Two-dimensional FIR Digital Filters Research Articles

Design of FIR Digital Filter with Two Dimensions Using Particle Swarm Optimization

This paper proposes a novel method which is based on particle swarm optimization (PSO) algorithm for the two-dimensional FIR digital filter design. In the PSO algorithm, it simply uses two adjusting mechanisms including particle’s velocity and position updating to achieve the optimization. In addition, numerical representations for each candidate solution are completely real numbers. The PSO algorithm is utilized to design the two-dimensional FIR digital filter with linear-phase characteristic so that its frequency response can approximately meet the desired specification. Finally, we will illustrate the design performance of the proposed method with two experiments. Simulation results reveal that the proposed scheme has a good design performance on the two-dimensional FIR digital filter.

Design of Two-Dimensional Zero-Phase FIR Digital Filter by McClellan Transformation and Interval Global Optimization

The McClellan transformation is widely used to design the 2-D FIR filters. It is an essential task to determine the transform coefficients so that the square errors are minimized. This issue can be viewed as a nonlinear optimization problem with constraint conditions. This brief proposed the interval analysis (IA) to solve this nonlinear optimization problem. There are two distinguishing features of the proposed method when compared with conventional methods, such as quadratic programming, eigenfilter approach or Lagrange multiplier method, etc. First, the transform parameters are obtained by minimizing the integral of the squared errors along the desired contour, instead of discrete sampling. Second, the IA guarantees that the constraint conditions could be always satisfied, thus ensuring the reliability of the optimization. A 2-D fan filter and a diamond-shaped filter are designed, which demonstrate the feasibility of the presented method; images are processed to verify the effectiveness of the designed 2-D fan filter.

Design of Variable Two-Dimensional FIR Digital Filters by McClellan Transformation

In this paper, the technique of McClellan transformation is applied to design variable 2-D FIR digital filters. Compared with the conventional transformation, the 2-D transformation subfilter and the 1-D prototype filter are designed such that their frequency characteristics are adjustable. Moreover, they are tunable by the same variable parameter, so the variable characteristics of 1-D prototype filters are coincident with those of 2-D subfilters. Several examples, including variable fan filters, variable circularly symmetric filters, and variable elliptically symmetric filters with arbitrary orientation, are presented to demonstrate the effectiveness and the flexibility of the presented method.

Design of two-dimensional FIR digital filters by McClellan transform and quadratic programming

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.

Minimax design of 2-D linear-phase FIR filters with continuous and powers-of-two coefficients

This paper deals with the minimax design problem of two-dimensional (2-D) linear-phase FIR digital filters with continuous and powers-of-two (POT) coefficients. First, the minimax continuous-coefficient design problem is formulated as a linear programming problem with inequality constraints. We present a method based on a variant of Karmarkar's algorithm to solve the resulting design problem. During each iteration, the main computing cost required for finding the filter coefficients is to solve a set of linear equations. Based on the obtained continuous coefficients, an efficient method is presented for designing a minimax 2-D FIR filter with POT coefficients in the spatial domain. Simulation results are provided for illustration and comparison.

A Numerical Calculation of the Contact Area and Pressure of Real Surfaces in Sliding Wear

A numerical simulation technique based on elastic asperity deformation is presented to analyze real surface contact and pressure distributions in sliding wear. The calculations have been applied to experimentally produced surfaces whose topography has been determined using an atomic force microscope. A variational approach is applied to minimize the stored energy in the contact, which determines contact area without additional iteration. Two-dimensional FIR digital filter techniques are used and an FFT procedure is used to improve the efficiency of the filter implementation. The model is used to obtain the pressure distribution, real contact area, and the distribution of real contact area under sliding conditions either parallel or perpendicular to the grinding lay. The calculated results of real contact stress at different stages of wear are given. The calculated and experimental results suggest that the stress distribution of real contact follows an exponential function. The contact stress distribution index β governs the stress distribution form and reflects the performance of the frictional components in sliding wear. The proportion of plastic contact deformation ψ is also related to β; therefore, reflecting the frictional property in sliding wear. The experimental and calculated results show that the smaller frictional coefficient and more homogeneous distribution of stress occur when the sliding direction is parallel rather than perpendicular to the grinding-lay direction.

