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This paper proposes the design of transformation based two dimensional (2D) elliptical filters using multi-objective artificial bee colony (MOABC) algorithm. The MOABC algorithm finds the one dimensional (1D) cut-off frequencies and McClellan transformation coefficients by optimizing the contour approximation errors at pass-band and stop-band regions of elliptical filters. This design approach is compared with the state of the art approaches in terms of contour approximation error, pass-band ripple and stop-band attenuation to ensure the efficiency. It is seen that an efficient mapping of 1D filter to 2D filter is possible with minimum contour approximation error using the proposed approach. The second proposal in this paper is the design of low complexity variable bandwidth and variable orientation elliptical filters with direct 2D tunability. This is achieved by mapping the coefficients of different 2D filters into a 2D Farrow structure. The performance of the proposed variable elliptical filter is measured in terms of mean error, mean square error, root mean square error, pass-band ripple, stop-band attenuation and 2D cut-off frequencies. The main feature of the proposed 2D variable filter design lies in the considerable reduction in the number of multipliers when compared to the existing methods, which in turn reduces the resource utilization and power consumption.

This paper proposes a low-complexity convolutional neural network (CNN) for super-resolution (SR). The proposed deep-learning model for SR has two layers to deal with horizontal, vertical, and diagonal visual information. The front-end layer extracts the horizontal and vertical high-frequency signals using a CNN with one-dimensional (1D) filters. In the high-resolution image-restoration layer, the high-frequency signals in the diagonal directions are processed by additional two-dimensional (2D) filters. The proposed model consists of 1D and 2D filters, and as a result, we can reduce the computational complexity of the existing SR algorithms, with negligible visual loss. The computational complexity of the proposed algorithm is 71.37%, 61.82%, and 50.78% lower in CPU, TPU, and GPU than the very-deep SR (VDSR) algorithm, with a peak signal-to-noise ratio loss of 0.49 dB.

This paper presents a low complexity two dimensional (2D) circular symmetric Finite Impulse Response (FIR) filter design and implementation of architecture. The optimized circular symmetric 2D FIR filter is designed using a modified Park–McClellan transformation method and filter coefficients are quantized using a canonical signed digit (CSD) binary number format. The CSD encoded coefficients are optimized to reduce the number of adder/subtractors using common subexpression elimination (CSE) algorithms. Based on the modified filter coefficients, the two structures fully direct form and hybrid-II form 2D FIR filter architectures are implemented using CSD and CSD with Horizontal CSE and Vertical CSE techniques. The proposed architectures compared with the conventional symmetry 2D filters and state-of-the-art architectures in terms of area, power, and speed.

This work presents an analytic design procedure for 2D filters with wedge-shaped frequency response. The design starts from a wide-band, maximally-flat zero-phase low-pass prototype filter, to which a frequency mapping is applied, which leads to the 2D filter with the desired shape. The overall frequency response of the wedge filter is determined in a factored form, and the filter matrices result directly decomposed as a convolution of smaller matrices, a major advantage in implementation. The resulted filter is parametric, being adjustable depending on specifications, namely orientation and aperture angles. Several wedge filter design examples are provided, for various specifications.

An analytical design procedure is proposed for 2D Gaussian orientation-selective FIR filters, based on a frequency transformation applied to a Gaussian prototype. The synthesis starts from a Gaussian filter with specified selectivity with a frequency response approximated as a factored trigonometric polynomial. An efficient frequency mapping is derived and applied to each factor, leading to the desired oriented filter, whose transfer function finally results in matrix form. The 2D filters have a correct shape, with good linearity, a low ripple and negligible distortions. Several design examples for imposed specifications are provided, and also applications in directional filtering are shown, proving the filter capabilities.

