2D 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.

Prevention of Overflow Oscillations in Fixed-Point 2D Digital Filters Based on the Fornasini–Marchesini Second Model

Prevention of Overflow Oscillations in Fixed-Point 2D Digital Filters Based on the Fornasini–Marchesini Second Model

Design and applications of adjustable 2D digital filters with elliptical and circular symmetry

Design and applications of adjustable 2D digital filters with elliptical and circular symmetry

Designing Energy-Efficient Approximate Multipliers

This paper proposes a novel approach suitable to design energy-efficient approximate multipliers using both ASIC and FPGAs. The new strategy harnesses specific encoding logics based on bit significance and computes the approximate product performing accurate sub-multiplications by applying an unconventional approach instead of using approximate computational modules implementing traditional static or dynamic bit-truncation approaches. The proposed platform-independent architecture exhibits an energy saving of up to 80% over the accurate counterparts and significantly better behavior in terms of accuracy loss with respect to competitor approximate architectures. When employed in 2D digital filters and edge detectors, the novel approximate multipliers lead to an energy consumption up to ~82% lower than the accurate counterparts, which is up to ~2 times higher than that obtained by state-of-the-art competitors.

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>

Novel Results for Markov Jump 2D Interfered Digital Filters with State-Delay and Saturation Nonlinearities

Existing results on [Formula: see text] stability analysis problems for 2D digital filters are limited to external interference and saturation arithmetic. Unfortunately, developed results so far are not sufficient to tackle Markovian jumping parameters (MJPs) and state-delay. Such stability problem for 2D digital filters under MJPs, saturation arithmetic, state-delay and external interference has not been considered in the existing literature. In this paper, novel [Formula: see text] performance analysis criterion is first proposed for 2D interfered digital filters in which state-delay, saturation nonlinearities and MJPs are considered. The mathematical model of the underlying 2D system is described by the Roesser model. Furthermore, improved [Formula: see text] performance analysis criterion over the existing result is also obtained for 2D interfered digital filters with saturation nonlinearities only. At the end, two examples are employed to illustrate the effectiveness of the devised stability results.

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.

Criterion for non‐existence of limit cycles in 2D state‐space digital filters described by the Fornasini–Marchesini second model with finite wordlength non‐linearities

This study investigates the problem of global asymptotic stability of fixed-point two-dimensional (2D) digital filters described by the Fornasini–Marchesini second local state-space model with the combined effects of quantisation and overflow non-linearities. Utilising a more precise characterisation of the non-linearities, an improved criterion for the limit cycle-free realisation of 2D digital filters is brought out. The criterion is compared with several previously reported criteria.

Design of efficient circularly symmetric two-dimensional variable digital FIR filters

Circularly symmetric two-dimensional (2D) finite impulse response (FIR) filters find extensive use in image and medical applications, especially for isotropic filtering. Moreover, the design and implementation of 2D digital filters with variable fractional delay and variable magnitude responses without redesigning the filter has become a crucial topic of interest due to its significance in low-cost applications. Recently the design using fixed word length coefficients has gained importance due to the replacement of multipliers by shifters and adders, which reduces the hardware complexity. Among the various approaches to 2D design, transforming a one-dimensional (1D) filter to 2D by transformation, is reported to be an efficient technique. In this paper, 1D variable digital filters (VDFs) with tunable cut-off frequencies are designed using Farrow structure based interpolation approach, and the sub-filter coefficients in the Farrow structure are made multiplier-less using canonic signed digit (CSD) representation. The resulting performance degradation in the filters is overcome by using artificial bee colony (ABC) optimization. Finally, the optimized 1D VDFs are mapped to 2D using generalized McClellan transformation resulting in low complexity, circularly symmetric 2D VDFs with real-time tunability.

Improved performance of digital filters approximation

The work presented in this paper concerns with analysis and synthesis of the two-dimensional (2D) digital systems based on model order reduction, and application to the 2D digital filters. The synthesis of the 2D systems is performed with the semi-definite iterative programming (SDP) method, in the frequency domain. After the synthesis, we make an order reduction of the synthesised model by the quasi-Gramians method. From several results and their interpretations, the 2D filter synthesised by the model reduction proposed method, present advantages compared to the conventional direct synthesised filters.

Improved performance of digital filters approximation

The work presented in this paper concerns with analysis and synthesis of the two-dimensional (2D) digital systems based on model order reduction, and application to the 2D digital filters. The synthesis of the 2D systems is performed with the semi-definite iterative programming (SDP) method, in the frequency domain. After the synthesis, we make an order reduction of the synthesised model by the quasi-Gramians method. From several results and their interpretations, the 2D filter synthesised by the model reduction proposed method, present advantages compared to the conventional direct synthesised filters.

Condition of the elimination of overflow oscillations in two‐dimensional digital filters with external interference

This study is concerned with the problem of the elimination of overflow oscillations (EOOs) for two-dimensional (2D) digital filters with external interference. The main purpose is the presentation of a new unified criterion such that the underlying 2D digital filter is stable with a positive prescribed interference attenuation level. A performance index is proposed for the first time, which is referred to as generalised dissipativity property. By using this index and two harmonic slack matrices, a novel criterion is established, which can be used to solve ℋ∞ EOOs, passive EOOs and l 2–l ∞ EOOs for 2D digital filters with external interference in a unified framework, and reduce the conservatism of the existing results. The effectiveness of the criterion is demonstrated by a numerical example.