A method of designing two-dimensional complex coefficient FIR digital filters for broadband digital beamforming antennas by a combination of spectral transformation and a window method

In digital beamforming (DBF) antennas, received propagation signals are first converted down into baseband inphase and quadrature signals, then DBF signal processing is done. We propose a method for designing two-dimensional (2D) digital filters utilized in such DBF networks to handle the signals with wide fractional bandwidths up to 40%. First, we consider the relationship between DBF and its 2D normalized frequency description. Here, we show that 2D complex coefficient digital filters with nonsymmetric characteristics are necessary to form broadband beams. Next, based on this consideration, we describe the proposed method, which combines spectral transformation and a window method. Note that approximation is achieved such that the beam pattern, including its sidelobe characteristics, from the resulting broadband DBF network is virtually frequency-independent. As a result, it has become possible to design DBF networks suitable for a multibeamforming network for use in the broadband beamspace adaptive array antenna proposed in Sekiguchi, Miura, and Karasawa [9]. © 1998 Scripta Technica. Electron Comm Jpn Pt 3, 81(3): 22–34, 1998

Design of two-dimensional FIR digital filters by a two-dimensional WLS technique

For two-dimensional (2-D) FIR filter design, the conventional weighted least squares (WLS) technique rearranges the filter parameters of 2-D form into their corresponding one-dimensional (1-D) form, thus resulting in expensive computation. This paper presents a new computationally efficient WLS technique for the design of 2-D FIR filters. We introduce an updating desired frequency response which implicitly includes the weighting function such that the sum of weighted square errors to be minimized can be represented in a 2-D matrix form. This makes it possible to keep all filter parameters in their natural 2-D form, thereby reducing the computational complexity from O(N/sup G/) to O(N/sup 3/). It is confirmed through design examples that the new technique is computationally very efficient and leads to nearly optimal approximations. This technique is suitable for the design of 2-D real zero-phase FIR filters with quadrantal symmetric or antisymmetric frequency response and can also be applied to the design of 1-D FIR filters.

Order reduction of 2-D FIR filters with applications

The author develops two algorithms for the order reduction of two-dimensional (2-D) FIR digital filters, which lead to two indirect design methods. Specifically, it is shown how an optimal L/sub 2/ design can be derived as a matrix approximation problem in the Frohenius norm, and how a suboptimal L/sub /spl infin// design can he obtained by solving a matrix approximation problem in the 2-norm using the Davis-Kahan-Weinberger theorem on norm-preserving dilations. A case study is included to demonstrate the usefulness of the proposed methods.

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.

Shape parameter in the two-dimensional low-pass FIR digital filters design by transformation

The concept of shape parameter is introduced and applied to the design of two-dimensional filters. This concept together with the simple points fitting technique, the two-dimensional FIR digital filter whose passband contour approximates to the desired shape is designed via McClellan transformation.

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

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.

