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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 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.

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.

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.

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.

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.

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 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, 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.

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.

This work presents an analytical design method for a category of two-dimensional IIR filters, specifically with circular symmetry, which have useful applications in image processing. The design is based on efficient digital elliptic filters, used as 1D prototypes, to which some complex frequency transformations are applied; this allows to obtain directly a factored form of the transfer function for the 2D circularly-symmetric filter. The design procedure involves some accurate approximations, but no global optimization algorithm. As a result, the 2D filter matrices are derived. The filter has the advantage of being adjustable, as its bandwidth is determined by a parameter which appears in the filter coefficients. The designed 2D filters have an accurate circular shape, exhibiting very low distortions even near the margins of the frequency plane, and are efficient, of high selectivity and relatively low order. The designed filters can be used as a bank of circular filters, useful in a multi-resolution analysis of an image. To prove their filtering capabilities, simulation results are provided for circular filtering of a biomedical image, namely a retina angiogram.

2-D maximally flat diamond-shaped half-band linear phase FIR digital filters are used in sampling structure conversion. In some cases, this filter is expected to have different filter order for each dimension. However, the conventional methods can realize such filters only if difference between each order is 2, 4 and 6. In this paper, we proposed a closed-form transfer function of 2-D low-pass maximally flat diamond-shaped half-band FIR digital filters with arbitrary filter orders. The constraints to treat arbitrary filter orders are firstly proposed. Then, a closed-form transfer function is achieved by using Bernstein polynomial.

An ultra-low complexity three-dimensional (3-D) linear-phase infinite-extent impulse response (IIR) velocity filter is proposed for attenuating moving artifacts in videos while enhancing objects moving on smooth approximately-linear trajectories. The proposed 3-D linear-phase IIR velocity filter consists of an ultra-low complexity 3-D wide-angle linear-phase IIR cone filter bank between two two-dimensional (2-D) spatial variable-shift filters. The ultra-low complexity 3-D wide-angle linear-phase IIR cone filter bank consists of a one-dimensional (1-D) temporal modified discrete Fourier transform filter bank and 2-D spatial allpass, IIR highpass and allstop filters. A typical 3-D linear-phase IIR velocity filter of order $$4\times 4\times 510$$4×4×510, applied to enhance a heavily corrupted test video signal, requires only 26 real multiplications and 60 real additions to process a sample and provides a scene-complexity-independent signal-to-interference-and-noise ratio improvement of 13.86 dB. The proposed 3-D linear-phase IIR velocity filter is employed to attenuate sunlight flicker patterns in shallow underwater videos, and experimental results are presented to confirm the effectiveness of the proposed method and its robustness to motion estimation errors.

This paper presents a novel approach for the design of two-dimensional (2D) Finite Impulse Response (FIR) filters. The design of FIR filters is generally non-differentiable, multimodal and higher dimensional; especially for 2D filters. A large number of filter coefficients are optimized either using constrained or unconstrained optimization approach. Due to the large number of constraints, traditional design methods cannot produce optimal filters required for some crucial applications. This makes meta-heuristic algorithms as good alternatives for addressing such constraints more efficiently. In order to improve the performance of 2D filters, we propose an Accelerated Artificial Bee Colony algorithm, termed as AABC algorithm. The earlier reported ABC based methods perform the modification of a single parameter of the solution in each cycle. But in this proposed AABC algorithm, we have adopted multiple parameters change of search equation at each step. This in turn improves the convergence speed of the algorithm by three times than the classical ABC algorithm and two times with respect to recently developed CABC method. In order to achieve better exploration behaviour of abandoned bees, we have also introduced a change during the initialization strategy of scout bees in the proposed AABC algorithm. The efficiency and robustness of the proposed algorithm are demonstrated by comparing its performance with classical Genetic Algorithm (GA), Particle Swarm Optimization , ABC and CABC methods.

