Two-dimensional Digital Filters Research Articles

Overflow Oscillation Elimination in Fixed-Point 2D Digital Filters Based on the Roesser Model

This paper investigates the overflow oscillation elimination problem in the fixed-point two-dimensional (2D) digital filter (DF) based on Roesser model subjected to two’s complement overflow (TCO) nonlinearities. By utilizing the system information and behavior of TCO nonlinearities more effectively, a new global asymptotic stability (GAS) criterion for 2D DFs is presented. A comparison of the obtained criterion with existing criteria is made with the help of examples.

Hankel norm performance of 2-D digital filters described by Roesser model with overflow arithmetic

ABSTRACT This paper is concerned with the problem of asymptotic stability with Hankel norm performance (HNP) of two-dimensional (2-D) digital filter characterised by Roesser model, where the 2-D system includes overflow nonlinearities and external interference or excitation of finite duration. The underlying nonlinearities cover the usual types of overflow arithmetic utilised in practice such as saturation, two’s complement, zeroing and triangular. To solve this problem, new sufficient criterion is proposed by employing quadratic 2-D Lyapunov function. The proposed criterion guarantees that the addressed system has 2-D HNP bound. This criterion can examine the unwanted memory effect (ME) reduction of 2-D interfered digital filters for past excitations. In the absence of external inputs, the asymptotic convergence of 2-D digital filters is established under the proposed criterion. The developed HNP criterion is in linear matrix inequality framework and, therefore, computationally tractable. In addition, the optimisation problem is formulated to obtain the minimum HNP of the 2-D interfered digital filter. To illustrate the effectiveness of the proposed criterion, a numerical example is provided. The criteria addressed in current paper can give a whole analysis framework for the unwanted MEs of filters.

Efficient ADMM-Based Algorithm for Regularized Minimax Approximation

Minimax approximations have found many applications but are lack of efficient solution algorithms for large-scale problems. Based on the alternating direction method of multipliers (ADMM) for convex optimization, this letter presents an efficient scalarwise algorithm for a regularized minimax approximation problem. The ADMM-based algorithm is then applied in the minimax design of two-dimensional (2-D) digital filters and the training of randomized neural networks for regression on a realworld benchmark dataset. Experimental results demonstrate the fast convergence rate and low computational complexity of the proposed algorithm, as well as the good approximation/prediction performance of the learned approximation model.

Digital Filter Architecture Based on Modified Winograd Method F(2× 2, 5× 5) and Residue Number System

Improving the characteristics of digital signal processing devices is an important task in many practical problems. The paper proposes the architecture of a two-dimensional digital filter with a 5×5 mask, in which calculations are performed according to the Winograd method in the Residue Number System (RNS) with moduli of a special type. Theoretical analysis and hardware Field-Programmable Gate Array simulation are presented. The results show that the fragment throughput fr/s (number of fragments per second) of the device is 29.6% – 724.7% higher than state-of-the-art solutions. This is achieved by the combination of the Winograd method, which reduces the number of multiplications, with the RNS arithmetic, which performs addition and multiplication under smaller operands in parallel. However, our experiments showed that the proposed method requires up to 2.54% – 11.01% more Look-Up Tables and 3.58% – 19.83% higher power consumption compared to known analogues.

Design and implementation of two-dimensional digital finite impulse response filter using very high speed integrated circuit hardware description language

<span>The main purpose of this paper is to design a two-dimensional digital finite impulse response (FIR) filter using data broadcast and non-broadcast structure. The implementation of two-dimensional digital FIR filter is done using very high speed integrated circuit hardware description language (VHDL). Rectangular window method is used for calculating 2D digital FIR filter coefficients for data broadcast and non-broadcast structure. The coefficients of the one-dimensional digital FIR filter are obtained using the MATLAB filter design and analysis (FDA) tool for two different cut-off frequencies and are multiplied to get the necessary coefficient for the two-dimensional FIR filter to be designed; the simulation is done on Artix-7 series field programmable gate array (FPGA), target device (xc7a35t-cpg236) using Vivadov.2015.2. The proposed design reduces the area utilization and the power consumption when compared with the existing literature. The experimental result shows that the power consumption is improved by 97% and there is an improvement of 24% in area utilization for the two-dimensional with and without data broadcast one dimensional FIR filter structures.</span>

