Parks-McClellan Research Articles

A new design methodology for window‐based FIR filters

AbstractThis letter describes a novel window‐based approach to FIR filter design. The window is constructed on the use of equispaced Gaussian basis functions. Unlike other known window‐based methods that do not allow for a satisfactory degree of control over band edges, the proposed method affords very good solution for controlling critical frequencies. In addition, the proposed window method is easier to implement than Kaiser's and affords a better passband flatness than any known design approach. It also yields stopband attenuations and control of critical frequencies which turn out to be very close to those obtainable with Parks–McClellan's method. So the proposed GBR window approach appears to be a significant step forward.

Optimal High Pass FIR Filter Based on Adaptive Systematic Cuckoo Search Algorithm

Abstract This paper presents the design of a desired linear phase digital Finite Impulse Response (FIR) High Pass (HP) filter based on Adaptive Systematic Cuckoo Search Algorithm (ACSA). The deviation, or error from the desired response, is assessed along with the stop-band and pass-band attenuation of the filter. The Cuckoo Search algorithm (CS) is used to avoid local minima because the error surface is typically non-differentiable, nonlinear, and multimodal. The ACSA is applied to the minimax criterion (L∞-norm) based error fitness function, which offers a better equiripple response for passband and stopband, high stopband attenuation, and rapid convergence for the developed optimal HP FIR filter algorithm. The simulation findings demonstrate that when compared to the Parks McClellan (PM), Particle Swarm Optimization (PSO), CRazy Particle Swarm Optimization (CRPSO), and Cuckoo Search algorithms, the proposed HP FIR filter employing ACSA leads to better solutions.

Minimax Design of Graph Filter Using Chebyshev Polynomial Approximation

In this brief, the minimax design problem of graph filter using Chebyshev polynomial approximation (CPA) is studied. First, conventional CPA graph filter design is investigated to show that it does not provide the minimax design, so the peak error of the spectral response of the designed filter is not minimized. Then, a spectral transformation is used to convert the minimax design problem of CPA graph filter into the one of the type-I linear-phase FIR digital filter such that the Parks-McClellan method can be employed to obtain the optimal filter coefficients of minimax design. Next, using the recurrence relation of Chebyshev polynomials, an implementation structure of CPA graph filter with low computational complexity is presented. Finally, a graph signal denoising application example is illustrated to show the usefulness of the proposed CPA graph filter.

Least squares linear phase FIR filter design and its VLSI implementation

In this work we present least squares (LS) approach to design linear phase Finite Impulse Response (FIR) filter. Since the design of FIR digital filters is non-analytic, we aim at ideal zero-phase magnitude response and minimize the weighted error in passband and stopbands. The problem of least squares can then be solved non-iteratively by solving system of linear equations. Solution of which yields impulse response that is both real and symmetric. Frequency response of the proposed LS FIR filter shows a flat passband, and higher stop-band attenuation than traditional window based FIR design and comparable attenuation with Parks–McClellan method of the same order. In addition we have implemented LS FIR filter on FPGA based VLSI architectures. Performance evaluation of proposed LS FIR design on VLSI architecture shows comparable throughput, area and power consumption compared to classical filter design approaches.

Design and implementation of sharp edge FIR filters using hybrid differential evolution particle swarm optimization

The filter is an important building block of modern communication and electronic systems. Based on well-defined bandwidth, it extracts the desired portion of the spectrum when the raw input signal is applied. Efficacy of filtering depends on the preciseness of bandwidth to avoid co-channel interference and signal loss. In addition, it must provide higher stopband attenuation and passband attenuation very close to unity with a tolerable quantity of pass/stop band ripple. Design/implementation of sharp edge modern FIR filter is structured as a multi-objective, constrained, complex, and highly nonlinear (hence multimodal) error minimization challenge. Hence, this work proposes a novel objective (normalized error fitness) function and a robust hybrid algorithm for the effective searching of the optimal filter coefficients for providing excellent sharp edge frequency response during the filtering action. Most popular particle swarm optimization (PSO) and differential evolution (DE) algorithm are effectively combined together to frame the proposed hybrid DE-PSO algorithm for enhancing the exploration and exploitation abilities of it. The proposed hybrid algorithm is validated using twelve different benchmark functions. Through simulations, the qualitative performance of the proposed approach is compared with the conventional PSO, DE, real-coded genetic algorithm and the Parks–McClellan method.