A new greedy search method is applied in this paper to design the optimal digital infinite impulse response (IIR) filter. The greedy search method is based on binary successive approximation (BSA) and evolutionary search (ES). The suggested greedy search method optimizes the magnitude response and the phase response simultaneously and also finds the lowest order of the filter. The order of the filter is controlled by a control gene whose value is also optimized along with the filter coefficients to obtain optimum order of designed IIR filter. The stability constraints of IIR filter are taken care of during the design procedure. To determine the trade-off relationship between conflicting objectives in the non-inferior domain, the weighting method is exploited. The proposed approach is effectively applied to solve the multiobjective optimization problems of designing the digital low-pass (LP), high-pass (HP), bandpass (BP), and bandstop (BS) filters. It has been demonstrated that this technique not only fulfills all types of filter performance requirements, but also the lowest order of the filter can be found. The computational experiments show that the proposed approach gives better digital IIR filters than the existing evolutionary algorithm (EA) based methods.

The proposed research work on the topic Infinite Impulse Response "IIR Structure and Its Application" is basically state space representation for the digital filter of different form obtained from analog filter and transformation to digital one. In the normal course of analysis the digital filter transfer function are realized in different forms using time delay elements and multipliers. This realization can be eased if digital filter are represented in state space techniques opening a new field for computation analysis. This aspect has been incorporated in the proposed research work things outlining the introduction of IIR filter and different structure including ladder and wave structure realization, state space description of IIR filter is presented in detail including the normal form which has complex structure but simple form of state equation. IIR filter design is based on state space technique using Lattice structure. The generalized technique of state space equation realized from general form of digital filter transfer function has been developed then the technique is demonstrated using differential form of various filter like LPF, HPF and BPF for the required order of analog filters. Statistical analysis of digital filter like round off error and dynamic scaling has been incorporated, where the two direct computes have been lumped together in the common state space representation. Autocorrelation and uncorrelation between noise and input samples gives round off noise and dynamic scaling give expression for the factor forms, round off error and dynamic range. This aspect on statistical analysis of digital filter has opened a new field for research.

In order to implement fractional order transfer function (FOTF) model in digital systems, transfer function discretization methods are developed to obtain discrete filters that provide acceptable amplitude or phase response approximations to FOTFs in operating frequency ranges. This paper presents an approach to improve discrete IIR filter approximations to FOTFs according to application requirements by using Particle Swarm Optimization (PSO). For this purpose, particles of PSO are initialized around the solution of a well-known analytical approximation method and then, these particles search stable IIR filter solutions in the filter design space to improve magnitude and phase response approximation performance over a desired frequency region. Specifically, PSO algorithm is used to fine-tune results of Tustin recursive discretization method according to a weighed multi-objective cost function. This cost function is expressed as the weighted sum of magnitude and phase response matching objectives with a frequency weighting. The frequency weighting is employed for prioritization of frequency regions in optimization. The proposed method also ensures the stability of optimized IIR filter approximations by enforcing particles to move into stable filter solution regions of the search space. This design approach can contribute to the digital realization of fractional order systems for practical applications.

This paper presents a design method of the audio digital appodizing filters, by using B-spline and continuous polynomial functions in the transition frequency band. It is known that an appodizing filter can be used to control the time smear for a recording and a reproducing chain. The choice of the frequency response above 20 kHz can reduce the time extent of the impulse response. In the proposed approach, the appodizing filter is optimized with the novelty of using spline functions and continuous polynomials in the transition band. Several design examples are included to illustrate the proposed algorithm.

In order to attenuate the added noise by electric network used by myoelectric signals acquisition equipment, in this research work, it is developed an IIR digital filter implemented on FPGA. This filter removes a specific spectra frequencies without adding noise to the signal, which allows a better performance in the usage that is given to the signals. The filter coefficients are taken and proved from MATLAB functions. Then, those are transferred to the filter design in the FPGA. For this purpose, it was used a Basys 3 of Xilinx Artix-7 family and the design was implemented in Vivado Design Suite. The filtered signal does not present additional noise and it was eliminated the desired frequency.

A relatively recent innovation in the domain of digital filtering has been the introduction of signal processing applications with effective power utilization. No scope towards the effective and efficient architecture realization with existing part of literature, and hence investigation is made and is confined with cascade form of filter design. In this paper, architectures are realized based on common set of specifications to arrive at the high performance recursive filter for low power applications using Xilinx System Generator. Infinite Impulse Response (IIR) filters can be realized in many forms those are Direct form-I, Direct form-II, Cascade, parallel form. All these structures provide a space for selection of an appropriate architecture for reduction of power consumption and improvement in speed of digital filters. In this particular work, a 5th order low pass IIR filter is realized in Direct form-I, Direct form-II, Cascade form (Direct form-I/ Direct form-II) as an example of the methodology in a Xilinx FPGA device. Also corresponding power analysis was performed and finally concluded that cascade (Direct form-I) realization is the best technique to implement higher order IIR filters when power is a main constraint, cascade (Direct form-II) technique is best with area and speed as constraints.