High-speed recursive-separable image processing filters

The development of modern technologies in the field of image formation leads to an increase in the size of the generated images, as a result the question of reducing the processing computational costs arises, and this is an important factor in the creation of real-time systems. The study provides a description of high-speed recursive-separable filters for improving the quality of images, which, due to the peculiarities of their implementation, can reduce the number of computational operations required for the image processing process. This type of filters is obtained from two-dimensional linear digital filters, which are modified by applying recursive and separable properties to them. The MATLAB environment computing method for implementation of these filters is described. An extensive performance research of the developed filters has been carried out at various sizes of the test image and on various experimental installations. The comparison with the classical two-dimensional convolution method of the developed filters is demonstrated, and it shows the time gain required for the image processing. The results obtained can be applied in biomedical image processing systems or in vision systems working in heavy weather conditions.

A comparative study for selecting and using simulation methods of Gaussian random surfaces

Conventional methods for generating Gaussian random surfaces, including the moving average (MA) time series model with nonlinear conjugate gradient method (NCGM), two-dimensional (2-D) digital filter method, and spectral representation method (SRM), are implemented with a wide range of autocorrelation length and truncation length values of the autocorrelation function (ACF). The ACF, power spectral density function (PSDF), and essential roughness parameters of the simulated surfaces are calculated and compared. Based on the simulation results, the mechanism of the truncation length of ACF affecting the simulated surfaces can be summarized as that the step formed by truncating ACF is not sufficiently small, thus resulting in non-negligible errors in the corresponding PSDF. Such errors will be propagated to the simulated surfaces. A conservative criterion is proposed to avoid the adverse effects of truncating ACF: make the autocorrelation length less than 8% of the surface dimensions and the truncation length at least seven times autocorrelation length. The results show that the MA model with NCGM overestimates the PSDF values of simulated surfaces in the high-frequency region, meaning significant high-frequency noise in the simulated surfaces. The 2-D digital filter method and the SRM have almost the same performance, and both methods are better than the MA model with NCGM when the criterion of truncating ACF is fulfilled. The SRM generates rough surfaces with the smallest standard deviation in terms of the roughness parameters, ACF, and PSDF in most cases, meaning that it can generate accurate surfaces at every single simulation and is more stable and efficient. Therefore, the SRM is the most recommended method among the three methods studied.

Novel Realizability Criterion for Saturation Overflow Oscillation-Free 2-D Digital Filters Based on the Fornasini-Marchesini Second Model

The problem of global asymptotic stability (GAS) of two-dimensional (2-D) digital filters based on the Fornasini-Marchesini second local state-space (FMSLSS) model with saturation arithmetic is studied in this paper. A novel GAS criterion for the 2-D digital filter is presented. The obtained criterion is compared with several previously reported criteria.

Expected power bound and stability of two-dimensional digital filters with multiplicative noise in the FMLSS model

This paper studies the two-dimensional (2-D) expected power bound (EPB) for 2-D digital filters with multiplicative noise in the Fornasini-Marchesini local state-space (FMLSS) model. By virtue of a class of linear matrix inequalities (LMIs), the novel existence criterion of 2-D EPB for 2-D digital filters in the considered model is obtained. The corresponding stabilization controller design method is presented based on the above criterion. Finally, two examples are presented to verify the effectiveness of our results.

Design of Two-Dimensional Recursive Digital Filter Using Multi Particle Swarm Optimization Algorithm

Particle Swarm Optimization (PSO) is an evolutionary algorithm widely used in optimization problems. It is characterized by a fast convergence, which can lead the algorithm to stagnate in local optima. In the present paper, a new Multi-PSO algorithm for the design of two-dimensional infinite impulse response (IIR) filters is built. It is based on the standard PSO and uses a new initialization strategy. This strategy is relayed to two types of swarms: a principal and auxiliaries. To improve the performance of the algorithm, the search space is divided into several areas, which allows a best covering and leading to a better exploration in each zone separately. This solved the problem of fast convergence in standard PSO. The results obtained demonstrate the effectiveness of the Multi-PSO algorithm in the filter coefficients optimization.

