Polynomial-Based Interpolation Filters—Part I: Filter Synthesis

This paper introduces a generalized design method for polynomial-based interpolation filters. These filters can be implemented by using a modified Farrow structure, where the fixed finite impulse response (FIR) sub-filters possess either symmetrical or anti-symmetrical impulse responses. In the proposed approach, the piecewise polynomial impulse response of the interpolation filter is optimized directly in the frequency domain using either the minimax or least mean square criterion subject to the given time domain constraints. The length of the impulse response and the degree of the approximating polynomial in polynomial intervals can be arbitrarily selected. The optimization in the frequency domain makes the proposed design scheme more suitable for various digital signal processing applications and enables one to synthesize interpolation filters for arbitrary desired and weighting functions. Most importantly, the interpolation filters can be optimized in a manner similar to that of conventional linear-phase FIR filters.     

基于FIR与相位补偿IIR滤波器的雷达回波信号处理

FIR与IIR频率选择滤波器的设计,被广泛应用于数字信号处理领域之中。文章以雷达回波信号的数字处理为例,首先分别设计FIR,IIR滤波器完成了对信号特定频率分量的滤除。进而,针对IIR滤波器的非线性相位,基于最优化设计全通系统实现了相位补偿,并对FIR,IIR滤波器进行了综合比较。     

Closed-Form Design of Generalized Maxflat$R$-Regular FIR$M$th-Band Filters Using Waveform Moments

$M$th-band filters have found numerous applications in multirate signal processing systems, filter banks, and wavelets. In this paper, the design problem of generalized maxflat$R$-regular finite impulse response (FIR)$M$th-band filters with a specified integer group delay at$ omega =0 $is considered, and the closed-form expression for its impulse response is presented. The filter coefficients are directly derived by solving a linear system of Vandermonde equations that are obtained from the regularity condition of the maxflat$R$-regular FIR$M$th-band filters via the blockwise waveform moments. Differing from the conventional FIR$M$th-band filters with exactly linear phase responses, the generalized FIR$M$th-band filters proposed in this paper have an arbitrarily specified integer group delay at$ omega =0 $. Moreover, a new efficient implementation of the generalized maxflat$R$-regular FIR$M$th-band filters is proposed by making use of the relationship between the filter coefficients in the closed-form solution. Finally, several design examples are presented to demonstrate the effectiveness of the proposed FIR$M$th-band filters.     

基于可重构FPGA技术的自适应FIR滤波器的实现

有限冲激响应(FIR)滤波器设计遇到的难题是滤波要进行大量乘法运算,即使是在全定制的专用集成电路中也会导致过大的面积与功耗.对于用硬件实现系数是常量的专用滤波器,可以通过分解系数变为应用加、减和移位而实现乘法.FIR滤波器的复杂性主要由用于系数乘法的加法器/减法器的数量决定.而对于自适应FIR滤波器,大多数场合下可用数字信号处理器(DSP)或CPU通过软件编程的方法来实现,但是对于要求高速运算的场合,VLSI实现是很好的选择.基于这一考虑,可以用符号数的正则表示(CSD)码表示系数, 再利用可重构现场可编程门阵列(FPGA)技术实现.可重构结构的应用,能保证系统的其余部分同时处于运行状态时实现FIR滤波器系数的更新.文中利用CSD码和可重构思想,提出了用FPGA实现自适应FIR滤波器的一种方案.     