The evolution of multi-feature portable devices with high speed processors and with drastic growth in component density turns the designer attention towards power aware design schemes. In low power VLSI designs an adaptive filter can obtain a reduction in terms of area and power consumption. A system with a linear transfer function controlled by variable parameters and a means to adjust those parameters according to an optimization algorithm is called adaptive filter. The Least Mean Square (LMS) filter is one of adaptive filters type which is used commonly, because of its simplicity and also because of its satisfactory convergence performance. The current IIR adaptive filter uses LMS to reduce area-delay product and energy-delay product. To reduce this delay one can implement filter in pipelined structure. Shift-add tree efficiently minimizes the critical path and silicon area without increasing the number of adaptation delays. The structure of IIR adaptive filter designing is done by using two main blocks: IIR block and new coefficients block (weights block). Weights block consists of series of partial product generators and shift/add tree. Partial product generators has 2 to 3 decoders and AND/OR cells. Weights block performs multiply accumulate operations. Filter block depends upon on the new filter coefficients obtaining from weights block. The proposed filter is designed in MATLAB (2013a) for its performance characteristics and its constraints are verified using XILINX (verl4.7) implemented on FPGA.

The chapter opens with the discussion of infinite impulse response filters. The complex topic of IIR filter is more intricate than FIR filter and it probes deeper linking fundamental concepts of DSP. It leads to discussion of bilinear transform which specifies the filter response sand design of an analog filter using analog filter techniques. It also shows the mapping techniques in different domains and the responses from each domain and discusses the characteristics and method of frequency preparing techniques which prepares an analog filter and ends with the notes on how analog filter which itself is a complex subject converts into a digital IIR filter. It delves deeper into the subject matter to use the software programs which can help in designing and convert them into a digital IIR design.

Filter design is one of the perennial topics in signal processing. FIR filters are often preferred for their simple implementation and robustness, so they are an appropriate subject for this first chapter devoted to applications. All the design methods presented here are based on positive trigonometric polynomials and the associated optimization tools; they are optimal for 1D filters and practically optimal for 2D filters. This is in contrast with many other methods that approximate the optimum, either from a desire to obtain rapidly the solution or from a lack of instruments that give optimality. We treat here three basic design problems: 1D filters, 2D filters, and deconvolution. For each problem, we consider several design specifications. In the 2D (and multidimensional) case, at the time of apparition, the methods were very different from those present in the literature.

The design of two-channel quadrature mirror filter banks can be constructed based on real infinite impulse response (IIR) all-pass digital filters without yielding magnitude distortion. The design problem is first formulated as a phase optimization using IIR all-pass filters in the least-squares sense. Then the nonlinear phase optimization is further converted into solving an eigenproblem of an appropriate real, symmetric, and positive-definite matrix. In this paper, the minor component analysis algorithm based on the neural learning rule is exploited to the design of eigenfilter. When the learning algorithm achieves convergence, the weights of the neural system approximate the smallest eigenvector, which are the optimal filter coefficients of the IIR all-pass filters. The simulation results confirm that the proposed neural-based method can achieve accurate performance by incorporating the simple neural model.

This paper addresses, for the first time, the digital representation of spectrally periodic signal-interference microwave passive filters. Starting from the theoretical rational transfer function of a synthesized transmission-line signal-interference analog filter, the real-valued coefficients of its digital-domain filter counterpart are derived. This discrete-time formulation for this type of microwave filters allows to clarify some confusing concepts into them, such as filter order. Moreover, some particular phenomena observed in associated experimental proof-of-concept planar prototypes, such as the appearance of out-of-band/spurious resonance peaks, are also explained by this study as zero-pole quasi-cancellations. In addition, it is demonstrated here that the use of the adjective “transversal” for this class of microwave passive filters could be no rigorous as it is understood in a digital sense since its discrete-time modeling commonly obeys an infinite-impulse-response structure. For validation, the expounded theoretical framework is applied to three examples of signal-interference passive filters exhibiting quasi-elliptic-type single-passband, six-passband, and low-pass responses.