Two-dimensional general fan-type FIR digital filter design

Conventional transform methods can only design ordinary and quadrant fan-type filters with 90° pass-angle. In this paper, three efficient approaches are proposed for designing general arbitrary pass-angle fan-type filters. They include the analytic closed form, the rotated, and the frequency sampling design methods. Each approach has its features and is very suitable for directional filtering and image processing applications. Konventionelle Transformationsmethoden ermöglichen nur den Entwurf von gewöhnlichen und Quadrant Fan-Typ Filtern mit 90° Durchlaßphase. In dieser Arbeit werden drei effiziente Lösungen für den Entwurf von allgemeinen Fan-Typ-Filtern mit beliebigen Durchlaßwinkeln vorgeschlagen. Sie umfassen die analytische geschlossene Form, die Rotations- und die Frequency Sampling Entwurfsmethode. Jeder Entwurf hat seine Vorteile und ist sehr gut zur richtungsabhängigen Filterung und für Bildverarbeitungsanwendungen geeignet. Les méthodes de transformation conventionnelle ne permettent que la description des filtres quadrants et ordinaire d'angle de passage à 90°. Dans cet article, trois approaches efficaces sont proposées pour définir des filtres généraux à angle de passage arbitraire. Ces approaches utilisent les méthodes basées sur lar forme analytique close, la rotation, et la description d'échantillon fréquentielle. Chaque approche possède ses propres caractéristiques et est très bien adaptée au filtrage directionnel et aux applications de traitement d'images.

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

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.

McClellan transform based design techniques for two-dimensional linear-phase FIR filters

This paper considers the design problem of two-dimensional (2-D) linear-phase FIR digital filters through the use of the McClellan transform method. We present two methods for determining the coefficients of the McClellan transform when designing 2-D linear-phase FIR digital filters with continuous and powers-of-two coefficients, respectively. Based on the proposed methods, the contour approximation for 1-D (one-dimensional) to 2-D digital filter transformation and finding the band-edge frequencies of the corresponding 1-D FIR digital filter can be achieved simultaneously. This results in that the required complexity of the designed 2-D digital filter satisfying the design specifications can be minimized. Moreover, the proposed methods allow us to employ the McClellan transform with order more than one for enhancing the capability of the original McClellan transform. Considering the determination of the McClellan transform coefficients and the band-edge frequencies for the design, we formulate the design problem as a linear programming optimization problem. Then, an efficient design procedure is presented to avoid the use of time consuming simplex algorithms. For the powers-of-two coefficient design, a discrete design procedure is presented to avoid the use of time-consuming mixed integer linear programming algorithms. Computer simulations for showing the effectiveness of the proposed design techniques are also presented.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

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. >

A unified approach to the design of quadrantally symmetric linear-phase two-dimensional FIR digital filters by eigenfilter approach

Instead of the design procedures restricted to same special filter types, a unified approach is proposed to design sixteen possible cases for quadrantally symmetric linear-phase 2-D FIR filters. The original forms of the sixteen possible cases are formulated properly such that the eigenfilter method can design them with the same approach. The conversions between the filter coefficients are tabulated in a complete table. Also two numerical examples are shown to demonstrate the usefulness and flexibility of the present approach.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Three different criteria for the design of two-dimensional zero phase FIR digital filters

An error criterion for the design of FIR filters is proposed. Filters with relatively many free filter coefficients are designed using the Chebyshev, the weighted-least-squares (WLS), and a new partitioned minimax error criterion, and the performance of the filters is compared. A general and fast technique for the WLS design is also presented.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Fast block implementation of two-dimensional FIR digital filters by systolic arrays

A systolic block implementation is described of two-dimensional (2D) FIR and quarter-plane digital filters. Initially, a general 2D block realization model is presented, which does not assume any restricted relation with respect to the block lengths. A high degree of concurrency is achieved by exploiting the pipelining of the array processors in conjunction with the inherent parallelism of the block realization structures. The resulting systolic implementation is characterized by a high degree of modularity, regularity, repetitiveness and local communications and permits very high sampling rates. The increase of the block lengths of the implementation is analogous to the attained throughput rate, with respect to the cost of supporting hardware. The proposed systolic implementation is suitable for real-time image processing applications.

Systolic implementation of the complex Chebyshev structure

The complex Chebyshev structure is the implementation technique for linear-phase two-dimensional complex FIR digital filters, designed by the McClellan transform. In this paper a systolic realization of this structure is proposed, which has all the advantages of systolic designs. The analysis of the implementation shows its hardware and computational efficiency.