Hybrid Approach to Design of Two Dimensional Stable IIR Digital Filter

In this paper, the magnitude optimization for the design of two dimensional digital filter is attempted and new design method for a two-dimensional (2-D) recursive digital filter is proposed via appropriate genetical swarm optimization with the introduction of the desired stability constraints. The method is tested on a numerical example and the obtained results are presented with previously published methods.

Global Asymptotic Stability of 2-D Digital Filters With a Saturation Operator on the State-Space

This brief investigates the global asymptotic stability (GAS) problem of two-dimensional (2- ${D}$ ) digital filters represented by Roesser model subject to saturation nonlinearities. A new sufficient GAS condition for the underlying 2- ${D}$ system is derived. The condition is compared with several existing stability conditions.

Gravimeter with two-dimensional digital filtering and error compensation of measuring information on mechanical quantities

The methods of two-dimensional digital filtering of the output signal of a gravimeter as part of an aviation gravimetric system are considered. The result of filtering is to increase the accuracy of measuring the acceleration of gravity as a result of eliminating the effect of vertical acceleration, translational and angular vibration accelerations of the aircraft. The problem of filtering and compensating for errors in measuring information on mechanical quantities was solved by algorithmic processing of the gravimeter output signal. Two-dimensional digital filtering of measurement information is performed on the basis of the formation of a two-dimensional array of digital readings of gravimetric measurement information about anomalies of gravitational acceleration, taking into account the coordinates of the Earth's surface where these readings were taken. This array corresponds to a number of adjacent flight lines of an aviation gravimetric system. After that, the generated array is filtered using a two-dimensional digital low-pass filter. The filtering process additionally takes into account the two-dimensional correlations that are present in the useful signal of the gravitational acceleration anomalies. Such filtering can be performed during the post-flight processing of the results of gravimetric measurements. The use of two-dimensional digital filtering of measurement information about mechanical quantities allows to increase the accuracy of determining the gravitational acceleration anomalies up to 2 times (compared to one-dimensional filtering) and 3 ... 5 times (compared to the output signal of the integrating gravimeter).

Symmetry Incorporated Cost-Effective Architectures for Two-Dimensional Digital Filters

Professor Fettweis as far back as 1977 published a paper generalizing McClellan transformation to obtain circular symmetry in 2-D and spherical, hyper-spherical symmetries in multidimensional digital filters [1]. This survey paper presents stateof-the-art two-dimensional (2-D) VLSI digital filter architectures possessing various symmetries in the filter magnitude response. Preceding the symmetry structures, a generalized formulation is given that allows the derivation of various new 2-D VLSI filter structures of any order without global broadcast. Following this, two types (namely, Type 1 [20] and Type 3 [21], [25], [26]) of cost-effective 2-D magnitude symmetry filter architectures possessing diagonal, four-fold rotational, quadrantal, and octagonal symmetries with reduced number of multipliers are given. By combining the identities of the Types-1 and 3 symmetry filter structures, multimode 2-D symmetry filters which enable the above four symmetry modes are discussed. The Type-1 and Type-3 multimode filters can result in a 65.3% cost reduction in terms of number of multipliers compared with the sum of the multipliers of the four individual Type-1 symmetry filter structures studied in this paper. Furthermore, Type-3 has shorter critical path than Type-1 multimode filter. The paper is concluded with the presentation of a 2-D filter design example and a corresponding structure.

An improved global-best-driven flower pollination algorithm for optimal design of two-dimensional FIR filter

The design of two-dimensional (2D) digital filter is a higher-order, nonlinear, and multi-modal optimization problem. This paper presents an improved Global-best-driven Flower Pollination Algorithm, named as GFPA, for the design of 2D Finite Impulse Response (FIR) filters. Two methods have been proposed—the first method minimizes the weighted square error via GFPA and the second method finds the coefficients of one-dimensional FIR filter by GFPA before McClellan transformation. The performance of proposed algorithm has been compared with state-of-the-art algorithms and the simulation results show significant improvements. For the design of a $$15\times 15$$ circular symmetric filter, an average reduction of 55% in fitness function evaluation and 72% in execution time is observed. Further, the experiment on CEC 2014 benchmark functions demonstrates better optimal solution than existing algorithms.