In wireless sensor networks (WSNs), distributed algorithms are used to estimate desired parameters for minimizing the communication overheads and make the network energy efficient. In literature, distributed estimation of finite impulse response (FIR) systems has been studied, because it is stable. In fact in many sensor network-based applications such as target tracking and fast rerouting, infinite impulse response (IIR) systems are required to be modeled. Thus, each sensor node uses the adaptive IIR filter and interact with each other under diffusion mode of cooperation to estimate the parameters. But the IIR filter inherently produces non-quadratic and multimodal error surfaces. Therefore gradient search algorithms that work well for FIR filters is not suitable for IIR system because they are likely to be trapped in the local minima. Keeping this in view, population based derivative free diffusion particle swarm optimization (DPSO) algorithms are proposed here to estimate the parameters of IIR systems. The algorithms are simulated for benchmark IIR systems and the steady state and transient performances are analyzed. The simulation results demonstrate that the proposed diffusion algorithms provide admirable improvement by resulting in faster convergence and low steady state value compared to that of conventional least mean squared algorithms. Keywords: IIR system, Distributed estimation, Wireless sensor networks, Diffusion least mean squared, Particle swarm optimization

A metalens opto-electronic camera for spatial frequency filtering under inco- herent illumination is introduced. By inverse-designing the phase on the metasurface, near arbitrarily structured 2D filters are realized for depth-invariant operation.

A single-lens implementation of optoelectronic spatial frequency filtering for incoherent illumination is demonstrated utilizing metasurface engineering. By inverse-designing the phase on the metasurface, arbitrarily structured 2D filters are realized for depth-invariant, broadband operation.

Current unmanned aerial vehicle (UAV) visual tracking algorithms are primarily limited with respect to: (i) the kind of size variation they can deal with, (ii) the implementation speed which hardly meets the real-time requirement. In this work, a real-time UAV tracking algorithm with powerful size estimation ability is proposed. Specifically, the overall tracking task is allocated to two 2D filters: (i) translation filter for location prediction in the space domain, (ii) size filter for scale and aspect ratio optimization in the size domain. Besides, an efficient two-stage re-detection strategy is introduced for long-term UAV tracking tasks. Large-scale experiments on four UAV benchmarks demonstrate the superiority of the presented method which has computation feasibility on a low-cost CPU., 8pages, 8 figures, accepted by 2020 IEEE/RSJ International Conference on Intelligent Robots and Systems(IROS)

This work proposes an efficient analytic method for designing a class of 2D filters useful in image processing, namely wedge-shaped filters, which can be considered components of a directional filter bank. The design starts from a 1D digital filter prototype transfer function. Using accurate approximations and specific frequency mappings, first an unilateral, half-plane filter with a given orientation is obtained. Using two such unilateral 2D filters with imposed orientation angles, a desired directional wedge filter is derived, with specified orientation and aperture angles. Its transfer function results directly in a factored form, which is an advantage in implementation. The resulted wedge filter is parametric and tunable, since the specified parameters occur in the final matrix form of the filter transfer function.

An analytical design procedure is described in this paper for a type of 2D recursive filter, with a frequency response elliptical or circular in shape. The design is based on a specially determined frequency mapping, applied to an digital prototype filter. This analytical design approach yields the transfer function of the desired 2D filter in a factored, closed form. Some efficient, accurate approximations are used, like Chebyshev-Pade method, without resorting to global optimization algorithms. The filter matrices are a convolution of smaller size matrices, an obvious advantage in implementation. Moreover, the obtained filter is tunable, since its coefficients depend on the specified orientation and bandwidth. As proven by given design examples, these 2D filters have a precise shape, with negligible distortions even near the margins of frequency plane, good selectivity and low order.

The design of adaptive finite impulse response filters is a linear optimization problem and the design of adaptive infinite impulse response (IIR) filters in the presence of observation noise is a nonlinear optimization problem. This paper considers the parameter estimation issues of an infinite impulse response (IIR) filter with colored noise which is treated as an autoregressive process. The key is to investigate novel estimation methods of an IIR filter with an autoregressive disturbance noise from the viewpoint of the observation data filtering. Firstly, we simply give the least mean square (LMS) algorithm for an IIR filter with autoregressive noise and derive a multi-innovation LMS (MI-LMS) algorithm for improving the parameter estimation accuracy. Secondly, we present a data filtering based LMS algorithm and a data filtering based MI-LMS algorithm for further improving the parameter estimation accuracy. The theoretical analyses show that the proposed algorithms are convergent and the simulation results indicate that the MI-LMS algorithm and the data filtering based MI-LMS algorithm are superior to the LMS algorithm and the data filtering based LMS algorithm in accuracy, respectively. The proposed methods in this paper have been extended to an IIR filter with autoregressive moving average noise. Finally, two simulation examples test the performances of the proposed algorithms.

