Filter digitization based on polynomial interpolation

Describes a polynomial interpolation based filter digitization technique which aims to preserve an analog system's frequency response. It is shown that the procedure is capable of digitizing non-bandlimited, including highpass, analog filters. In most cases considered, it results in digital filters whose frequency response is closer to the frequency response of the analog filter than that of filters designed using impulse invariance or the bilinear transformation     

通信对抗中的自适应滤波技术

自适应滤波是在维纳滤波和Kalman滤波等线性滤波基础上发展起来的一种最佳滤波方法,具有较强的适应性和较优的滤波性能。这里将自适应滤波技术应用于电子对抗领域,利用自适应滤波原理计算出一个数字滤波器,对各信道的增益失配与相移失配进行精确的通道均衡补偿;利用自适应滤波方法设计具有特定频率响应的FIR滤波器,可实现时域宽带波束形成技术,并实现了基于自适应滤波的同平台干扰抵消技术。     

Design of Microwave Filters With Arbitrary Frequency Response Based on Digital Methods

This letter presents a novel general technique for the design of microwave filters with arbitrary frequency response. It is based on the translation of the microwave specifications to the digital domain, where the well known and readily available digital filter design techniques are applied. By means of these digital techniques, the method provides a straightforward procedure to calculate the poles and zeros corresponding to the analog frequency response that satisfies the target specifications. From the poles and zeros, the microwave filter can be readily obtained using conventional techniques. As an example to demonstrate the proposed technique, a filter with user-defined specifications over two independent passbands has been implemented and successfully tested in microstrip technology.     

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。     

Evaluation de la complexité des filtres numériques

This paper is an attempt to estimate the computational complexity in several major digital filtering techniques. Simple expressions are given for the multiplication rate, the coefficient wordlength and the internal data wordlength, in finite impulse response filters, infinite impulse response filters, and multirate filters. The parameters are the filter specifications and the signal characteristics. These estimations are of primary interest to the digital processing system designer, for evaluation and comparison purposes. They also could eventually lead to the determination of some kind of fundamental limits in digital filtering.     

A digital signal processing approach to interpolation

In many digital signal precessing systems, e.g., vacoders, modulation systems, and digital waveform coding systems, it is necessary to alter the sampling rate of a digital signal Thus it is of considerable interest to examine the problem of interpolation of bandlimited signals from the viewpoint of digital signal processing. A frequency dmnain interpretation of the interpolation process, through which it is clear that interpolation is fundamentally a linear filtering process, is presented, An examination of the relative merits of finite duration impulse response (FIR) and infinite duration impulse response (IIR) digital filters as interpolation filters indicates that FIR filters are generally to be preferred for interpolation. It is shown that linear interpolation and classical polynomial interpolation correspond to the use of the FIR interpolation filter. The use of classical interpolation methods in signal processing applications is illustrated by a discussion of FIR interpolation filters derived from the Lagrange interpolation formula. The limitations of these filters lead us to a consideration of optimum FIR filters for interpolation that can be designed using linear programming techniques. Examples are presented to illustrate the significant improvements that are obtained using the optimum filters.     

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     

Recursive realization of finite impulse filters using finite field arithmetic

Recursive filter design techniques are described and developed for finite impulse filters using finite field arithmetic. The finite fields considered have the formGF(q^{2}), the Galois field ofq^{2}elements, and are analogous to the field of complex numbers whenqis a prime such that(-1)is not a quadratic residue. These filters can be designed to yield either a desired finite impulse or finite frequency response function. This filtering technique has other possible applications, including the encoding or decoding of information and signal design. Infinite signal trains can be decomposed naturally into orthogonal sequences which may be useful in the encoding and decoding process and may provide another approach to convolutional coding. Since the recursive filters developed here do not have the accumulation of round-off or truncation error that one might expect in recursive computations, such filters are noise-free transducers in the sense of Shannon.     

Low-Area/Power Parallel FIR Digital Filter Implementations

This paper presents a novel approach for implementing area-efficient parallel (block) finite impulse response (FIR) filters that require less hardware than traditional block FIR filter implementations. Parallel processing is a powerful technique because it can be used to increase the throughput of a FIR filter or reduce the power consumption of a FIR filter. However, a traditional block filter implementation causes a linear increase in the hardware cost (area) by a factor of L, the block size. In many design situations, this large hardware penalty cannot be tolerated. Therefore, it is important to design parallel FIR filter structures that require less area than traditional block FIR filtering structures. In this paper, we propose a method to design parallel FIR filter structures that require a less-than-linear increase in the hardware cost. A novel adjacent coefficient sharing based sub-structure sharing technique is introduced and used to reduce the hardware cost of parallel FIR filters. A novel coefficient quantization technique, referred to as a scalable maximum absolute difference (MAD) quantization process, is introduced and used to produce quantized filters with good spectrum characteristics. By using a combination of fast FIR filtering algorithms, a novel coefficient quantization process and area reduction techniques, we show that parallel FIR filters can be implemented with up to a 45% reduction in hardware compared to traditional parallel FIR filters.     