Evaluation of Frequency Characteristics Approximation Error at the Output of Fir-Filter Calculated by Parks-Mcclellan Algorithm

Рассмотрен метод проектирования КИХ-фильтра высокого порядка, рассчитываемого алгоритмом Паркса – Макклеллана, построенного на использовании процедуры Ремеза. Показано, что причинами ограниченности порядка фильтра являются ошибки описания полиномов Чебышева высокого порядка, возникающие при дискретном представлении полиномов. Предложено строить квазиоптимальные КИХ-фильтры высокого порядка в виде каскадного соединения КИХ-фильтров более низкого одинакового порядка, допускающих применение процедуры Паркса – Макклеллана. Амплитудная частотная характеристика результирующего фильтра определится как произведение амплитудных частотных характеристик отдельных каскадов, фазочастотная характеристика результирующего фильтра – как сумма фазо-частотных характеристик отдельных каскадов. Разделение проектируемого фильтра на каскады одинакового порядка позволяет обеспечить оптимальность построения фильтра при сохранении линейности его фазочастотной характеристики. Получены оценки погрешностей аппроксимации для амплитудной частотной характеристики фильтра в случае его каскадной реализации. Показано, что методика проектирования фильтра, выполненного в виде каскадного соединения, упрощается по сравнению с проектированием фильтра высокого порядка и сводится к проектированию звена более низкого порядка. Соответственно, уменьшается объем памяти, отводимой для запоминания коэффициентов фильтра, и снижается погрешность аппроксимации в полосе задерживания. К ограничениям предлагаемого каскадного построения квазиоптимальных КИХ-фильтров следует отнести рост погрешности аппроксимации в полосе пропускания пропорционально количеству каскадов.

A Novel 2-D FIR Filter Design Methodology Based on a Gaussian-Based Approximation

This letter presents a novel design method for multidimensional finite-impulse response (FlR) filters based on the representation of the desired frequency response by using a Gabor system generated by a Gaussian function. A direct synthesis of the desired filter frequency response is obtained from standard design specifications. Further, we report some comparative tests with the well known Parks–McClellan's methodology in order to illustrate the concrete advantages of the novel design approach that we have proposed. With such an approach, the design procedure turns out to be especially simple to implement, as it employs closed design formulas which directly link filter coefficients to design specifications, and moreover, affords a better pass-band flatness than any known design approach. It also yields stop-band attenuations and grants control over critical frequencies, which turn out being very close to those obtainable with Parks–McClellan method. The enhanced performance of the 2-D filters thus obtained are well suited for space applications.

Design of optimal band-stop FIR filter usingL1-norm based RCGA

Abstract In this paper, an optimal design of linear phase digital finite impulse response (FIR) band stop (BS) filter using the L 1 -norm based real-coded genetic algorithm ( L 1 -RCGA) is presented. Although RCGA has proved its ability to overcome the drawbacks associated with conventional gradient-based optimization methods of filter design, it is applied here with a novel fitness function based on the L 1 -norm. This leads to a global optimal solution along with the improvement in filter design with same specifications. The designed filter pursues a better response in terms of flat passband, high stopband attenuation and fast convergence. The simulation results justify that the proposed FIR BS filter using L 1 -RCGA outperforms the existing optimization techniques, the L 1 -method and particle swarm optimization (PSO) and the conventional methods such as least-squares (LS) approach, Kaiser window method and the Parks McClellan (PM) algorithm. A detailed analysis is performed to evaluate the performance of the designed filters.

Spectral Analysis of Rectangular, Hanning, Hamming and Kaiser Window for Digital Fir Filter

Digital filters are extensively used in the world of communication. In order to design a digital finite impulse response (FIR) filter that satisfies all the required conditions is challenging. In this paper, design techniques of digital low pass FIR filters using Rectangular window method, Hamming window, Hanning window, and Optimal Parks McClellan method are presented. The stability, number of components required and filter coefficients are demonstrated for different design techniques. It is demonstrated that filter design using hamming window is comparatively better than rectangular and hanning window though the components required for all of the windowing technique are same, hamming shows higher stability. The stability is shown with the help of magnitude and phase spectrum of each window. Simulation is carried out using MATLAB and comparisons are made entirely based on the output of the simulation.