This Letter deals with a practical signal processing problem where the filter is zero-phase and is specified by the frequency response. The authors show that if the signal is symmetrically extended, then the fast Fourier transform (FFT)-based algorithm can be efficiently implemented by using the discrete cosine transform without signal extension. They extend the proposed algorithm to 2D filters and show that computationally it is at least four times more efficient than the FFT-based algorithm. A practical application of the new algorithm is a fast Wiener inverse filter, which is used to estimate images taken under the condition of air turbulence.

We present a new optimization-based approach for synthesizing photonic infinite impulse response filters formed using microresonators. Taking into account the finite internal losses in these resonators, we cast the synthesis of filter coefficients as a semidefinite programming problem designed to restrict root-magnitudes set by the internal loss, while meeting filter-mask specifications. We provide a discussion on the formulation of the algorithm, and show how it can be used to design the optical components in a second-order unit cell. In addition, we provide an example of forming a fourth-order low-pass filters by cascading two unit cells. Our simulations show that fourth-order low-pass filters can achieve band-rejection ratios of 60 dB with integrated microresonators that possess an intrinsic quality-factor Q0 of ${\text{1.1}}\times{\text{10}}^5$ .

Digital systems are placed at the core of information technology and they are used extensively in electronics. The digital filter realization has become a central topic of signal processing studies. This paper presents a discrete IIR filter design method for approximate realization of fractional order continuous filters in digital systems. For this purpose, Fractional Order Darwinian Particle Swarm Optimization (FODPSO) method is modified to provide better fitting of a discrete IIR filter function to a fractional order continuous filter and we implemented a hybrid version of FODPSO method, where the initial particle generation is carried out by arithmetical candidate point selection technique of the Base Optimization Algorithm (BaOA). This modification expands the search range of the FODPSO and thus the optimized discrete IIR filter can provide better approximation to amplitude response of fractional order continuous filter functions. In the paper, several illustrative examples are presented to demonstrate the performance of proposed methods. (C) 2017 Elsevier Ltd. All rights reserved.

Design problem of infinite impulse response (IIR) filters is generally a non-linear optimization problem due to the presence of denominator polynomial. Additionally, the stability condition (positi...

In many applications of notch filters, high quality factor and short transient duration are simultaneously desired. Being contradictory in nature these two requirements pose design challenges. This paper presents an innovative application of a hyperbolic tangent sigmoid (HTS) function to vary the time-varying pole-radius (TVPR) of the pole-zero-constrained (PZC) IIR notch filter to optimally attain these two requirements together. Application of HTS function has allowed the pole-radius to maintain its desired minimum value during the initial phase of filtering, leading to faster transient suppression. This is followed by a steep rise in the pole-radius which allowed the notch filter to attain its desired quality factor soon after the transient suppression was achieved. Therefore, prime emphasis of the proposed notch filter design approach is on the significant reduction of the duration during which pole-radius makes a transition from its minimum to maximum designed values. The performance of proposed notch filter was assessed for transient suppression and selectivity responses in addition to removal of the power line interference from an ECG signal in the LabVIEW™ based simulation and hardware implementation environment. Based on significant improved performances over recent reported exponential TVPR PZC IIR notch filter in all the presented investigations, it is concluded that the proposed design is a better candidate for enhancing the post-transient performance of IIR PZC notch filter.

Digital filters are now key components in many modern digital systems. This paper proposed a novel evolutionary method to design structure-diversified digital filters. On the investigation of the existing evolution-based digital filter design methods, most state-of-the-art works concentrate on the evolution of appropriate transfer functions for digital filters. However, a transfer function is not equivalent to a practical digital filter that has proper structure and can be implemented by a hardware directly. Some researchers proposed a synthesis method to generate the structure of digital filter from a specified transfer function. However, this method needs an existing transfer function as the prior knowledge. Compared with existing works on the evolution of digital filters, the proposed method is novel at the following aspect: the proposed method can directly evolve the structure and parameters of digital filter without the pre-definition of the transfer function. The only prior knowledge we need is the specification of the design target, such as the frequency range of the passband and stop-band. In the experimental study, a significant characteristic is revealed that the proposed method is able to evolve structure-diversified filters with approximate frequency response. The proposed method is a prototype, and it is demonstrated to be a promising way of digital filter design.