Low-power digital filtering using approximate processing

We present an algorithmic approach to the design of low-power frequency-selective digital filters based on the concepts of adaptive filtering and approximate processing. The proposed approach uses a feedback mechanism in conjunction with well-known implementation structures for finite impulse response (FIR) and infinite impulse response (IIR) digital filters. Our algorithm is designed to reduce the total switched capacitance by dynamically varying the filter order based on signal statistics. A factor of 10 reduction in power consumption over fixed-order filters is demonstrated for the filtering of speech signals     

Least-squares design of IIR filters with prescribed magnitude andphase responses and a pole radius constraint

This paper presents a method for the frequency domain design of infinite impulse response (IIR) digital filters. The proposed method designs filters approximating prescribed magnitude and phase responses. IIR filters of this kind can have approximately linear-phase responses in their passbands, or they can equalize magnitude and phase responses of given systems. In many cases, these filters can be implemented with less memory and with fewer computations per output sample than equivalent finite impulse response (FIR) digital filters. An important feature of the proposed method is the possibility to specify a maximum radius for the poles of the designed rational transfer function. Consequently, stability can be guaranteed, and undesired effects of implementations using fixed-point arithmetic can be alleviated by restricting the poles to keep a prescribed distance from the unit circle. This is achieved by applying Rouche's theorem in the proposed design algorithm. We motivate the use of IIR filters with an unequal number of poles and zeros outside the origin of the complex plane. In order to satisfy simultaneous specifications on magnitude and phase responses, it is advantageous to use IIR filters with only a few poles outside the origin of the z-plane and an arbitrary number of zeros. Filters of this type are a compromise between IIR filters with optimum magnitude responses and phase-approximating FIR filters. We use design examples to compare filters designed by the proposed method to those obtained by other methods. In addition, we compare the proposed general IIR filters with other popular more specialized structures such as FIR filters and cascaded systems consisting of frequency-selective IIR filters and phase-equalizing allpass filters     

A general weighted median filter structure admitting negativeweights

Weighted median smoothers, which were introduced by Edgemore in the context of least absolute regression over 100 years ago, have received considerable attention in signal processing during the past two decades. Although weighted median smoothers offer advantages over traditional linear finite impulse response (FIR) filters, it is shown in this paper that they lack the flexibility to adequately address a number of signal processing problems. In fact, weighted median smoothers are analogous to normalized FIR linear filters constrained to have only positive weights. It is also shown that much like the mean is generalized to the rich class of linear FIR filters, the median can be generalized to a richer class of filters admitting positive and negative weights. The generalization follows naturally and is surprisingly simple. In order to analyze and design this class of filters, a new threshold decomposition theory admitting real-valued input signals is developed. The new threshold decomposition framework is then used to develop fast adaptive algorithms to optimally design the real-valued filter coefficients. The new weighted median filter formulation leads to significantly more powerful estimators capable of effectively addressing a number of fundamental problems in signal processing that could not adequately be addressed by prior weighted median smoother structures     

The architectures and design of a 20-MHz real-time DSP chip set

A set of four real-time 20-MHz digital signal processor (DSP) chips has been designed, fabricated, and tested. The chips include a 64-tap programmable FIR (finite impulse response) filter, a 1024-tap binary filter and template matcher, a 64-tap rank-value filter, and an eight-line 512-pixel video line delay. The circuits were implemented in a 1.5-μm CMOS process and are fully functional with a 20-MHz clock rate. The processors have reconfigurable windows to allow processing on both one-dimensional and two-dimensional data. The FIR filters can be used in multiprocessor systems to increase the window size and the data precision     

Signal Processing by Generalized Receiver in?DS-CDMA Wireless Communication Systems with?Frequency-Selective Channels

The generalized receiver (GR) based on a generalized approach to signal processing (GASP) in noise is investigated in a direct-sequence code-division multiple access (DS-CDMA) wireless communication system with frequency-selective channels. We consider four avenues: linear equalization with finite impulse response (FIR) beamforming filters; channel estimation and spatially correlation; optimal combining; and partial cancellation. We investigate the GR with simple linear equalization and FIR beamforming filters. Numerical results and simulation show that the GR with FIR beamforming filters surpasses in performance the optimum infinite impulse response beamforming filters with conventional receivers, and can closely approach the performance of GR with infinite impulse response beamforming filters. Channel estimation errors are taken into consideration so that DS-CDMA wireless communication system performance will not be degraded under practical channel estimation. GR takes an estimation error of a maximum likelihood (ML) multiple-input multiple-output (MIMO) channel estimation and GR spatially correlation into account in computation of minimum mean square error (MMSE) and log-likelihood ratio (LLR) of each coded bit. The symbol error rate (SER) performance of DS-CDMA employing GR with a quadrature sub-branch hybrid selection/maximal-ratio combining (HS/MRC) scheme for 1-D modulations in Rayleigh fading is obtained and compared with that of conventional HS/MRC receivers. Procedure of selecting a partial cancelation factor (PCF) for the first stage of a hard-decision partial parallel interference cancellation (PPIC) of the GR employed in DS-CDMA wireless communication system is proposed. A range of optimal PCFs is derived based on the Price’s theorem. Computer simulation results show superiority in bit error rate (BER) performance that is very close to that potentially achieved and surpasses the BER performance of the real PCF for DS-CDMA systems discussed in literature.     

