Design Of Digital Filters Research Articles

Nonlinear Circuit Simulation by Means of Alfred Fettweis' Wave Digital Principles

A dependable circuit simulation plays an elementary part in the process of commercial circuit design. However, when Alfred Fettweis invented the concept of Wave Digital Filters (WDFs) back in the early 1970s, that was clearly not the case as tools like SPICE hadn't been published yet. But even though Fettweis' new WDFs were able to provide an accurate digital model of analogue reference circuits, they were mostly perceived as an elaborated technique for digital filter design. In this article we provide an insight into Wave Digital Filters with a focus on nonlinear circuit simulation, highlighting assets and drawbacks of the method. In particular, recent results that extend the Wave Digital concept towards a general circuit simulation strategy with interesting properties are presented.

Interpolation Filter Design Based on All-Phase DST and Its Application to Image Demosaicking

Based on a deep understanding of all-phase digital filter (APDF) design and all-phase biorthogonal transform (APBT), this paper will further study the windowed all-phase digital filter (WAPDF) and windowed all-phase biorthogonal transform (WAPBT), discuss the principle of the WAPBT, and provide a unified construction method of the all-phase transform (APT). Based on a type of orthogonal transform, i.e., discrete sine transform (DST), an interpolation filter called an all-phase DST (APDST) filter is constructed and used for image demosaicking; it is compared with bilinear interpolation and all-phase inverse discrete cosine transform (APIDCT) interpolation filters, to test its performance in image interpolation and provide analysis and discussion. The experimental results show that APIDCT and APDST filters with a size of 7 × 7 are similar in interpolation performance, but better than the bilinear interpolation method. In addition to its use in image interpolation demosaicking, the low-pass filter designed in this paper can also be widely used in image interpolation, image denoising, image resizing, and other fields of image processing.

An Area-Efficient Column-Parallel Digital Decimation Filter With Pre-BWI Topology for CMOS Image Sensor

This paper presents an area-efficient design of a column-parallel second-order digital decimation filter for a $\Sigma \Delta$ analog-to-digital converter-based CMOS image sensor. By using the proposed pre-bitwise-inversion topology having the same mathematical function, the chip area could be curtailed, where the bit-wise-inversion block, required by the correlated-double-sampling, is moved to the front of the adder. Following such a technique as this, more than six inverters and multiplexers can be reduced. This paper also proposes an adder scheme with only 118 transistors to implement the 13-bit dynamic range integrator. Moreover, the number of MSB cells inside the ripple counter is optimized to balance leakage current and active power consumption. Compared with the prior art, the proposed decimation filter core (without registers) can achieve a reduction of about 24% in transistor count. The proposed design is implemented with a 130-nm standard CMOS process. The total chip area of the digital decimation filter is only $4.5\times 145~\mu \text{m}^{2}$ per column, which is less than half area compared against the prior art. According to the post-layout simulation, the maximum operating frequency is 124 MHz, and the total power consumption, including the filter core and 13-bit registers, is less than 6.35 $\mu \text{W}$ under a typical 50-MHz clock frequency.

Optimal design of minimum multiplier lattice wave digital lowpass filter using metaheuristic techniques

This study aims towards the efficient design of arbitrary-band and halfband lowpass (LP) filter based on lattice wave digital filter (LWDF) structure with the usage of minimal number of multipliers in its structural realisation. The designing of the LP filter is formulated as an optimisation problem where coefficients of LWDF transfer function are iteratively optimised by the evolutionary algorithms. The potential of four optimisation algorithms, real-coded genetic algorithm, particle swarm optimisation, differential evolution algorithm, and cuckoo search algorithm, are explored for determining the optimal LWDF coefficients by minimising the error objective function. The structural realisation of LP using LWDF structure enhances the design accuracy as the usage of multiplier prominently reduces. The simulation and statistical results of the proposed lattice wave digital lowpass filter (LWDLF) and bireciprocal lattice wave digital lowpass filter (BLWDLF) design show significant improvement in the mean square error, passband ripples, transition bandwidth, stopband attenuation, rate of convergence, and execution time. To manifest the efficient design of the proposed LWDLF and BLWDLF, the results are compared with the designed arbitrary-band, halfband canonic-LP filters and previous published works.