Second-order IIR low-pass filter is widely used in digital signal processing. A fast filter algorithm without multiplication is proposed for it in this paper. A configuration method for the filter coefficient of fast algorithm is put forward, considering the characteristic of second-order IIR low-pass filter coefficient and the filter’s mathematical model. A performance analysis of fast second-order IIR low-pass filter without multiplication is shown in the paper, and the performance of the fast filter is shown by example using MATLAB simulation. What’s more, the algorithm’s rapidity is verified by an implementation of the filter on FPGA, which turns out that fast filtering algorithm takes only 54.7% of common algorithm’s operation time to realize the same filer function.

A solution methodology for the design of digital infinite impulse response (II R) filter considering multiple conflicting objectives has been proposed. The nucleus of the method is that multiple objectives can be attuned suitably, to optimize the performance in pass bands, stop bands and transition bands of IIR digital filters. The p roposed method uses multiobjective optimization approach for designing stable IIR filter using real-coded genetic algorithm (RCGA). Digital IIR filters are designed by minimizing magnitude response and phase response simultaneously, using weighted sum approach. The value of weights are searched using RCGA along with filter coefficients thus assigning different weight vector to each indiv idual population thereby finding multiple pareto-optimal solutions in one simulation run. The order of the filter is controlled by a contro l gene whose value is also optimized along with the filter coefficients to obtain optimum order of designed IIR filter. The compu tational experiments show that the proposed approach gives better digital IIR filters than the existing genetic algorithm based methods.

Compared to time-interleaved ADC system, the performance of frequency-interleaved ADC (FIADC) system is extremely sensitive to the parameter uncertainties of the analog analysis filters. In this paper, a new method is launched to estimate the amplitude and phase responses of the analog analysis filters, which will help us grasp the actual filter status in real applications. Then, two algorithms are presented to obtain the digital synthesis filters aiming at minimize the reconstruction error. Design example and verification results show that the analysis filters can be estimated effectively and the designed synthesis filters meet the need of the FIADC system.

This paper presents a novel, control parameter independent evolutionary search technique known as Seeker Optimization Algorithm (SOA) for the design of a eighth order Infinite Impulse Response (IIR) Band Pass (BP) filter. A new fitness function has also been adopted in this paper to improve the stop band attenuation to a great extent. The performance of the SOA based IIR BP filter design has proven to be much superior as compared to those obtained by real coded genetic algorithm (RGA) and standard particle swarm optimization (PSO) in terms of highest sharpness at cut-off, smallest pass band ripple, highest stop band attenuation, smallest stop band ripple and also the fastest convergence speed with assured stability recognized by the pole-zero analysis of the designed optimized IIR filter.

This paper describes a method for implementing a digital Infinite Impulse Response (IIR) filters using different registered adders and shift method to improve occupied area and delay. Canonical Signed Digit (CSD) representation for defined filter coefficients has been extensively used to reduce the number of adders. The method using different adders is effectively applied to a four-order IIR filter. The performance of IIR filter using parallel prefix adders is compared with the filter using Ripple Carry Adder. Number of additions has been reduced to 33% by using CSD representation as compared to Binary representation. The proposed IIR filters are synthesized and implemented using Xilinx ISE Simulator. The designs perform significantly better than conventional IIR filters.

In this paper the AC power 50Hz power interference, we use IIR digital notch filter method for industrial frequency interference filter. From the design of IIR digital filter method proceed with, on the IIR digital notch filter simulation, the algorithm deduced, on the fixed-point DSP programming method and overflow handling problems made elaborate incisively, and in digital audio signal processing system has been applied.

The paper develops a technique for the robust and stable design of digital infinite impulse response (IIR) filters. As the error surface of IIR filters is generally multi-modal, global optimization techniques are required to design efficient digital IIR filter in order to avoid local minima. In this paper a real-coded genetic algorithm (RCGA) with arithmetic- average-bound-blend crossover and wavelet mutation is applied to design the digital IIR filter. A multicriterion optimization is employed as the design criterion to obtain the optimal stable IIR filter that satisfies the different performance requirements like minimizing the Lp-norm approximation error and minimizing the ripple magnitude. The proposed real-coded genetic algorithm is effectively applied to solve the multicriterion, multiparameter optimization problems of low-pass, high-pass, band-pass, and band-stop digital filters design. The computational experiments show that the proposed method is superior or atleast comparable to other algorithms and can be efficiently used for higher order filter design.

