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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.

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.

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 sparse coding approaches, which learn over-complete bases for efficiently representing a given set of data, are being extensively studied for various image analysis tasks. However, since sparse analysis of individual bands does not consider inter-spectral characteristics, adaptation of these approaches to hyperspectral domain has been quite limited. In this regard, we investigate convolutional frameworks for simultaneously learning sparse codes and dictionaries so as to efficiently represent the spectral–spatial characteristics of hypercubes. This study also reviews prominent convolutional sparse coding algorithms relevant to hyperspectral datasets. Unlike conventional approaches, in order to address the issues due to huge spectral dimension and high inter-band correlation, the proposed approaches implement sparse coding in a convolutional encoder–decoder framework. Two architectures, one based on shrinkage thresholding algorithm and other based on structured sparse regularization, are proposed. These architectures adopt 3D convolutions in such a way as to model both spectral and spatial features. Although Architecture-1 gives better results than other prominent approaches, its accuracy deteriorates with increase in spectral dimension of input. This can be attributed to the bottleneck due to shrinkage thresholding operation. To address the issue, Architecture-2 adopts structured sparse regularizations over filter weights and feature tensors. Results indicate that the proposed approaches achieve significant improvement in reconstruction accuracy when compared to the existing approaches. The frameworks are also evaluated with respect to super-resolution and dimensionality reduction of hyperspectral datasets. From different experiments, it is observed that the simultaneous usage of 3D and 2D filters along with sparse regularizations significantly improve learning capability of the networks.

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.

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.

Scene refocusing beyond extended depth of field for users to observe objects effectively is aimed by researchers in computational photography, microscopic imaging, and so on. Ordinary all-in-focus image reconstruction from a sequence of multi-focus images achieves extended depth of field, where reconstructed images would be captured through a pinhole in the center on the lens. In this paper, we propose a novel method for reconstructing all-in-focus images through shifted pinholes on the lens based on 3D frequency analysis of multi-focus images. Such shifted pinhole images are obtained by a linear combination of multi-focus images with scene-independent 2D filters in the frequency domain. The proposed method enables us to efficiently synthesize dense 4D light field on the lens plane for image-based rendering, especially, robust scene refocusing with arbitrary bokeh. Our novel method using simple linear filters achieves not only reconstruction of all-in-focus images even for shifted pinholes more robustly than the conventional methods depending on scene/focus estimation, but also scene refocusing without suffering from limitation of resolution in comparison with recent approaches using special devices such as lens arrays in computational photography.

There are two major types of digital filters in terms of structure: infinite impulse response (IIR) and finite impulse response (FIR). Digital IIR filters often provide a much better performance and less computational cost than FIR filters and have become the target of growing interest. Since the problem of the error surface of designing digital IIR filters is generally nonlinear and multimodal, global optimization techniques are required in order to avoid local minima. In this paper, an evolutionary method has been proposed to design digital IIR filters. This method is based on Imperialist Competitive Algorithm (ICA) and by adding a step to the existing steps of ICA, performance of it has been improved in searching solution space and convergence to the global minima. Obtained results from simulation using proposed method and other algorithms show that the proposed method is suitable for designing digital IIR filter.

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.

IIR implementation of filters exhibiting critical monotonic amplitude characteristic (CMAC) in the pass-band is introduced for the first time. After short description of the CMAC filters in the s -domain and discussion of the choice between FIR and IIR filters, IIR filters will be adopted and the bilinear transform will be chosen for transformation of the analog into digital transfer functions. Parallel realization of the IIR filter will be enabled by proper preparation of the analog data. The influence of the truncated coefficients will be considered and its effects will be demonstrated by an example proving the robustness of the transformed function. A design procedure will be proposed for the CMAC filter functions with arbitrary maximum pass-band attenuation.

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 some measurement applications, it is required to have digital filters which simultaneously possess a constant group delay in the passband and a narrow transition band. This kind of filters is usually implemented using allpass filter section which compensates the unfavorable run of the group delay response of the original filter. Unfortunately, the process of equalisation affects the time domain characteristics of the (whole) equalised system. This paper presents theoretical concept and simulation results of a new class of low-pass time-varying infinite impulse response (IIR) filters with equalised group delay response and a transient response of short duration. The improvement of the filters in the time domain is achieved by means of temporary change in the value of the filter parameters. Computer simulations verifying the effectiveness of the proposed IIR filters with equalised group delay response and reduced transient response are presented and compared to the performance of traditional filters.

In this brief, a fast design technique based on a multiband mapping relation is discussed for infinite-impulse-response digital filters with a general Chebyshev characteristic, which is suitable for single- and multiband operations. Each bandwidth and the ripple in it can be accurately controlled. Without increasing the order of the filters, the out-of-band performance of the filters can be easily adjusted by appropriately placing transmission zeros wherever they are desired. In addition, complex transmission zeros can also be introduced to improve the group delay to some extent. The proposed technique is analytical and easy to implement.