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

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

An Improved Digital FIR Filter Design Using Fast FIR Algorithm and Modified Carry Save Addition

Adders and multipliers are the two important arithmetic units in any form of digital filters. Though the adders and multipliers are the fundamental arithmetic units in digital FIR filters, the multipliers are more responsible for power consumption. In existing fast FIR algorithm based digital filters, the number of multipliers is reduced at the expense of adder circuits. This paper presents an arithmetic optimization of reconfigurable digital FIR filters using fast FIR algorithm and modified carry save addition to reduce the power consumption. The modified carry save addition is incorporated to efficiently combine the partial products of the multiplication process. The mathematical analysis reveals that significant amount of hardware savings can be achieved using the proposed design. The ASIC implementation using TSMC 65 nm technology shows that the proposed methodology occupies less area and consumes less power while comparing with conventional approach.

Design of IIR Multiple-Notch Filters with Symmetric Magnitude Responses About Notch Frequencies

A novel all-pass-based infinite impulse response (IIR) digital multiple-notch filter design method is presented in this paper. The proposed method ensures that, for an arbitrary pass-bands ripple value, specifications regarding positions of notch, left- and right-hand cutoff frequencies are exactly met, which leads to symmetric magnitude responses about notch frequencies. Although iterative in its nature, proposed method requires a small number of iterations to find coefficients of the multiple-notch filter, making it very useful for designers. Since the magnitude response of the all-pass-based IIR multiple-notch filter is more sensitive in the stop-bands than in the pass-bands, sensitivity analysis along with simulation in limited word-length environment is performed.

High performance continuous variable bandwidth digital filter design for hearing aid application

A low complexity, low delay reconfigurable digital filter structure for hearing aids is proposed in this paper. The main objective is to match a given human audiogram, with minimum error. The high computational complexity in the conventional uniform and non-uniform filter bank techniques, probes to shift the design paradigm towards variable filter structure. In this paper, Farrow structure based design is used to realize an arbitrary sample rate converter, making use of a differentiator based model, by which the bandwidth can be continuously varied. The proposed design also considers the importance of the power, area, and” delay in such a critical scenario. Exhaustive comparisons are performed with the existing literature on audiogram matching, and our design is very competitive when compared to the designs in the literature, not only with respect to the matching error but also with respect to area, power dissipation, and hardware complexity.

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

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

A new approach for the design of digital frequency selective FIR filters using an FPA-based algorithm

Efficient digital filter design is an essential signal processing task. Finite Impulse Response (FIR) filters are used in many applications due to its properties of linear phase and frequency stability. Most traditional design methods suffer from the problem of insufficient control over the frequency response of the designed filter. For this reason, the use of a recently developed optimisation technique called flowers pollination algorithm (FPA), –based on the natural process of pollination of flowers– along with a novel multiple fitness function, is proposed in order to obtain optimised filter coefficients that best approximate ideal specifications. Results have been compared to both traditional methods (mainly windowing and the Parks-McClellan algorithm) as well as to several nature-inspired schemes. Finally, processing of a real EEG signal is used to quantitatively evaluate performance of designed filters. Numerical results show that our method achieves better fit to desired filter specifications, a 5−10 times larger attenuation in the stop band and a narrower transition band, at the expense of slightly increasing the pass-band ripple (5−15%) in 3 out of 4 of the cases.

