Implementation of 2-D denominator-separable digital filters using first-order all-pass sections

It is established that denominator-separable transfer functions which characterize an important subclass of 2-D filters can be expressed as a linear combination of first-order (1-D or 2-D separable) all-pass transfer functions with real or complex coefficients. This type of expansion is referred to as all-pass expansion of the corresponding transfer function. Based on this all-pass expansion, we derive some efficient structures for the realization of 2-D denominator-separable filters using all-pass sections.On leave from S.V. University College of Engineering. Tirupati-517502, India.     

On the use of continued fraction filter structures for the design of 2-D digital filters

In this paper a method for the realization of 2-D recursive digital filters of second order by means of continued fraction filter structures is presented. The proposed method is based on the interconnection of basic filter structures of first order and gives also the set of all 2-D transfer functions that are realizable by these structures. The general rule for interconnecting these basic structures is described. It is proved that, on the set of second order fraction filter structures, some classes of structures and ordering relations can be defined, so that the set of all the classes form a partially ordered set (poset). Those structures which least constrain the coefficients of the transfer function are defined maximum elements of the poset. It is shown that among all possible continued fraction structures of second order only six are suitable for realization of two dimensional filters. Some results following from the use of spectral transformations are discussed.     

Design of separable-denominator 2-D digital filters using the reduced-dimensional decomposition model

A separable-denominator 2-D digital filter (SD-2DDF) can be decomposed into the cascade form of a pair of 1-D digital filters (1DDFs) with different delay elements. Based on this reduced-dimensional decomposition, in this paper, we propose a new technique for designing SD-2DDFs in the spatial domain. The technique determines the coefficient matrices of 1DDFs by nonlinear optimization techniques first, and then a SD-2DDF can be easily synthesized. In addition, since the existent 1-D linear system realization techniques can be used to choose a good starting point for the optimization, extremely accurate design results can be easily achieved.     

Design of 3-D Noncausal Filters with Small Roundoff Noise and No Overflow Oscillations

The contribution of this paper consists of two individual parts. First, an invertible mapping technique is presented for 3-D digital system design, and it is applied to approximate 3-D noncausal filters in the spatial domain. Secondly, an algorithm is proposed for obtaining a structure for 3-D IIR filters with small roundoff noise and no overflow oscillations. The design of noncausal filters can be carried out by three steps: 1), a given noncausal impulse response is transformed into the first octant using the proposed 3-D invertible mapping technique; 2), the transformed impulse response in the first octant is approximated by balanced model reduction of 3-D separable denominator systems;3), the resultant 3-D IIR filter is transformed back to the original coordinates.     

A novel nonnegative decomposition method and its application to 2-D digital filter design

In designing two-dimensional (2-D) digital filters in the frequency domain, an efficient technique is to first decompose the given 2-D frequency domain design specifications into one-dimensional (1-D) ones, and then approximate the resulting 1-D magnitude specifications using the well-developed 1-D filter design techniques. Finally, by interconnecting the designed 1-D filters one can obtain a 2-D digital filter. However, since the magnitude responses of digital filters must be nonnegative, it is required that the decomposition of 2-D magnitude specifications result in nonnegative 1-D magnitude specifications. We call such a decomposition the nonnegative decomposition. This paper proposes a nonnegative decomposition method for decomposing the given 2-D magnitude specifications into 1-D ones, and then transforms the problem of designing a 2-D digital filter into that of designing 1-D filters. Consequently, the original problem of designing a 2-D filter is significantly simplified.     

Design of 2-D FIR Filters by a Feedback Neural Network

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.     

On 2-D partial fraction decomposition

In this paper we introduce a mapping technique of two-dimensional (2-D) auto correlation sequences to one dimensional (1-D) auto correlation sequences and obtain certain results useful in the test for existence of the decomposition of the form

$\text{A(Z}{}_1\text{,Z}{}_2\text{)A(Z}{}_1{}^{\mathrm{?1}}\text{)}\text{B(Z}{}_1\text{,Z}{}_2\text{)B(Z}{}_1{}^{\mathrm{?1}}\text{)}\text{=}\text{P(Z}{}_1\text{,Z}{}_2\text{)}\text{B(Z}{}_1\text{,Z}{}_2\text{)}\text{+}\text{P(Z}{}_1{}^{\mathrm{?1}}\text{)}\text{B(Z}{}_1{}^{\mathrm{?1}}\text{)}$

for a stable 2-D transfer function of a recursive digital filter defined by

$\text{H(Z}{}_1\text{,Z}{}_2\text{)=}\text{A(Z}{}_1\text{,Z}{}_2\text{)}\text{B(Z}{}_1\text{,Z}{}_2\text{)}$

These results are simple alternative to that reported in the literature [7] earlier.     

A technique for the design of 2-D recursive digital filters with guaranteed stability

In the present technique, the denominator and numerator in the filter are designed separately and recursively. First, the denominator coefficients, derived from the stable matrix of the Roesser model (the Fornasini-Marchesini second model), are found by minimizing a performance index through the alternating variable method. The numerator coefficients are then determined analytically by solving linear simultaneous equations. The above process will be repeated until there is negligible change in the objective function. Finally, a numerical example is given to illustrate the utility of the proposed technique.     