Digital filters are generally designed by identifying the transfer functions. Most researches are focused on the goal of approaching the desired frequency response, and take less additional consideration of structure characteristics which can greatly affect the performance of the digital filter. This paper proposes a structure-evolution based optimization algorithm (SEOA) which allows the integrated consideration of structure issues and frequency response specifications in design stage. The method generates digital filter structures by a structurally automatic-generation algorithm (SAGA) which can randomly generate and effectively represent digital structures. The structures, seen as chromosomes, are evolved over genetic algorithm (GA) for the search of the optimal solution in structure space. They are evaluated according to the mean squared error (MSE) between the designed and the desired frequency responses. Simulation results validate that the algorithm designs diversified structures of digital filters and they meet target frequency specifications and structure constraints tightly. It is a promising way for optimized and automated design of digital filters.

We propose a neural network architecture, which operates on the raw speech signal, where the first layer contains a series of 1D time-domain filters. The output of this layer is fed to the second layer, which is a bank of 2D-convolution filters that capture the spectro-temporal modulations in the speech signal. The outputs of these two layers are concatenated, normalized and then fed to a feed-forward neural network to predict the senone posteriors, which are used for ASR decoding. During the training of the neural network, we have employed different strategies, where the 1D and 2D filters are initialized with (a) Gabor filters and (b) random values and the filter coefficients are either (a) allowed to be updated along with the other affine transform parameters of the network or (b) fixed during training. ASR experiments are conducted on 160 hours of Tamil speech data and the proposed architecture gives an absolute improvement in word error rate (WER) of 1.35% and 1.21% with respect to the neural network models trained on mel-frequency cepstral coefficients and log-filterbank energy features, respectively. We have also compared the performances of various strategies for filter initialization and training and reported the WERs.

In this paper we propose an efficient deep learning encoder-decoder network for performing Harmonic-Percussive Source Separation (HPSS). It is shown that we are able to greatly reduce the number of model trainable parameters by using a dense arrangement of skip connections between the model layers. We also explore the utilisation of different kernel sizes for the 2D filters of the convolutional layers with the objective of allowing the network to learn the different time-frequency patterns associated with percussive and harmonic sources more efficiently. The training and evaluation of the separation has been done using the training and test sets of the MUSDB18 dataset. Results show that the proposed deep network achieves automatic learning of high-level features and maintains HPSS performance at a state-of-the-art level while reducing the number of parameters and training time., Comment: Accepted for publication at WASPAA 2019, 5 pages, 5 figures

In this paper, a new multiplier-free transformation is proposed for the design of low complexity two dimensional (2D) finite impulse response (FIR) filters with improved circularity at wideband radii. By designing the 1D filter multiplier-free and using proposed multiplier-free transformation, a 2D circularly symmetric multiplier-free filter can be realized. Accuracy of the circular contour is measured based on contour approximation error. To prove the hardware efficiency of the proposed transformation, a 2D band-pass filter and a low-pass filter are designed and the overall complexity in terms of the number of multipliers required to implement the 2D filters is compared. From the results it is clear that the proposed transformation have good circularity at wideband radii and have less implementation complexity.

This paper proposes two new recursive filtering structures based on the nonlinear myriad operator. First, we develop the general class of recursive weighted myriad (RWMy) filters as a robust filtering structure against impulsive noise that includes, as particular cases, a normalized version of the linear infinite impulse response (IIR) filter, the recursive mode-type filter, and the non-recursive weighted myriad filter. Secondly, considering the fact that the additive noise that contaminates the previous filter's outputs is no longer impulsive, we introduce a novel class of recursive hybrid myriad (RHMy) filters whose structure gathers the advantages of both the weighted myriad and the weighted mean in a single cost function to be minimized. Some properties of the RHMy filter are derived and a fast algorithm to compute the RHMy filter output is proposed. Furthermore, adaptive algorithms for designing the proposed recursive structures, under the equation error formulation framework, are developed. Finally, extensive numerical simulations are shown to evaluate both the iterative update of the adaptive algorithms and the performance of the proposed recursive filters against impulsive noise.

Designing and implementing systems as an interconnection of smaller subsystems is a common practice for modularity and standardization of components and design algorithms. Although not typically cast in this framework, many of these approaches can be viewed within the mathematical context of functional composition. This paper re-interprets and generalizes within the functional composition framework one such approach known as filter sharpening, i.e., interconnecting filter modules which have significant approximation error in order to obtain improved filter characteristics. More specifically, filter sharpening is approached by determining the composing polynomial to minimize the infinity-norm of the approximation error, utilizing the First Algorithm of Remez. This is applied both to sharpening for FIR, even-symmetric filters and for the more general case of subfilters that have complex-valued frequency responses including causal IIR filters and for continuous-time filters. Within the framework of functional composition, this paper also explores the use of functional decomposition to approximate a desired system as a composition of simpler functions based on a two-norm on the approximation error. Among the potential advantages of this decomposition is the ability for modular implementation in which the inner component of the functional decomposition represents the subfilters and the outer the interconnection.