A Fuzzy Gravitational Search Algorithm to Design Optimal IIR Filters

The goodness of Infinite Impulse Response (IIR) digital filters design depends on pass band ripple, stop band ripple and transition band values. The main problem is defining a suitable error fitness function that depends on these parameters. This fitness function can be optimized by search algorithms such as evolutionary algorithms. This paper proposes an intelligent algorithm for the design of optimal 8th order IIR filters. The main contribution is the design of Fuzzy Inference Systems able to tune key parameters of a revisited version of the Gravitational Search Algorithm (GSA). In this way, a Fuzzy Gravitational Search Algorithm (FGSA) is designed. The optimization performances of FGSA are compared with those of Differential Evolution (DE) and GSA. The results show that FGSA is the algorithm that gives the best compromise between goodness, robustness and convergence rate for the design of 8th order IIR filters. Moreover, FGSA assures a good stability of the designed filters.

Combined digital filter for electric microprocessor protection based on distributed algorithm

Combined digital filters are the basis of fault selection and identification in electric microprocessor protection. The commonly used combined digital filters based on wavelet transform cannot eliminate the interference components of traditional filter, resulting in low reliability of electric microcomputer protection. To this end, a design method of combined digital filter for electric microcomputer protection is proposed based on distributed algorithm. First, the combined digital filter and each implementation module are designed. Then, the principle of distributed algorithm is introduced, and realization of distributed algorithm is analysed, so as to realize the design of combined digital filter. The experimental results show that calculation of the filter designed by this method is simple and effective, and the development of electric microprocessor protection is promoted.

A Sequential Partial Optimization Algorithm with Guaranteed Convergence for Minimax Design of IIR Digital Filters

Challenges for optimal design of infinite impulse response digital filters include the high nonconvexity of design problem and inevitable stability constraints on the filters. To reduce the nonconvexity and tackle the stability constraints, a sequential partial optimization (SPO) algorithm was recently developed to divide the design problem into a sequence of subproblems, each updating only two second-order denominator factors. But the convergence of that algorithm is not guaranteed. By applying an incremental update with an optimized step length in each subproblem, this paper presents an improved SPO algorithm which is guaranteed to converge to a Karush–Kuhn–Tucker (not necessarily global) solution of the design problem. This paper also extends the SPO algorithm to a more general case where the number of denominator factors optimized in the subproblems can be any positive number smaller than half of the denominator order. Convergence performance of the algorithm is shown by the design of two example filters with typical specifications widely adopted in the literature. Comparisons with state-of-the-art methods demonstrate that the improved SPO algorithm obtains better filters than the competing methods in terms of the maximum magnitude of frequency-response error.

Infinite impulse response systems modeling by artificial intelligent optimization methods

Artificial Intelligent Optimization (AIO) algorithms learn from the past searches via using a group of individuals or agents. These Artificial Intelligence-based optimizing techniques are able to solve complex optimization problems with complicated constraints. They find the optimal in the low possible number of iterations, where optimal means the best from all possibilities selected from a special point of view. This paper presents a research on employing AIO methods with aim to Infinite Impulse Response (IIR) system modeling for design and optimization of IIR digital filters. The proposed methods cover a variety of AIO methods; algorithm based on evolution strategy (genetic algorithm) and heuristic algorithms (particle swarm optimization, population-based; gravitational search algorithm, and inclined planes system optimization, both population-based and based on Newton’s laws). In this paper, the IIR system modeling is solved as a constrained single-objective optimization problem in the Mean Squared Error (MSE) fitness function and is evaluated for two different benchmark IIR plants with high and low orders. To evaluate performance, efficiency and efficacy of the methods, two important criteria are used: “Indicator of Success (IoS)” and “Degree of Reliability (DoR)”. In addition, the effect of decreasing population size (search agents) is analyzed on the performance and efficiency of the algorithms. Simulation results clarify the success of the research in terms of the MSE, IoS and DoR.