A new procedure for design of linear phase IIR notch filters is presented in this paper. Resulted filter is realized using parallel connection of two IIR all-pass filters with approximately linear phase. Adequate amplitude characteristic is obtained by approximation of all-pass filter phase. Amplitude characteristic satisfies all prescribed demands but it is not equiripple no matter both all-pass filters have equiripple phase. Algorithm exhibits fast convergence and easy initial values determination.

The research on optimal design of infinite-impulse response (IIR) filter design based on various optimization techniques, including evolutionary algorithms (EAs), has gained much attention in recent years. Previously, the parameters of digital IIR filters are encoded with floating-point representations. It is known that a fixed-point representation can effectively save computational resources and is more convenient for direct realization on hardware. Inherently, compared with the floating-point representation, the fixed-point representation would make the search space miss much useful gradient information and therefore, surely rises new challenges for continuous EAs. In this paper, we first analyze the fitness landscape properties of optimal digital IIR filter design. Based on the fitness landscape investigation, a two-stage ensemble evolutionary algorithm (TEEA) is applied to digital IIR filter design with fixed-point representation. In order to fully evaluate the performance of TEEA, we experimentally compare it with five state-of-the-art EAs on four types of digital IIR filters with different settings. Based on the experimental results, we can conclude that TEEA has higher convergence speed, better exploration, and higher success rate. In order to benchmark TEEA further, we apply it to some more difficult problems with shorter word length or higher order. We can find that TEEA can provide satisfying performance on these hard tasks as well.

In this paper for implementation of IIR digital filters, it is offered to use structures, which have a number of degrees of freedom significantly more than a number of degrees of freedom of transfer function. Such redundancy allows reducing a length of a fractional part of the filter coefficients without loss of accuracy of transfer function implementation.

A competent architecture for IIR filter is designed. It is configured and folded, which will be used in the real time applications like loud speaker and equalization of digital signal processing. A basic feature of digital signal processing is filtering. Filtering is a choosy system which passes an assured choice of frequency and attenuating the others frequency. Digital filtering is a prevailing sector of DSP allied works. A system of digital filter performs mathematical operations on a sampled or discrete time variant signal to contract or improve certain aspects of that signal. The configurable folded IIR filter for sixth order is designed using three series of second order IIR filter. This IIR filter architecture is used to carry out three second order or a one sixth order. It can be also used to execute one fourth order and one second order in parallel according to the requirement where, each second order IIR filter is designed using multiply accumulate circuit which as floating point. Here pipelining of IIR filter for second order is proposed to increase the throughput by reducing the critical path delay. The proposed sixth order IIR filter using three second order IIR filter with pipelining achieves 39.7% of increased throughput and it operates at high frequency of 85.068MHz compared with conventional MAC based architecture.

As a basic function unit of digital signal processing, digital filter design is the main subject of research in the field of digital signal processing, it is widely used in the field of communication, radar and so on. The traditional design method is difficult to satisfied high performance requirements of digital filter. A kind of simplified artificial fish swarm algorithm is introduced into optimize the design of digital filter. The effectiveness and practicability of the presented method are verified with simulation experiments. The designed IIR digital filter has little pass-band fluctuation, smaller stop-band and more attenuation. It means that that the proposed IIR digital filter design method based on simplified artificial fish swarm algorithm is effective.

This paper is on the use and performance of M-path polyphase Infinite Impulse Response (IIR) filters for channelisation, conventionally where Finite Impulse Response (FIR) filters are preferred. This paper specifically focuses on the Discrete Fourier Transform (DFT) modulated filter banks, which are known to be an efficient choice for channelisation in communication systems. In this paper, the low-pass prototype filter for the DFT filter bank has been implemented using an M-path polyphase IIR filter and we show that the spikes present at the stopband can be avoided by making use of the guardbands between narrowband channels. It will be shown that the channelisation performance will not be affected when polyphase IIR filters are employed instead of their counterparts derived from FIR prototype filters. Detailed complexity and performance analysis of the proposed use will be given in this article.