FIR Beamforming for Frequency-Selective Channels with Linear Equalization

In this letter, we consider transmit beamforming with finite impulse response (FIR) filters for frequency-selective channels and simple linear equalization at the receiver. Since a closed-form solution for the optimum FIR beamforming filters (BFFs) does not seem to exist, an efficient numerical method for their recursive calculation is developed. Our numerical results show that for typical GSM/EDGE channels short FIR BFFs can closely approach the performance of the optimum infinite impulse response (IIR) BFFs derived in [1] and yield significant gains over single-antenna transmission.     

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.     

Digital filter design techniques in the frequency domain

Digital filtering is the process of spectrum shaping using digital components as the basic elements. Increasing speed and decreasing size and cost of digital components make it likely that digital filtering, already used extensively in the computer simulation of analog filters, will perform, in real-time devices, the functions which are now performed almost exclusively by analog components. In this paper, using the z-transform calculus, several digital filter design techniques are reviewed, and new ones are presented. One technique can be used to design a digital filter whose impulse response is like that of a given analog filter; other techniques are suitable for the design of a digital filter meeting frequency response criteria. Another technique yields digital filters with linear phase, specified frequency response, and controlled impulse response duration. The effect of digital arithmetic on the behavior of digital filters is also considered.     

Realization of IIR LDM digital filters

A method is presented of realizing an infinite impulse response (IIR) digital filter (DF) using linear delta modulation (LDM) as a simple analog/digital (A/D) converter. This method makes the realization of IIR digital filters much simpler than that of conventional ones because it does not require hardware multipliers or a pulse code modulation (PCM) A/D converter. Compared to the finite impulse response (FIR) LDMDF, this IIR LDMDF requires significantly less computation time     

A new class of nonlinear filters-neural filters

A class of nonlinear filters based on threshold decomposition and neural networks is defined. It is shown that these neural filters include all filters defined either by continuous functions, such as linear finite impulse response (FIR) filters, or by Boolean functions, such as generalized stack filters. Adaptive least-mean-absolute-error and adaptive least-mean-square-error algorithms are derived for determining optimal neural filters. As special cases, adaptive generalized stack and adaptive generalized weighted order statistic filtering algorithms under both error criteria are derived. Experimental results in 1D and 2D signal processing are presented to compare the performances of the adaptive neural filters and other widely used filters     

基于FPGA的FIR滤波器设计

数字滤波器在数字信号处理中占有很重要的地位,该文介绍了FIR滤波器的两种实现算法：乘累加算法和优化的分布式算法,其中分布式算法作为优化算法进行研究。其次,根据FIR滤波器理论,采用线性相位结构优化滤波器的设计。并给出了FIR滤波器的模块划分和FIR滤波器的主要模块的实现,最后对FIR滤波器进行了系统仿真和验证。     

Performance Analysis of FIR ADM Digital Filters

Performance and realization of finite impulse response (FIR) digital filters that use an adaptive delta modulator as an analog/ digital converter have been studied. These filters require no multiplication and offer many advantages over conventional PCM filters including low power consumption, small size, and cost effectiveness. Analytical formulas have been derived for the expected mean-squared errors and also for the word length necessary to achieve the desired performance. Computer simulation has been done to optimize the parameter values and to verify the results of performance analysis. In addition, design of FIR ADM digital filters for processing single and multichannel signals has been considered.     