Review and Analysis of Evolutionary Optimization-Based Techniques for FIR Filter Design

Recent times have witnessed a wide application of evolutionary optimization by researchers, in design of digital FIR filters, based on frequency domain specifications. A significant growth has been reported in the field of evolutionary optimization-based FIR filter design. Optimization-based techniques are used to solve the filter design problem by framing the design task as an error function which is further solved to determine the filter coefficients that satisfies the desired specifications. However, the nonlinear, non-differentiable, non-convex, multimodal nature of the associated optimization problem makes the design task quite challenging. In this regard, a number of evolutionary optimization- based techniques have been applied for FIR filter design. This paper provides a comprehensive review of the various evolutionary optimization-based techniques for FIR filter design. In addition to the review, the reported techniques have been analyzed by implementing them on a common platform and comparing them in terms of their effectiveness in meeting the desired specifications.

Design of optimal high pass and band stop FIR filters using adaptive Cuckoo search algorithm

This paper presents an efficient design of digital FIR high pass and band stop filters using an adaptive cuckoo search algorithm (ACSA). The important features of ACSA are — (i) the step size is independent and (ii) it is accurately decided from the current fitness value. The step size is decided according to the current fitness value within the iteration process. This increases the convergence speed. The other five global optimizers are also used for optimization. The optimal solutions obtained by the ACSA are compared with the other global optimizers. CEC 2005 benchmark test functions are considered for the comparison. The results are compared in terms of the convergence speed, accuracy, deviation from the desired response, minimum stop-band attenuation and maximum pass-band attenuation. The statistical analysis, i.e. t-Test is performed to claim the superiority of the proposed approach. The simulation results presented in this paper reveal the fact that the performance of the ACSA is better than the other algorithms.

Design and Realization of FIR Digital Filter for Optical IM/DD-OFDM System Using FPGA

We present a finite impulse response (FIR) filter by using field programmable gate array (FPGA). It is designed in MATLAB, and we get filter coefficient from it. The implementation results showed decent performance in filtering.

The Design Of Intelligent Filter For EEG

EEG data processing method is usually digital filter designed by the traditional method. Its disadvantage is the transition zone is wide and the filtering effect is poor. Using an improved particle swarm optimization algorithm on IIR digital filters design, the performances of filters designed by various methods are compared and analyzed. Experiments illustrate particle swarm optimization algorithm is effective in IIR filter design and its performance is promising.

Graphical User Interface Design of FIR Filter

FIR digital filter is a stable linear phase filter. Relying on the powerful computing power of MATLAB software and its GUI platform, this graduation project has completed the GUI design and implementation of FIR digital filter through programming. Through the FIR filter to achieve the program, you can design and implement a variety of amplitude characteristics of the FIR digital filter, according to the user input filter design indicators, select the corresponding filter design method (window function, frequency sampling method) to design the corresponding filter. According to the different amplitude characteristics, the parameters of the filter design parameters will change accordingly; when the Kaiser window design filter is selected, the user is allowed to input the stopband attenuation of the filter; when using the frequency sampling method to design the filter, the user must input the filter length and the transition zone sample value; when the parameter is entered incorrectly, the system will prompt for an error message. GUI can also provide intuitive filter amplitude characteristics, phase characteristics and the unit impulse response graphics to help users to confirm whether the design of the filter meets the design specifications; by setting the global shortcut keys, the user after all parameters and options is confirmed by the Shortcut keys to achieve the rapid implementation of filter design.

Time-domain aliasing and anti-aliasing effects in differentiating a band-unlimited signal

In this paper, we investigate time-domain errors occurring in the two extreme discrete-time differentiation modes of band-unlimited signals: in the full-band processing mode and in the processing mode with ideal anti-aliasing filtering (AAF) with a cut-off at the Nyquist frequency. We disclosed that regardless sampling frequency the error from AAF is greater than the aliasing error. It is found that type IV differentiators designed by three commonly known digital filter design methods approximately equally process the high frequency portion of the signal above the Nyquist frequency with nearly equal aliasing errors having a weak dependence on differentiator length. In contrast, the differentiators very differently compute the derivatives of the low frequency portion bellow the Nyquist frequency providing rather dissimilar the common differentiation accuracy. The results show that the differentiators derived by using maximal linearity constraints are more accurate than those designed by the Parks-McClellan algorithm and the impulse response truncation method.