Optimal Design of 2D FIR Filters with Quadrantally Symmetric Properties Using Fractional Derivative Constraints

In this article, an optimal design of two-dimensional finite impulse response (2D FIR) filter with quadrantally even symmetric impulse response using fractional derivative constraints (FDCs) is presented. Firstly, design problem of 2D FIR filter is formulated as an optimization problem. Then, FDCs are imposed over the integral absolute error for designing of the quadrantally even symmetric impulse response filter. The optimized FDCs are applied over the prescribed frequency points. Next, the optimized filter impulse response coefficients are computed using a hybrid optimization technique, called hybrid particle swarm optimization and gravitational search algorithm (HPSO-GSA). Further, FDC values are also optimized such that flat passband and stopband frequency response is achieved and the absolute \(L_1\)-error is minimized. Finally, four design examples of 2D low-pass, high-pass, band-pass and band-stop filters are demonstrated to justify the design accuracy in terms of passband error, stopband error, maximum passband ripple, minimum stopband attenuation and execution time. Simulation results have been compared with the other optimization algorithms, such as real-coded genetic algorithm, particle swarm optimization and gravitational search algorithm. It is observed that HPSO-GSA gives improved results for 2D FIR-FDC filter design problem. In comparison with other existing techniques of 2D FIR filter design, the proposed method shows improved design accuracy and flexibility with varying values of FDCs.     

B-spline design of maximally flat and prolate spheroidal-type FIRfilters

A digital FIR filter is described that offers excellent passband and stopband characteristics for general applications. Design formulae include parameters that adjust the magnitude response from one having characteristics like the maximally flat designs of Hermann (1971) and Kaiser (1975, 1979) to one having characteristics like the minimum-sidelobe energy approximations of Kaiser and Saramaki (1989). The impulse response coefficients are more straightforward to obtain than these filter designs while offering preferable response characteristics in many instances. Unlike FIR filters designed by window- or frequency-sampling methods, the filter coefficients are determined from the inverse Fourier transform in closed form once B-splines have been used to replace sharp transition edges of the magnitude response. Although the filters are developed in the frequency domain, a convergence window is identified in the convolution series and compared with windows of popular FIR filters. By means of example, adjustment of the transitional parameter is shown to produce a filter response that rivals the stopband attenuation and transition width of prolate spheroidal designs. The design technique is extended to create additional transitional filters from prototype window functions, such as the transitional Hann window filter. The filters are particularly suitable for precision filtering and reconstruction of sampled physiologic and acoustic signals common to the health sciences but will also be useful in other applications requiring low passband and stopband errors     

Interpolated narrowband lowpass FIR filters

The article describes a class of digital filters, called interpolated finite impulse response (IFIR) filters that can implement narrowband lowpass FIR filter designs with a significantly reduced computational workload relative to traditional FIR filters. Topics discussed include: optimum expansion factor choice, number of FIR filter taps estimation, IFIR filter performance modeling, passband ripple considerations, implementation, and filter design.     

Algebraic Design of Some Equiripple Linear-Phase Half-Band FIR Filters

A closed form solution for the approximation of a linear-phase FIR (finite impulse response) filter with equiripple magnitude responsein the passband and stopband was not known. In this letter we present a closed form solution of some equiripple linear-phase half-band FIR filter approximation.     

Designing IIR filters with a given 3-dB point

Often in infinite impulse response (IIR) filter design, our critical design parameter is the cutoff frequency at which the filter's power decays to half (-3 dB) the nominal passband value. This article presents techniques that aid in the design of discrete-time Chebyshev and elliptic filters given a 3-dB attenuation frequency point. These techniques place Chebyshev and elliptic filters on the same footing as Butterworth filters, which traditionally have been designed for a given 3-dB point. The result is that it is easy to replace a Butterworth design with either a Chebyshev or an elliptic filter of the same order and obtain a steeper rolloff at the expense of some ripple in the passband and/or stopband of the filter.     

A design algorithm for optimal low-pass nonlinear phase FIR digital filters

The transfer function of the low-pass nonlinear phase finite impulse response (NLPFIR) digital filter is decomposed into a nonlinear phase part and a linear phase part. An algorithm is proposed to iteratively design the magnitude of the linear phase part and the squared magnitude of the nonlinear phase part by directly calling the Remez algorithm of McClellan, et al. [1]. In the design of the nonlinear phase part, we assume that the linearity constraint on the phase is dropped but the phase response is not specified. A scheme is incorporated into our algorithm so that it can design the filter with the desired ripple ratio. This approach also leads to a method for finding the minimum ripple ratio for the given orders of the two parts and band edges of the filters. The filters with ripple ratio larger than this minimum value can be designed by our algorithm and neither passband nor stopband ripples are required to be prescribed. Analysis of roundoff noise reveals that the cascade filter implementation usually needs higher wordlengths than its direct for counterpart for the same roundoff noise performance.     