Performance of the IEEE 802.15.4a UWB System using Two Pulse Shaping Techniques in Presence of Single and Double Narrowband Interferences

In Cognitive radio (CR) applicationsUltra-wideband (UWB) impulse radio (IR)signals can be designed such as they can co-exist with licensed primary users. Thepulse shape should be adjusted such that the power spectral characteristics not only meet the Federal Communications Commission (FCC) constrains, but also mitigate multiple narrow -band interference at the locations of existing primary users. In this paper, the Parks-McClellan (PM) Algorithm and the Eigen Value Decomposition (EVD) approach for UWB impulse radio waveform shaping areconsidered. The power spectral density (PSD) and the bit -errorrate (BER) performance of the two methods are compared in the presence of single and double narrowband interference (NBI). The interference rejection capabilities of the two methods are evalua ted and compared for different interference and additive noise levels. In particular, the simulations considerthe coexistence of practical IEEE 802.15.4a UWB systems with both IEEE 802.11 wireless LAN systems operating at 5.2 GHz and radio location servic es operating at 8.5 GHz.

UltraWide Band Cognitive Pulse Shaping under Physical-Layer QoS Constraints

Ultra Wide Band (UWB) communication systems operate in the frequency range between 0 and 10.6 GHz so they induce the Scientific Community to solve the problem of coexistence with concurrent telecommunication services. This is the leading reason why both the Federal Communications Commission (FCC) and the European Telecommunications Standards Institute (ETSI) gave strict indications about the spectral limits to be respected and require the transmitter and receiver to be compliant with these spectral masks. To this end, it is mandatory to carefully shape the UWB pulse, for this can be accurately designed so as to avoid severe performance reduction while guarding inter-systems coexistence. The UWB technology and, more, the pulse shaping allow to apply the cognitive paradigm where the transmitter and receiver are the actors of this functionality since the performance are tied to channel features and interference presence. The widespread choice of Gaussian-like pulses has proven, however, largely suboptimal from a power emission point of view since they fail to optimize performance. Goal of this contribution is to show how to achieve a good compromise between spectral emission, rate and synchronization errors robustness, via a modified version of the Parks-McClellan method, considering channel impairments due to its frequency-selective nature and to the inter-pulse interference.

GENERATION OF TIME DOMAIN DRIVE SIGNALS IN MIMO RANDOM VIBRATION CONTROL SYSTEM

� � � ABSTRACT � The new generation algorithm of time domain drive signals is presented to reduce the loop time in MIMO(multi input multi output) random vibration control system. The Parks-McClellan method is used to design the FIR (finite impulse response) filter. And then the drive signals in time domain is generated by filtering a series of independent white noise with the designed filter. For avoiding the time domain randomization process in the conventional frequency-to-time transformation, the new method is favorable to improve the real-time property of the control system. Two tests are run in one 6 DOF(degree of freedom) hydraulic shaker with the conventional algorithm and the improved algorithm differently. The results demonstrate the effectiveness of the improved algorithm.

Linear phase FIR filter design using particle swarm optimization and genetic algorithms

In this paper, a linear phase FIR filter is designed using particle swarm optimization (PSO) and genetic algorithms (GA). Two design cases are considered. In the first case, the filter length, passband and stopband frequencies, and the ratio of the passband and stopband ripples size are specified. In the second case, a feasible passband and stopband ripples size in addition to the other three filter specifications are specified. The later situation is not explicitly considered by the Parks–McClellan (PM) algorithm. Furthermore, the PSO and the GA are used to design optimum FIR filters for which the filter coefficients are represented using finite word length. In all cases, the design goal is successfully achieved using the PSO and compared with that obtained using the GA. For the problem at hand, it is found that the PSO outperforms the GA in some of the presented design cases.

Anti-image FIR filters for large interpolation factors

In this paper, the design of FIR filters using novel window families is introduced. These window functions are having high side-lobe-fall-off-rate (SLFOR). The designed filters can be used as anti-imaging filters for large interpolation factors used in multirate signal processing. The performance of the proposed filters is compared with similar filters designed with Kaiser window, Dolph-Chebyshev window and optimum filters designed using Parks-McClellan method. It is observed that, filters designed with high SLFOR combinational window families are providing better image suppression with large interpolation factor. These filters provide smaller aliasing and imaging errors at the cost of smaller initial stopband attenuation.

Anti-image FIR filters for large interpolation factors

In this paper, the design of FIR filters using novel window families is introduced. These window functions are having high side-lobe-fall-off-rate (SLFOR). The designed filters can be used as anti-imaging filters for large interpolation factors used in multirate signal processing. The performance of the proposed filters is compared with similar filters designed with Kaiser window, Dolph–Chebyshev window and optimum filters designed using Parks–McClellan method. It is observed that, filters designed with high SLFOR combinational window families are providing better image suppression with large interpolation factor. These filters provide smaller aliasing and imaging errors at the cost of smaller initial stopband attenuation.