In adaptive control applications for noise and vibration, finite ımpulse response (FIR) or ınfinite ımpulse response (IIR) filter structures are used for online adaptation of the controller parameters. IIR filters offer the advantage of representing dynamics of the controller with smaller number of filter parameters than with FIR filters. However, the possibility of instability and convergence to suboptimal solutions are the main drawbacks of such controllers. An IIR filtering-based Steiglitz–McBride (SM) algorithm offers nearly-optimal solutions. However, real-time implementation of the SM algorithm has never been explored and application of the algorithm is limited to numerical studies for active vibration control. Furthermore, the prefiltering procedure of the SM increases the computational complexity of the algorithm in comparison to other IIR filtering-based algorithms. Based on the lack of studies about the SM in the literature, an SM time-domain algorithm for AVC was implemented both numerically and experimentally in this study. A methodology that integrates frequency domain IIR filtering techniques with the classic SM time-domain algorithm is proposed to decrease the computational complexity. Results of the proposed approach are compared with the classical SM algorithm. Both SM and the proposed approach offer multimodal vibration suppression and it is possible to predict the performance of the controller via simulations. The proposed hybrid approach ensures similar vibration suppression performance compared to the classical SM and offers computational advantage as the number of control filter parameters increases.

The application of two-dimensional (2-D) infinite impulse response (IIR) spatially-bandpass (SBP) filters as a digital beamformer for a wide spectrum of practical applications spanning wireless cognitive radio communications, doppler radar, and radio astronomy instrumentation is discussed. The paper starts with an introduction of the recently proposed 2-D SBP filter. The first application is a spectrum sensing scheme for dynamic spectrum access based cognitive radios. A 2-D IIR SBP filter is used in conjunction with a sub-Nyquist wideband signal reconstruction technique to achieve aperture-array directional spectrum sensing using sub-Nyquist sparse sampling based on the recently reported Eldar algorithm. The second application is related to wideband pulse and continuous-wave frequency modulated Doppler radar sensing. The SBP filter is integrated with a wideband radar back-end connected to an electronically-steerable aperture antenna. A a low-complexity directional localization algorithm is presented, which estimates the range and angle of a target scatterer with a signal to interference ratio improvement of 10 dB. We also present applications of 2-D IIR SBP in the fields of classification and remote sensing of unmanned aerial vehicles. Finally, a digital aperture-array wideband beamforming model using the 2-D IIR SBP filters is presented for radio telescope systems based on dense aperture arrays and time-domain beamforming. A well-known example is the study of pulsar astrophysics using a highly-directional aperture antenna system. The 2-D IIR SBP beamformer is simulated as the digital backend of the time-domain beamforming system with array signals synthesized using measured time-domain signatures from the Crab pulsar obtained from the GAVRT. The SBP filter shows a gain of 12.3 dB with an order of magnitude lower circuit complexity compared to traditional phased-array digital beamformers. To obtain comparable levels of SINR improvement, the wideband phased-array beamformers require 48-point FFTs per antenna. Assuming the optimum three real-multiplications per complex multiplication for the Gauss algorithm, it is discovered that the proposed 2-D IIR SBP beamformers are more than 97 % lower in digital multiplier complexity compared to traditional FIR phased-array FFT-beamformers.

Linear phase is an important characteristic of digital filters in many signal processing applications. In this paper, two iterative reweighted minimax phase error algorithms are proposed to design nearly linear-phase infinite impulse response (IIR) digital filters with prescribed or simultaneously minimized magnitude errors and preset transition-band gain. In each iteration of the algorithms, a weighted minimax phase error problem with a fixed weight function is firstly solved using a modified Gauss-Newton method with a variable step length, and the weight function of the phase error is then updated using the square root of a modified envelope of the group-delay error of the filter. With the proposed methods, both very small phase error and group-delay error have been obtained while meeting the requirements on the passband and stopband magnitude errors and the transition-band gain. Design examples demonstrate the effectiveness of the proposed methods and the excellent performance of the designed filters.