基于雷米兹交换算法设计线性相位对数FIR滤波器

根据线性相位对数FIR滤波器幅度响应与线性相位FIR滤波器幅度响应的关系 ,将线性相位对数滤波器设计转换为线性相位FIR滤波器设计。该方法直接采用雷米兹交换算法即可获得线性相位对数滤波器通带和阻带的等纹波特性。另外 ,该方法既可基于频域均匀采样也可基于频域非均匀采样 ,具有一定的通用性和灵活性     

Adaptive Complex-Coefficient 2D FIR Trapezoidal Filters for Broadband Beamforming in Cognitive Radio Systems

A novel design method is proposed for an adaptive discrete-domain beamformer for the beamforming of temporally broadband-bandpass signals in cognitive radio (CR) systems. The method is based on a complex-coefficient 2D finite impulse response (FIR) filter having a trapezoidal-shaped passband. The temporally broadband-bandpass signals are received by a 1D uniformly distributed antenna array (1D UDAA), where the outputs of the antennas are complex-quadrature sampled by the front end of the CR system. This CR system is based on a software defined radio (SDR) architecture and can be instantly reconfigured by the control system to select the appropriate frequency band and the required sampling rate. The subsequent beamforming enhances the spectral components of the desired temporally broadband-bandpass signals by arranging for the asymmetric trapezoidal-shaped passband of the 2D filter transfer function to closely enclose the region of support (ROS) of the spectrum of the desired signal, whereas the ROSs of the spectral components of the interfering signals are enclosed by the stopband. The proposed novel closed-form design method facilitates instant adaptation of the shape and orientation of the passband of the beamforming 2D FIR trapezoidal filter in order to match the time-varying frequency band and the time-varying bandwidth of the signal, as well as to track and enhance received signals with time-varying directions of arrival (DOAs). Simulated results confirm that, compared with previously reported methods, the proposed method achieves the best overall tradeoff with respect to the instantaneous adaptations of the operating frequency band, the bandwidth, and the time-varying DOAs, the distortion of the desired passband signal, and the stopband attenuation of interfering signals.     

Digital Laguerre filter design with maximum passband-to-stopband energy ratio subject to peak and Group delay constraints

In this paper, we formulate a general design of transversal filter structures with maximum relative passband-to-stopband energy ratio subject to complex frequency response constraints in the passband and the stopband as well as additional constraints such as constraints. These constraints are important for applications where the suppression of noise at certain frequencies are important. Additional constraints are introduced allowing approximately linear phase and constant group delay in the passband. For a given set of basis functions, the design problem can be formulated as a semi-infinite quadratic optimization problem in the filter coefficients, which are the decision variables to be optimized. In this paper, we focus on the design of digital Laguerre filter and digital finite impulse response (FIR) filter structures. A modified bridging algorithm is developed for searching for the optimum pole of the Laguerre filters. Design examples are given to demonstrate the effectiveness of the proposed algorithm.     

二维线性相位FIR数字滤波器的优化设计

该文提出了一种用神经网络算法来设计二维线性相位数字滤波器的新方法。通过分析二维FIR线性相位滤波器的幅频响应特性,建立了神经网络算法。根据给定的幅频响应指标,按该算法可获得滤波器系数。为保证该算法的稳定性,提出并证明了该算法的收敛定理。文中给出了圆对称和矩形对称二维低通线性相位FIR数字滤波器优化设计实例。计算机仿真结果表明由该方法设计的二维数字滤波器,通带和阻带范围波动小,所需计算量非常少,稳定性强,因而是一种优异的设计方法。     

Two Classes of Frequency-Response Masking Linear-Phase FIR Filters for Interpolation and Decimation

This paper introduces two classes of frequency-response masking (FRM) linear-phase finite (length) impulse response (FIR) filters for interpolation and decimation by arbitrary integer factors M. As they are based on the FRM approach, the proposed filters are low-complexity (efficient) sharp-transition linear-phase FIR interpolation and decimation filters. Compared to previously existing FRM linear-phase FIR filter classes for interpolation and decimation, the new ones offer lower complexity and more freedom in selecting the locations of the passband and stopband edges. Furthermore, the proposed classes of FRM filters can, as special cases, realize efficient Mth-band FRM linear-phase FIR interpolation and decimation filters for all values of M. Previously, only half-band (M = 2) FRM linear-phase FIR filters have appeared in the literature. The paper includes design techniques suitable for the new filters and design examples illustrating their efficiency.     

A Novel Photonic Microwave Filter With Infinite Impulse Response

A novel design of a photonic microwave filter with infinite impulse response is presented and demonstrated experimentally, ft overcomes the problems due to optical coherence. The design exhibits substantial flexibility, permitting easy and continuous tunability of the free spectral range. In particular, when a Mach-Zehnder modulator is used in the filter, the passband of the filter response can be changed to stopband and vice versa. The design also provides scope for cascading more stages. Theoretical analysis and measured results are presented, showing a very good match between them.     