This paper introduces new algorithms for enhancing the resolution of interpolated images. The aim of this algorithm is to have a high resolution image from a single low resolution image. The new algorithms used the interpolation technique with the two dimensional filter that is specifically designed for the image by maximizing the peak signal to noise ratio and structural similarity. The processed images are assessed by comparing them with the ground truth images. The algorithm performance is assessed using the peak signal to noise ratio (PSNR) and structural similarity (SSIM). The new algorithm gives better result than the previous 2D filters algorithms.

This work proposes an analytical design method for 2D Gaussian-shaped directional IIR filters with single, double or multiple orientation selectivity in the frequency plane. The design starts from a 1D Gaussian prototype with adjustable selectivity, to which specific frequency transformations are applied in order to obtain oriented 2D filters. This design technique leads to the 2D filter frequency response expressed in matrix form, depending on the imposed specifications. Therefore, the resulted 2D filter with multiple orientation is adjustable, and its selectivity and orientation angles are specified independently. Several design examples of orientation-selective filters are provided. An example of image filtering with a two-directional filter with specified parameters shows the possibility of detecting and separating straight lines with various orientations from a given test image.

This chapter describes how to read video data from an attached webcam using Linux's Video4Linux feature. Together with the frame buffer introduced in the previous chapter, this chapter explores several example applications that involve real-time video processing. Examples include the two-dimensional (2D) Gaussian blur, 2D Sobel edge detection, and separable 2D filters.

This paper deals with the design and analysis of 2D filters for improving the resolution of interpolated satellite images. The images are reduced first by a certain factor and then interpolated back to the original size. Linear phase 2D filters are designed to optimize the structural similarity index measure (SSIM). Then the satellite image is enlarged by the same factor and the 2D filter is used to sharpen the image. The performance of the new sub-optimum filters was assessed by using the peak signal to noise ratio (PSNR) and the SSIM on a variety of satellite images. It has been found that this method yields better results than optimizing the mean square error (MSE) or by using the sparse method.

The resolution of satellite images is controlled by the number of imaging sensors on board the satellite. Once the satellite is launched then this resolution cannot be changed during the lifetime of the satellite. The only way to increase the resolution of the images is by using super-resolution techniques. This paper deals with the design and analysis of 2D filters for improving the resolution of interpolated satellite images. The images are reduced first by a certain factor and then interpolated back to the original size. Linear phase 2D filters are designed to optimize the mean squared error (MSE) between the interpolated and the original satellite image. Then the satellite image is enlarged by the same factor and the 2D filter is used to sharpen the image. The performance of the new sub-optimum filters was assessed by using the peak signal to noise ratio (PSNR) and the structure similarity index measure (SSIM) on a variety of satellite images. It has been found that this method yields better results than using standard sharpening filters and very close to the optimum case when the resolution of the enlarged image is known.

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.

Digital IIR filter design problem is a crucial research issue in control and signal processing. From the viewpoint of optimization, IIR filter designing problems can be formulated as a multi-modal optimization problem with multiple decision variables. This study investigate the feasibility of applying a newly proposed optimization method labeled as water wave optimization (WWO) algorithm to identify the unknown parameters for IIR filter. To enhance its fine (local) searching performance of WWO, Nelder-Mead simplex algorithm based local improvement is incorporated into WWO so as to continually search for the global optima through the reflection, expansion, contraction, and shrink operators. By working on well-known IIR designing benchmark problems, we evaluate the effectiveness and efficacy of the proposed improved WWO algorithm. Experimental results as well as the comparisons with some state-of-the-art algorithm illustrate merit of the hybrid algorithm in which the local search and global search are well balanced.

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.

We present the first continuous-time digital IIR filter with power consumption tracking the input activity and varying by over 50×, resulting in a FoM varying from 2.5iJ to 0.05IJ. Only two tapped delays are used for a sixth-order filter. The 1.2 V 65nm CMOS prototype achieves very high stopband rejection and includes an output converter to synchronous mode, allowing integration with discrete-time systems.

In this paper, we propose two types of noise shaping infinite impulse response (IIR) filters for ΔΣ modulators based on H2 and H∞ norms of the in-band quantization noise. We utilize the hybrid-design and the least-squares approximation method to obtain noise shaping IIR filters by taking an indirect approach for solving the non-convex optimization problem. In both methods, we also incorporate the non-ideal behavior of the output lowpass filter into the design criteria of our noise shaping IIR filter as a weighting function. To demonstrate the effectiveness of proposed noise shaping IIR filters, we compare it with existing design methods.

Stochastic cascaded IIR filters are used for area-efficient complicated filters in hardware, such as gammatone and gammachirp filters, but the effectiveness of the cascaded form has not been studied in stochastic computation. To evaluate the performance of the stochastic cascaded IIR filters, stochastic direct-form IIR filters are also designed as a baseline filter. The performance of both stochastic filters are simulated in MATLAB and compared with floating-point results in different orders and different stochastic bit lengths. The simulation results show that the cascaded form reduces errors in comparison with the direct form in stochastic IIR filters as well as the well-known effectiveness of the cascaded form in digital IIR filters. In addition, some interesting features of the stochastic IIR filters such as oscillations are exhibited, which are discussed based on spectral analysis.

