Several examples are presented to demonstrate the effectiveness of the approach.

Design of two-dimensional FIR digital filters with specified magnitude and group delay responses by analytical least-squares method

In this paper, an analytical least-squares approach to the design of quadrantally symmetric 2-D filters is extended to design complex-coefficient 2-D FIR filters with arbitrary complex frequency responses. Given the design specifications, the filter coefficients are determined directly from a closed-form transformation matrix, such that time-consuming optimization, matrix inversion and iteration procedures can be avoided. Several examples are presented to demonstrate the simplicity and effectiveness of the proposed method.

Design of finite-wordlength IIR digital filters in the time/spatial domain

An effective method is proposed to design discrete coefficient IIR digital filters in the time/spatial domain in this paper. The method associates the Lagrange multiplier approach and a tree search algorithm. For each branch of the tree, the Lagrange multiplier approach is used to optimize the remaining unquantized coefficients of the designed IIR filters when one or more of the coefficients takes on discrete values, such that the actual filter gives the best approximation to the ideal impulse response. For each node of the tree, one more unquantized coefficient is chosen to take on discrete values until all coefficients are quantized. The method is simple and effective, and the stability of the designed filters is easily obtained if the length of the dealed impulse response is long enough. Moreover, the method can be used to design 2-D discrete coefficient IIR digital filters as well as 1-D IIR digital filters.

Design of two-channel perfect-reconstruction linear-phase filter banks for subband image coding by the Lagrange multiplier approach

In this paper, a new approach is proposed for the design of two-dimensional two-channel perfect-reconstruction FIR filter banks employing diamond-shaped linear-phase filters. When one of the analysis filter pair is properly designed, the condition of perfect-reconstruction is formulated into a spatial-domain constraint equation for designing the other. The method is based on minimizing the integrated square error for the frequency response over the passband and stopband while imposing the spatial-domain constraint. One design example is given to demonstrate the perfect-reconstruction for the proposed system. >