An Improved Global-Best-Guided Cuckoo Search Algorithm for Multiplierless Design of Two-Dimensional IIR Filters

Cuckoo search algorithm (CSA) is relatively a new optimization technique with less control parameters and strong exploration ability. Due to the random search associated with CSA, it requires large number of functional evaluations for obtaining optimal solution. An improved algorithm, named as improved global-best-guided CSA, is presented here based on the best solution of previous iteration for the optimal design of multiplierless two-dimensional recursive digital filters. The most important feature of the proposed algorithm is that it is completely self-adaptive with no tuning parameters, whereas in CSA the replacement factor needs to be adjusted. The proposed algorithm exhibits 52% improvement in fitness function evaluation (for p = 2) and the execution time is reduced by 56% in comparison with the existing algorithms. Further, the proposed algorithm has been tested for several benchmark problems and found to exhibit significant performance improvement.

Kaiser-Hamming pencere yapısı ve Huang dönüşümü kullanılarak iki boyutlu sayısal süzgeç tasarımı ve imge iyileştirme uygulaması

Two dimensional digital filters which perform spatial filtering or frequency domain filtering are used for image enhancement operations. For high resolution image enhancement operations, two-dimensional digital filters which perform filtering in the frequency domain are preferred due to the computational advantage. However, in frequency domain based two dimensional digital filter design methods, there are various issues such as excess of computational complexity, suboptimal bad filter performance, and lack of elasticity. Moreover, in many design methods proposed in the literature, it is seen that there is no application on the image. The proposed method in this study presents a solution with improved filter performance and elasticity in less computational complexity. The proposed method, in which the effect on image enhancement is also studied, is based on the derivation of a two-dimensional Kaiser-Hamming window family obtained using the Huang’s method. The proposed method provides the design of many two-dimensional digital filters with various filter characteristics at a fixed length. Simulation results obtained from various filtering examples for two images show that two dimensional digital filters designed by the proposed method can provide different smoothing and sharpening on a wide scale according to the desired level for image enhancement applications such as image smoothing and image sharpening, and also the length and independent shape parameters of the proposed window have opposite effects on the image.

A novel word length selection method for a guaranteed $$H_\infty $$ H ∞ interference rejection performance and overflow oscillation-free realization of 2-D digital filters

This paper examines the problem of the local overflow stability and disturbance attenuation performance analysis of two-dimensional (2-D) Roesser digital filters in the presence of external interferences. In particular, by utilizing the local properties of saturation nonlinearity and Lyapunov stability theory, a novel linear matrix inequality (LMI)-based condition is proposed that not only ensures the nonexistence of overflow oscillations, but also yields the $$H_{\infty }$$ interference rejection performance of 2-D digital filters under the overflow constraint. It is worth mentioning here that in contrast to the traditional approaches based on modeling the saturation with a global sector-bound condition, the proposed approach provides a less conservative bound for the attenuation of disturbances and renders the idea of minimum word length for realizing the 2-D (Roesser) filter to eliminate overflow oscillations and attain the specified $$H_{\infty }$$ interference attenuation performance index. Finally, a numerical simulation example is also provided, which demonstrates the superiority of the proposed method over the existing techniques.

Lattice Structure Realization for The Design of 2-D Digital Allpass Filters With General Causality

This paper presents a lattice structure for the realization of two-dimensional (2-D) recursive digital allpass filters (DAFs) with general causality. We employ four basic lattice sections to realize 2-D recursive DAFs with wedge-shaped coefficient support region like a nonsymmetric half-plane (NSHP) support region. The theory and transfer functions of the realized 2-D lattice DAFs are derived. Some variations of the 2-D lattice structure are also presented. We use the Roesser state space model to verify the minimal realization of the proposed 2-D recursive lattice DAF. We present a least-squares design technique and a minimax design technique to solve the nonlinear optimization problems of the proposed 2-D lattice DAF structure. The novelty of the presented lattice structure is that it not only inherits the desirable attributes of 1-D Gray-Markel lattice allpass structure but also possesses the advantage of better performance over the existing 2-D lattice allpass structures. Finally, several design examples are provided for conducting illustration and comparison.

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.