IIR frequency-response masking (FRM) filter where the prototype filter is an IIR filter and the masking filters are FIR filters is effective in reducing the group delay of FRM filters. In this paper, we present a constrained optimization method for the design of near linear phase IIR FRM filters, where the phase error and magnitude error are independently controlled. A design example is presented to demonstrate the performance of the method.

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.

Noise removal continuous to be a challenging domain of work despite of several techniques which are proposed to overcome this issue are found to be efficient and reliable. In mobile communications, the time varying nature of signals and noise makes this issue more challenging. Among conventional signal processing techniques, finite impulse response (FIR) and infinite impulse response (IIR) structures provide their own set of advantages and disadvantages. Though gamma filters in FIR and IIR forms have been suggested for noise cancellation in speech, it is bottlenecked due to issue such as longer convergence time, delay generation and inability to provide phase variation compensation. This paper presents certain techniques to overcome this issue. Firstly, a modified gamma filter with a feedback structure is used to improve MSE convergence and provide better phase variation correction. The second method uses a transfer function approach for phase correction of the filtered signal. Experiments show that the MSE and phase difference(in degree) between the filtered signal and the desired signal are lower for the proposed structure than the MSE and phase difference values obtained for the FIR filter and original gamma filter structure. Thus the suggested techniques have been found to be more reliable and efficient.

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.

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.

A new optimization method for the design of fullband and lowpass IIR digital differentiators is proposed. In the new method, the passband phase-response error is minimized under the constraint that the maximum passband amplitude-response relative error is below a prescribed level. For lowpass IIR differentiators, an additional constraint is introduced to limit the average squared amplitude response in the stopband so as to minimize any high-frequency noise that may be present. Extensive experimental results are included, which show that the differentiators designed using the proposed method have much smaller maximum phase-response error for the same passband amplitude-response error and stopband constraints when compared with several differentiators designed using state-of-the-art competing methods.

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 presents a new method of the polynomial transfer function approximation both in the analog and the digital domain for the recursive digital filter design. The transfer function of these filters, referred as the transitional Legendre–Butterworth (TLB) filters, has properties that lie between Legendre and Butterworth filters. The so-designed TLB filters exhibit non-equiripple passband and monotonic transition and stopband responses. There are three types of TLB IIR filters which can be approximated in the digital domain. The closed form expressions for the magnitude squared functions coefficient of all types of transfer functions are provided, and a straightforward design technique for each approximation in the digital domain is described. Resulting digital filters are always stable.

This paper introduces the generalized IIR Chebyshev filters. The proposed filters are obtained by applying bilinear transformation to the corresponding analog filters. The novelty of the method is the introduction of a new rational Chebyshev function, which includes Chebyshev Type I and Chebyshev Type II IIR filters as special cases. The application of the proposed digital filters to design perfect reconstruction two-channel filter banks is described. The proposed filters can be applied in orthogonal discrete wavelet transform.

This paper deals with the application of Chebychev@?s approximation theory to IIR digital filter frequency response (FR) approximation. It explores the properties of the frequency response of IIR digital filters as a nonlinear complex approximating function; IIR digital filter frequency response is used to approximate a prescribed magnitude and phase responses. The approximation problem is closely related to optimization. If the set of approximating functions is non-convex, the optimization problem is difficult and may converge to a local minimum. The main results presented in the paper are proposing a convex stability domain by introducing a condition termed ''sign condition'' and characterization of the best approximation by the Global Kolmogorov@?s Criterion (GKC). The Global Kolmogorov@?s Criteria is shown to be also a necessary condition for the approximation problem. Finally, it is proved that the best approximation is a global minimum. The sign condition can be incorporated as a constraint in an optimization algorithm.

In this paper, the development of an improved Takagi Sugeno TS fuzzy model for identification and chaotic time series prediction of nonlinear dynamical systems is proposed. This model combines the advantages of fuzzy systems and Infinite Impulse Response IIR filters, which are autoregressive moving average models, to create internal dynamics with just the control input. The structure of Fuzzy Infinite Impulse Response FIIR is presented, and its learning algorithm is described. In the proposed model, the Butterworth analogue prototype filters are estimated using the obtained membership functions. Based on the founding orders of the analogue filters, the IIR filters could be constructed. The IIR filters are introduced to each TS fuzzy rule which produces local dynamics. Gustafson--Kessel GK clustering algorithm is used to generate the clusters which will be used to find the number of the IIR parameters for each rule. The hybrid genetic algorithm and simplex method are used to identify the consequence parameters. The stability of the obtained model is studied. To demonstrate the performance of this modeling method, three examples have been chosen. Comparative results between the FIIR model on one hand, and the traditional TS fuzzy model, the neural networks and the neuro-fuzzy network on the other hand. The results show that the proposed method provides promising identification results.

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 real time situations, IIR filter typically works in an under-modelling situation for a system where infinite impulse response (IIR) filter of the system is prodigiously long. In this anterior work there is an inadequate-length of fixed least-mean-square (FLMS), the convergence based on step value can be improved. Various methods for FLMS algorithm had been presented. This paper provides an Evolutionary Variable step size (EVSS) control method for improving convergence and MSE algorithm is proposed.