This paper presents the design method for Infinite Impulse Response (IIR) digital filter with the use of Real Coded Genetic Algorithm (RGA/RCGA). Generally, nonlinear and multimodal error surface is observed in case of digital IIR filter. Hence, to avoid problems such as local minima, global optimization techniques are required. This paper gives effective method to design digital IIR filters. This paper finds the optimum coefficients of IIR digital filter by using RGA. RGA works on real numbers and is a powerful global optimization algorithm. To obtain minimum transition band, this designing of low pass IIR digital filter is proposed. It is observed that the calculated values are more optimal than those which are obtained by FDA tool available for design of filter in MATLAB. The improved mean-square-error (MSE) is observed in simulation results for example taken. General Terms Digital filter design, optimization algorithm, Frequency response, filter coefficients

This paper presents a technique to estimate the temperature of each power electronic device in a thermally coupled, multiple device system subject to dynamic cooling. Using a demonstrator system, the thermal transfer impedance between pairs of devices is determined in the frequency domain for a quantized range of active cooling levels using a technique based on pseudorandom binary sequences. The technique is illustrated by an application to the case temperatures of power devices. For each cooling level and pair of devices, a sixth-order digital IIR filter is produced, which can be used to directly estimate temperature from device input power. When the cooling level changes, the filters in use are substituted and the internal states of the old filters are converted for use in the new filter. Two methods for filter state conversion are developed—a computationally efficient method, which is suited to infrequent changes in power dissipation and cooling, and a more accurate method, which requires increased memory and processing capacity. Results show that the temperature can be estimated with low error using a system which is suitable for integration on an embedded processor.

This paper proposes an integrated optimization technique which combines the features of the cat swarm optimization (CSO) algorithm with the traditional differential evolution (DE) algorithm and applies it for the optimal design of digital infinite impulse response (IIR) filters. Traditional design methods treat the digital IIR filter design as a single-objective optimization problem by taking into account the minimization of magnitude response error only and lack in considering the linear phase response error and the order of the filter. The aim of this paper was to design an IIR filter in multi-objective framework by equally considering the minimization of magnitude response error, the linear phase response error and the order of the filter. Firstly, the CSO algorithm is applied for digital IIR filter design. In order to start with a better solution set, the opposition-based learning strategy is then incorporated. To further improve the performance of CSO for designing stable digital IIR filters, the DE optimization algorithm is combined with CSO hence producing an integrated algorithm called multi-objective cat swarm and differential evolution algorithm (MOCSO-DE) which has the capability to explore and exploit the solution search space locally as well as globally. The developed integrated algorithm is effectively applied for the designing of the digital IIR low-pass (LP), high-pass (HP), band-pass (BP) and band-stop (BS) filters. To evaluate the effectiveness of the developed integrated algorithm, the computational results are compared with some well-established algorithms and it is observed that the developed algorithm is superior or at least comparable to other algorithms in getting better magnitude response and linear phase response together with lowest filter order and can also be implemented for the higher-order filter designs.

Adaptive infinite impulse response (IIR) filter has been preferably used in modeling real-world systems because of its reduced number of coefficients and better performance over finite impulse response (FIR) filter. However, it is still a challenging problem how to design an optimal IIR filter due to its nonlinear and multimodal error surface. This paper introduces membrane computing to design an optimal IIR filter and proposes a novel design method that employs a tissue-like membrane system with ring-shaped topology structure. A modification of the different evolution mechanism was developed as evolution rules for objects according to the special membrane structure. Under the control of the object's evolution-communication mechanism, the tissue-like membrane system can effectively find the global minima for an IIR filter design problem. The proposed method was evaluated over several benchmark IIR systems and was compared with several state-of-the-art evolutionary algorithms. The experimental results show that the proposed method has better identification performance compared with other algorithms.

Objectives: To design a stable Infinite Impulse Response (IIR) filter which minimizes the magnitude response. Methods/Statistical Analysis: The problem is perceived as a problem of optimization with many objectives. An efficient algorithm, namely Non-dominated Sorting Genetic Algorithm-II (NSGA-II), is used to solve it. To get assurance of stability, the poles of the filter are maintained inside the unit circle. Findings: As results show, the algorithm is well suited for the problem. Especially, it is very easy to design stable Low Pass (LP) and High Pass (HP) filters using this algorithm. Band Pass (BP) and Band Stop (BS) filters can also be designed by this algorithm, but sometimes it takes large number of iterations to converge. However, in offline applications, time is not an issue. Application/Improvement: The algorithm is an improvement over other researchers’ works which only minimize the magnitude response error treating the problem as a single objective one.