In almost all the digital filtering applications the digital infinite impulse response (IIR) filters are preferred over finite impulse response (FIR) filters because they provide much better performance, less computational cost and have smaller memory requirements for similar magnitude specifications. However, the digital IIR filters are generally multimodal with respect to the filter coefficients and therefore, reliable methods that can provide global optimal solutions are required. The artificial bee colony (ABC) algorithm is one such recently introduced meta-heuristic optimization algorithm which has proven to be more effective than other population based algorithms. But in some cases it shows insufficiency while searching the solution space resulting in a weak exchange of information and hence is not able to return better solutions. To overcome this deficiency, the opposition based learning strategy is incorporated in ABC and hence a modified version called oppositional artificial bee colony (OABC) algorithm is proposed in this paper. Duplication of members is avoided during the run which also augments the exploration ability. The developed algorithm is then applied for the design of optimal and stable digital IIR filter structure where designing of band-pass filter is carried out. To check the effectiveness of OABC, the results are compared with some well established filter design techniques and it is observed that in most cases OABC returns better or atleast comparable results.

Stochastic computing (SC) has received much recent attention due to its inherent fault-tolerance and low implementation cost compared to binary radix representations. SC has been proposed for various signal processing applications such as digital filters. The prior art in stochastic FIR filters can accurately implement the desired filtering function for low-order filters, however, their accuracy degrades as the filter order increases. Moreover, stochastic IIR filters demonstrate high hardware complexity and degraded accuracy. In this paper, we propose an architecture for high-order FIR filters with negligible accuracy loss compared to fixed-point implementation. The proposed architecture requires fewer random number generators. We also describe a novel cascaded second-order direct-form II structure for IIR filters. The implementation results of the proposed design show an improvement in latency and hardware complexity compared to the stochastic architectures reported to date.

We consider software-hardware implementation of a digital filter (FIR-filter) using the residue number system and scaling of output samples of each Alter channel. It is shown that scaling leads to a significant reduction in instrumental and temporal costs.

The problem of optimal high-frequency noise suppression and low-frequency signal transmission in sampled sensor systems is considered in this paper. Low-delay digital filters with linear phase and unity magnitude at the dc limit (i.e., maximally flat) are of particular interest. Savitzky-Golay smoothers with an infinite impulse response (IIR) are introduced and their properties are explored. The filter coefficients are derived via regression analysis using orthogonal Laguerre polynomials in the time domain. A generalized form with a shape parameter included in the error-weighting function is proposed. This extension may be used to further reduce the white noise gain of the filter. A design process that determines the optimal position of the repeated real poles, either to minimize the white noise gain, or to maximize the high-frequency attenuation, for a specified low-frequency group delay, is discussed. An alternative process for the design of a generic class of maximally flat repeated-pole filters is also presented. This allows colored noise to be handled and/or additional frequency-domain constraints, such as Nyquist flatness, to be applied. Refereed/Peer-reviewed

Digital Signal Processing (DSP) , there two types of filters are used to perform the filtering operations and they are the Infinite Impulse Response (IIR) filter and the Finite Impulse Response (FIR) filter. The present output sample of an IIR filter depends on the present input samples, past input samples and past output samples, i.e IIR filter is of recursive type. Now to design the Digital IIR filter, the coefficients are essentially required. There are a numbers of techniques available for designing the IIR filter. In this paper, the design and determination of the IIR filter coefficients are introduced using computer based approach. The program based on the algorithm proposed in this paper is simulated in Matlab which provides with the satisfactory results.

A method for design of linear phase notch IIR filters is presented in this paper. The filter is realized in the form of a parallel connection of two all-pass sub-filters. In order to achieve the resulting filter with an approximately linear phase in the pass-band, the applied all-pass sub-filters should be also with a linear phase. The desired amplitude characteristic of a resulting filter is obtained by all-pass sub-filter phase approximation. It can be achieved by applying either a pure delay or an IIR all-pass filter in one branch. If a pure delay is positioned in one branch, equiripple phase of all-pass sub-filter from the other branch is guaranteed for an equiripple amplitude characteristic of the resulting filter. Efficiency of the proposed algorithm is demonstrated on a few examples. The algorithm exhibits a fast convergence and an easy determination of initial values. In the case where IIR all-pass sub-filters are placed in both branches, the resulting amplitude characteristic satisfies all the prescribed demands, but the amplitude characteristic is not equiripple even when both all-pass sub-filters have equiripple phase.