基于并行FIR滤波器结构的数字下变频

对宽带信号进行并行处理,可同时满足低功耗和实时性的要求,已成为目前宽带信号处理的研究热点。本文提出了一种可在FPGA中实现的并行快速FIR滤波器设计方法。该方法通过应用并行多相处理技术中的一种新型分布式处理算法,在滤波器结构上实现了多级级联的形式,增强了中频处理的灵活性和通用性,节省了硬件开销。仿真结果表明,该算法很好的解决了原始低通滤波器速度跟不上A/D采样率的问题,把采样率提高到了320MHz以上。同时该方法应用软件实现并行信号处理,避免了使用DDC专用芯片,具有较强的通用性,可以很好的移植到其他CPLD中。     

Linear multichannel blind equalizers of nonlinear FIR Volterrachannels

Truncated Volterra expansions model nonlinear systems encountered with satellite communications, magnetic recording channels, and physiological processes. A general approach for blind deconvolution of single-input multiple-output Volterra finite impulse response (FIR) systems is presented. It is shown that such nonlinear systems can be blindly equalized using only linear FIR filters. The approach requires that the Volterra kernels satisfy a certain coprimeness condition and that the input possesses a minimal persistence-of-excitation order. No other special conditions are imposed on the kernel transfer functions or on the input signal, which may be deterministic or random with unknown statistics. The proposed algorithms are corroborated with simulation examples     

Novel design strategy of multiplier-less low-pass finite impulse response filter using self-organizing random immigrants genetic algorithm

Intelligent optimization techniques are playing a very vital role in solving a wide variety of problems of engineering and technology of late. In order to meet the challenges from various perspectives, researchers are always in favor of applying those approaches to get rid of numerous practical difficulties of concern. Digital signal processing, more specifically the design of digital filters in particular, has been immensely motivated and beneficiated by means of this amalgamation. In this communication, we have incorporated a recently proposed genetic optimization method, named as self-organizing random immigrants genetic algorithm, in multiplier-free finite impulse response filter (FIR) design algorithm. Our study has focused on the selection of optimum settlement of filter coefficients through the utilization of this population-based technique which results in power of two distribution of impulse response over a binary search space. The performance of our designed filter has been thoroughly analyzed by a number of design parameters of interest and compared with other state-of-the-art multiplier-less FIR models. It has been observed that the proposed approach outperforms the other designs by a considerably large margin in those areas of signal processing where the reduction in hardware cost is the biggest challenge.     

Design,evaluation and fault-tolerance analysis of stochastic FIR filters

Stochastic computing utilizes compact arithmetic circuits that can potentially lower the implementation cost in silicon area. In addition, stochastic computing provides inherent fault tolerance at the cost of a less efficient signal encoding. Finite impulse response (FIR) filters are key elements in digital signal processing (DSP) due to their linear phase-frequency response. In this article, we consider the problem of implementing FIR filters using the stochastic approach. Novel stochastic FIR filter designs based on multiplexers are proposed and compared to conventional binary designs implemented using Synopsys tools with a 28-nm cell library. Silicon area, power and maximum clock frequency are obtained to evaluate the throughput per area (TPA) and the energy per operation (EPO). For equivalent filtering performance, the stochastic FIR filters underperform in terms of TPA and EPO compared to the conventional binary design, although the stochastic design shows more graceful degradation in performance with a significant reduction in energy consumption. A detailed analysis is performed to evaluate the accuracy of stochastic FIR filters and to determine the required stochastic sequence length. The fault-tolerance of the stochastic design is compared with that of the binary circuit enhanced with triple modular redundancy (TMR). The stochastic designs are more reliable than the conventional binary design and its TMR implementation with unreliable voters, but they are less reliable than the binary TMR implementation when the voters are fault-free.