In this paper, we present a general approximation for 2D filters by using only power-of-two terms. This enables to easily implement these filters in electronic devices such as FPGA and ASIC just by using simple hardware shifters and adders/subtractors. Consequently, no division and no multiplication operators are required, which can reduce the memory and the power needed for computing operations such as convolution. Instead of using only additions and power-of-two terms for representing a number like in the standard binary decomposition, our model also uses subtractions for representing and approximating numbers. In addition, we propose a binary tree structure for computing a minimal representation in power-of-two terms in such a way that hardware shifters used for performing a convolution with a low-pass filter for example are well reduced to their minimum. Based on some experiments performed for contrast enhancement, which is a common image processing operation, we have noticed that good results can be obtained using our approximation in terms of image quality, hardware resources, and power consumption when compared to some other binary representations.

In this paper, a population-based robust enhanced teaching--learning-based optimization (ETLBO) algorithm with reduced computational effort and high consistency is applied to design stable digital infinite-impulse response (IIR) filters in a multiobjective framework. Furthermore, a decision-making methodology based on fuzzy set theory is applied to handle nonlinear and multimodal design problems of the IIR digital filter. The original teaching--learning-based optimization (TLBO) algorithm has been remodeled by merging the concepts of opposition-based learning and migration for the selection of good candidates and to maintain diversity, respectively. A multiobjective IIR digital filter design problem takes into consideration magnitude and phase response of the filter simultaneously, while satisfying stability constraints on the coefficients of the filter. The order of the filter is controlled by a control gene whose value is also along with filter coefficients, to obtain the optimum order of the designed IIR filter. Results illustrate that ETLBO is more capable and efficient in comparison to other optimization methods for the design of all types of filter, i.e. high-pass, low-pass, band-stop, and band-pass IIR digital filters.

The paper deals with method of designing of a digital equalizer for analog signal path with ADC and low-order low-pass filter on its front. The correction effect is achieved through use of the IIR digital filters, designed in equalization purposes of the magnitude frequency response. The application of an equalizer allows to gain high attenuation in cutoff band and expand the signal bandwidth. Simultaneously it allows using low order anti-aliasing analog filter on ADC front. The equalizer can operate as a separate device or could be build-in signal processor (or in any other signal processing ASIC). In the first case it could be prepared as a module, implemented in FPGA device.

This brief proposes an efficient very-large-scale integration architecture for folded configurable infinite-impulse response (IIR) filter design, which is used in modern real-time digital signal processing applications such as loudspeaker equalization. The proposed configurable sixth-order IIR filter is designed with three cascaded second-order IIR filters, and the same is used to perform one sixth-order or three second-order or one fourth-order and one second-order IIR filter operations in parallel, where floating-point multiply–accumulate circuit (MAC) is used to design each second-order IIR filter. The proposed sixth-order IIR filter achieves a 58.4% reduction in energy per operation compared with conventional MAC-based architecture using 45-nm technology.

In this paper, an efficient approximation of the ideal function of a low-pass filter is proposed. The approximation uses a function with an S-shaped graph with variable gradient. The theory is applied to 2D FIR filter design. The proposed method is simple and performs fast. It has been shown that the offered approximation has better properties than the minimax approximation. Consequently, the designed 2D filters possess improved selectivity.

This paper presents an analytic design technique for 2D IIR filters with elliptical symmetry, which have useful applications in image processing. The design is based on efficient elliptic digital filters, regarded as 1D prototypes, to which specific complex frequency transformations are applied; this allows to obtain directly a factored form of the transfer function for the 2D elliptically-shaped filter. The design procedure uses accurate approximations, but no global optimization algorithm. Finally the 2D filter matrices are obtained. The filter is adjustable, its coefficients depending explicitly on the specified orientation and bandwidth. Another advantage is versatility, since the design need not be resumed each time from the start for various specifications. The designed 2D filters have an accurate elliptical shape with low distortions even close to the frequency plane margins, being efficient, of high selectivity and low order.