基于均匀信道化滤波器组的研究与设计

信道化作为软件无线电系统和宽带数字接收机的关键技术之一,而多相滤波结构的信道化处理技术和滤波器组的设计一直是研究难点。根据多相滤波结构,本文给出一种有限冲激响应滤波器的设计方法,然后根据均匀信道化的要求设计出均匀滤波器组,设计出的原型滤波器能够无失真采样滤波并能重构。利用等波纹设计的同时,使优化所得通带波纹数量级达到10-3,衰减达到-100dB。利用MATLAB设计及仿真表明,该设计是可靠的,可作为高速率滤波器设计的方法。     

Projected least-squares algorithms for constrained FIR filter design

Constrained finite-impulse response (FIR) filter design with time- and frequency-domain linear constraints can be generally transformed into a, or a series of, constrained least-squares problems, which can be generally reformulated as positive definite quadratic programming (QP) problems. This paper presents a novel algorithm referred to as a projected least-squares (PLS) algorithm for the positive definite QP problems. The PLS algorithm essentially projects the unconstrained (least-squares) minimization solution successively onto the boundaries of active constraints that are identified by an active-set strategy. The PLS algorithm has been applied to the constrained least-squares design of FIR filters directly, and to the constrained Chebyshev design of FIR filters in an iterative fashion. The PLS algorithm is compared with the most widely used interior-point methods and an active-set method through design examples of low-pass filters with specified passband and stopband ripples, Nyquist filter constraints and step response constraints. All these examples demonstrate the high efficiency of the PLS algorithm.     

Design of 2-D FIR Filters by a Feedback Neural Network

A Hopfield-type neural network for the design of 2-D FIR filters is proposed. The network is contrived to have an energy function that coincides with the sum-squared error of the approximation problem at hand and by ensuring that the energy is a monotonic decreasing function of time, the approximation problem can be solved. Two solutions are obtained. In the first the 2-D FIR filter is designed on the basis of a specified amplitude response and in the second a filter that has specified maximum passband and stopband errors is designed. The network has been simulated with HSPICE and design examples are included to show that this is an efficient way of solving the approximation problem for 2-D FIR filters. The neural network has high potential for implementation in analog VLSI and can, as a consequence, be used in real-time applications.     

切比雪夫低通滤波器的仿真设计

设计了一个切比雪夫低通滤波器,切比雪夫滤波器的通带内有纹波,阻带内衰减快,它是以通带内的波纹换取截止频率处的最大衰减。波纹越大,截止频率处的衰减越大。该设计方案能达到较好的滤波效果,并用电路仿真软件对其进行了仿真,仿真结果非常接近于理想滤波器的频率响应曲线。     

Method for designing recursive digital filters with short wordlength

With specified passband ripple, stopband ripple and cutoff frequencies, this method employs Crochiere's 2-parameter optimisation to equalise the passband and stopband statistical wordlengths before optimising coefficients in a multi-dimensional discrete space. Better design can be obtained by investing more computational time. This method is applicable to any recursive digital filters.     

多通带低群延迟误差FIR滤波器设计的迭代算法

常数低群延迟有限冲击响应（FIR）滤波器在通信等领域得到了广泛应用,尤其是要求无波形失真、信号延迟小的场合。而低群延迟的FIR滤波器,其相位响应只能做到近似线性相位,其群延迟只能做到近似常数。为了减小与期望常数群延迟之间的误差,最近提出的通过迭代更新相位误差上界函数来逐步减小群延迟误差的方法,只考虑了单通带滤波器的minimax设计。本文将把该方法推广至多通带FIR滤波器的minimax设计和约束最小二乘设计,先对各通带单独处理使每个通带的最大群延迟误差有效降低后,再考虑各通带之间平衡,对各子带的最大群延迟误差进行折中,进而使整个通带上的最大群延迟误差继续减小。对约束最小二乘设计还特别考虑了通过修改收敛参数来解决相位误差约束过紧时设计问题无解的问题。仿真实例表明,该方法能有效减小多通带滤波器的最大群延迟误差。      

Design of some 2-D filters through the transformation technique

The transformation technique is a powerful tool for designing 2-D FIR filters. However, it is not useful for the design of specially shaped filters with passband/stopband regions not centred around the origin. The authors extend this technique to design two types of filters. A notch filter has a stopband centred about a small region in the 2-D frequency plane. The authors propose an extension to the transformation technique with the windowing concept to achieve the design of notch filters. A directional filter has a passband extending fully along a straight line passing through the origin. The transformation technique is further extended to yield such directional filters. Design and application examples for both these filters are also presented     

A new method for the design of IIR filters with flat magnitude response

This paper presents a new direct design of infinite-impulse response (IIR) filters with a flat magnitude response in both passband and stopband (Butterworth filters). The design specifications are passband and stopband frequencies and passband droop and stopband attenuation. The approach is based on an allpass filter with flatness at frequency points /spl omega/=0 and /spl omega/=/spl pi/. Depending on the parity of the IIR filter order, the allpass filter is either real or complex. However, in both cases, the resulting IIR filter is real.