New passivity criterion for limit cycle oscillation removal of interfered 2D digital filters in the Roesser form with saturation nonlinearity

The passivity concept plays an important role in circuit theory, signal processing, and control, but no criteria have yet been established for two-dimensional (2D) digital filters. In this article, we propose a new and first criterion for 2D digital filters in the Roesser form, to ensure passivity from the interference vector to the output vector with a certain storage function. The proposed criterion also guarantees the asymptotic stability of 2D digital filters in the Roesser form without interference. This criterion is described by linear matrix inequality, making it computationally attractive. A simulation example is presented, which demonstrates the usefulness of the 2D passivity criterion.

Lenticular-based 2D anti-aliasing digital filtering method for stereo image

Based on the characteristic of lenticular-based LCD auto-stereo display and its corresponding stereo image, aiming to solve spectrum aliasing problem, this paper proposed a novel 2D anti-aliasing digital filtering method. This method analyzed multiview LCD sub-pixel arrangement of slant lenticular, established the corresponding sub-sampling model with multi-dimensional sampling theory, and designed the corresponding 2D digital filter, so that 2D spectrum anti-aliasing filtering was performed on each view image and the distortion of stereo image was effectively eliminated. Experimental results show that the proposed method is of low complexity, good filtering effect, and strong applicability to similar auto-stereo displays.

Normals estimation for digital surfaces based on convolutions

In this paper, we present a method that we call on-surface convolution which extends the classical notion of a 2D digital filter to the case of digital surfaces (following the cuberille model). We also define an averaging mask with local support which, when applied with the iterated convolution operator, behaves like an averaging with large support. The interesting property of the latter averaging is the way the resulting weights are distributed: given a digital surface obtained by discretization of a differentiable surface of R^3, the masks isocurves are close to the Riemannian isodistance curves from the center of the mask. We eventually use the iterated averaging followed by convolutions with differentiation masks to estimate partial derivatives and then normal vectors over a surface. The number of iterations required to achieve a good estimate is determined experimentally on digitized spheres and tori. The precision of the normal estimation is also investigated according to the digitization step.

A Two-Stage Approach to the Establishment of State-Space Formulation of 2-D Frequency Transformation

This letter proposes a two-stage approach to the open problem of establishing state-space formulation of 2D frequency transformation for 2D digital filters. In the first stage, formulation of generating a 2D state-space representation that is not in the standard form of a Roesser model will be derived, while in the second stage, the desired state-space formulation to generate a 2D Roesser state-space representation will be established based on the results obtained in the first stage by utilizing certain linear transformation. Moreover, it will be seen that the proposed formulation includes the formulation of 1D frequency transformation for 2D digital filters given by Koshita and Kawamata as a special case, and thus can be viewed as a natural generalization of their result. Numerical examples are given to illustrate the effectiveness of the proposed formulation.

Design Two-Dimensional IIR Filters Based on Clonal Selection Algorithm with Singular Value Decomposition

In this letter, clonal selection algorithm (CSA) with singular value decomposition (SVD) method is investigated for the realization of two-dimentional (2D) infinite-impulse response (IIR) filters with arbitrary magnitude responses. The CSA is applied to optimize the sampled frequencies of transition band of digital filters, then producing a planar response matrix of a 2D IIR digital filter. By using the SVD, 2D magnitude specifications can be decomposed into a pair of 1D filters, and thus the problem of designing a 2D digital filter can be reduced to the one of designing a pair of 1D digital filters or even only one 1D digital filter. The stimulation results show the proposed method has the better performance of the minimum attenuation between the passband and stopband.

Two efficient structures for 2D digital filter implementation

In the paper, a new efficient structure for two-dimensional digital filters with separable denominator, denoted as 2D ZL, is derived based on a set of special polynomial operators. For a (M, N)th order filter, this structure possesses MN+3(M+N)+1 nontrivial parameters plus M+N free parameters, compared to the optimal state-space realisation which has (M+N+1)2 nontrivial parameters. The equivalent state-space realisation of the 2D ZL yields another interesting efficient structure. Performance analysis is carried out for both structures by deriving the expressions of roundoff noise gain and L2-sensitivity measure. A genetic algorithm is proposed to efficiently solve the optimal structure problems. Two examples are given to show that the optimised proposed structures can yield a better performance than the shift-operator and delta-operator based structures and even outperform the optimal fully parameterised state-space realisation.

Numerical simulation of the geometrical factors affecting surface roughness measurements by AFM

The atomic force microscope (AFM) is a powerful tool for measuring surface roughness on the nanometre scale. This paper numerically analyses the factors affecting roughness evaluation of the surface measured by AFM. Parameters of both tip and sample are considered such as tip radius, surface autocorrelation length, standard deviation of original rough surface and its height distribution. The rough surface is generated using a 2D digital filter and the Fourier analysis method with controlled autocorrelation function and height distribution. The AFM image is simulated by mathematical morphology. For a given tip radius, a surface with high standard deviation and low correlation length causes a large error in determining roughness by AFM. We also show that the effect of tip radius on roughness exhibits two different trends depending on the surface skewness. For a normally distributed surface with near zero skewness and a rough surface with negative skewness, the root mean square (RMS) roughness decreases monotonically as tip radius increases. For a surface with large positive skewness, the RMS roughness tends to increase initially and then decrease with increasing tip radius.

A constructive approach to stabilizability and stabilization of a class of n D D Systems

This paper presents a constructive approach to the problem of output feedback stabilizability and stabilization of a class of linear multidimensional ( nD, n>2) systems, whose varieties of the ideals generated by the reduced minors are infinite with respect to not more than two variables. The main idea of the proposed approach is to decompose the variety of an nD system in this class into a union of several varieties, each of which is defined by polynomials in just two variables. The new method can be considered as a combination of Grobner bases and existing results on two-dimensional (2D) digital filter stability tests and on stabilizability and stabilization of 2D systems. An example is illustrated.