具有任意频响的二维FIR数字滤波器设计的闭式最小二乘解

本文研究具有任意频响特性的二维ＦＩＲ数字滤波器的最小二乘设计问题。     

A simple method to test the existence of 2-D partial fraction decomposition

In this paper we give a simple method to test the existence of the decomposition of the form

$\text{A(Z}{}_1\text{, Z}{}_2\text{) A(Z}{}_1{}^{\mathrm{?1}}\text{, Z}{}_2{}^{\mathrm{?1}}\text{B(Z}{}_1\text{, Z}{}_2\text{B(Z}{}_1{}^{\mathrm{?1}}\text{, Z}{}_2{}^{\mathrm{?1}}\text{=}\text{(Z}{}_1\text{, Z}{}_2\text{)}\text{B(Z}{}_1\text{, Z}{}_2\text{+}\text{P(Z}{}_1{}^{\mathrm{?1}}\text{, Z}{}_2{}^{\mathrm{?1}}\text{)}\text{B(Z}{}_1{}^{\mathrm{?1}}\text{, Z}{}_1{}^{\mathrm{?1}}\text{)}$

for a stable two-dimensional transfer function of a recursive filter H(Z₁, Z₂) = A(Z₁, Z₂)/B(Z₁, Z₂).     

Design for 2-D error feedback networks with identical coefficient sets

In realization of recursive digital filters with fixed point arithmetic, an error caused by roundoff arises. It is known that the level of the roundoff noise of an IIR filter tends to be high when the poles are close to the unit circle. Error feedback (EF) is an effective method to reduce the roundoff noise. It is desirable to design an EF network using as few parameters as possible in order to keep computational costs low. In this paper, we propose a method for designing a 2D EF network with identical coefficient sets. That is, the EF coefficients are divided into several subsets such that all the elements within each set have the same absolute value. In order to optimize the coefficient sets, we propose an algorithm by using the genetic algorithm. In the numerical example, we demonstrate the effectiveness of the proposed method.     

Optimal McClellan transformation and its application to 2-D FIR digial filter design

A new method to choose the coefficients of the McClellan transformation is developed. The coefficients are obtained by using both analytic and nonlinear optimization approaches. The transformation using the proposed method has much better approximation performance for circular symmetry than the existing methods, especially when the cutoff frequency of the 2-D filter is very large. The proposed method also applies to choose the transformation coefficients to approximate elliptic contours. Two design examples of 2-D FIR digital filters demonstrate the good performance of the proposed method.     

Separate/joint optimization of error feedback and realization for roundoff noise minimization in a class of 2-D state-space digital filters

Techniques for the separate/joint optimization of error-feedback and realization are developed to minimize the roundoff noise subject to l ₂-norm dynamic-range scaling constraints for a class of 2-D state-space digital filters. In the joint optimization, the problem at hand is converted into an unconstrained optimization problem by using linear-algebraic techniques. The unconstrained problem obtained is then solved by applying an efficient quasi-Newton algorithm. A numerical example is presented to illustrate the utility of the proposed techniques.     

基于巴特沃斯逼近的二维IIR数字滤波器的设计

本文给出了一种基于巴特沃斯逼近的二维ＩＩＲ数字滤波器的设计方法，得到了由基本的全通节级联，并联实现的各种二维滤波器函数，包括，镜象对称互补滤波器，扇形滤波器和具有任意矩形通、阻带的滤波器，结果表明，这种实现结构具有通有灵敏度低、滤波器系数少的优点，并且由于巴特沃斯逼近的最大平坦性，得到的滤波器具有良好的相位特性。     

Fast realisation of 2-D digital filters using logarithmic number systems

Previous papers of mine have discussed the approximation of 2-D digital filter coefficients with algebraic sums of integer powers of the base in a logarithmic number system. The results already obtained suggest a sequential memory-oriented realisation which is faster than the standard implementation.     

基于DA算法的二维DCT的FPGA实现

研究了一种采用现场可编程门阵列(FPGA)实现超高性能二维离散余弦变换(DCT)的方法。在DCT算法结构上利用了变换的可分离性和行列的可分解性采用行列分解的方法将二维DCT转换为2个串行的一维DCT实现,同时采用了基于分布算法(Distributed Arithmetic)的乘法累加结构,从而极大地减少了硬件资源需求,提高了运算速度,使图像处理的实时性得到了大幅提高。最后还给出了FPGA的实现和仿真结果。     

Fast Implementation of 3-D Digital Filters Via Systolic Array Processors

In this paper a fast implementation architecture of three-dimensional (3-D) FIR or IIR digital filters via systolic VLSI array processors is described. The modular structure presented is comprised of similar processing elements in a linear cascade configuration with local interconnections. High speed throughput rates are attained due to high concurrency, which is achieved by exploiting both pipelining and parallelism. The considered 3-D FIR and IIR filters may be used for the processing of reconstructed 3-D images and in medical imaging applications.     

Implementation of non-linear filters using nanoelectronic single-electron circuitry

Non-linear filters are large family of filters used in signal and image processing. They have found numerous applications such as in digital image restoration, speech processing and coding, digital TV applications, etc. In this paper, two binary non-linear filters, the three-point median filter and the 2×2-pixel morphological opening filter are designed using nanoelectronic single-electron circuitry. In single-electron circuits bits of information are represented by the presence or absence of single electrons at conducting islands. The two nanoelectronic filters are simulated using a Monte Carlo technique and their correct and stable logical operation is confirmed.     

二维正方复式晶格的完全光子带隙

为产生光子晶体完全光子带隙,在二维正方晶格的介质柱中心构造一个空气柱孔缺陷,应用平面波展开的方法研究了光波在其中的传播规律,发现在特定的结构参数条件下,该结构产生了完全光子带隙,从而找到了在简单晶格结构条件下实现完全光子带隙的方法。     

二维数字系统的系数灵敏度和结构优化

本文从二维数字系统的Roesser模型出发,在Kawamata等人定义的灵敏度的基础上,导出了系统传输函数对全体系数的标量灵敏度的新的表达式,并给出了一种降低灵敏度的优化方法,该优化方法不仅可以降低系数灵敏度,还可以提高结构的效率.举例结果表明,新的表达式与Kawamata等人的表达式相比,能更好地与计算机模拟结果相符.