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     

Design of 2-D Linear Phase Digital Filters Using Schur Decomposition and Symmetries

In this paper we present a new and numerically efficient technique for designing 2-D linear phase octagonally symmetric digital filters using Schur decomposition method (SDM) and the diagonal symmetry of the 2-D impulse response specifications. This technique is based on two steps. First, the 2-D impulse response matrix is decomposed into a parallel realization of k sections, each comprising two cascaded linear phase SISO 1-D FIR digital filters. It is shown that using the symmetry property of the 2-D impulse response matrix and the fact that the left and right eigenspaces obtained by SDM are transpose of each other, the design problem of two 1-D digital filters is reduced to the design problem of only one 1-D digital filter in each section.     

Digital Filters for Real-Time ECG Signal Processing Using Microprocessors

Traditionally, analog circuits have been used for signal conditioning of electrocardiograms. As an alternative, algorithms implemented as programs on microprocessors can do similar filtering tasks. Also, digital filter algorithms can perform processes that are difficult or impossible using analog techniques. Presented here are a set of real-time digital filters each implemented as a subroutine. By calling these subroutines in an appropriate sequence, a user can cascade filters together to implement a desired filtering task on a single microprocessor. Included are an adaptive 60-Hz interference filter, two low-pass filters, a high-pass filter for eliminating dc offset in an ECG, an ECG data reduction algorithm, band-pass filters for use in QRS detection, and a derivative-based QRS detection algorithm. These filters achieve real-time speeds by requiring only integer arithmetic. They can be implemented on a diversity of available microprocessors.     

一种模拟滤波电路数字化方法

在信号处理中,滤波的优劣直接影响信息的准确性。模拟滤波虽然快捷但不灵活,数字滤波效果虽好但复杂。所以文中提出一种以模拟滤波器为基准,设计具有相同功能而且参数可调的数字滤波器的方法。并以二阶RC无源低通滤波电路为例对此过程进行说明,与模拟滤波电路和传统的数字滤波相比,该方法不仅比传统的数字滤波算法简单快捷,而且可有效防止模拟电路中器件的寄生参数、精度、温度等的影响,使滤波更加稳定。     

Synthesis of grating lattice circuits

The realization of high-performance components based on optical infinite impulse response (IIR) filter design theory is desirable for next-generation global optical networks. Previously proposed IIR filter synthesis methods are matrix factorization techniques for a lattice circuit using ring resonators. The size of ring resonator limits the bandwidth of the lattice filters. In this paper, two configurations of grating lattice filters are synthesized by using a scattering matrix representation for the grating. The grating is one of the most powerful optical elements both in fiber optics and photonic integrated circuits. One configuration is a serial grating lattice filter configuration and the other is a parallel grating lattice filter configuration. The actual frequency response of the synthesized grating lattice filter is calculated to show the design limitation due to the frequency response of the element gratings     

Mildly suboptimal digital filters using a host windowing approach

A digital-filter design technique is described which employs simple trigonometric windowing of a `host? digital filter. In contrast to the usual windowing rationale which uses a truncated ideal impulse response, this approach uses an optimal (finite-length-minimax) host impulse response. It is shown that optimal Hilbert-transform filters serve as suitable hosts for lowpass filters of even-length impulse response, and optimal differentiators can be used as hosts for odd-length impulse responses. The resulting windowed filters are no longer optimal, but yield approximation errors under most operating conditions.     

Generalized digital Butterworth filter design

This correspondence introduces a new class of infinite impulse response (IIR) digital filters that unifies the classical digital Butterworth filter and the well-known maximally flat FIR filter. New closed-form expressions are provided, and a straightforward design technique is described. The new IIR digital filters have more zeros than poles (away from the origin), and their (monotonic) square magnitude frequency responses are maximally flat at ω=0 and at ω=π. Another result of the correspondence is that for a specified cutoff frequency and a specified number of zeros, there is only one valid way in which to split the zeros between z=-1 and the passband. This technique also permits continuous variation of the cutoff frequency. IIR filters having more zeros than poles are of interest because often, to obtain a good tradeoff between performance and implementation complexity, just a few poles are best     

Extended-window interpolation applied to digital filter design

This paper develops a procedure for the design of frequency-selective interpolation operators that can be computed and saved once and for all. These operators are used to design real-time digital operators: interpolators, FIR differentiators, IIR filters, and composed interpolation and filtering operators. Each real-time operator is a matrix relating sets of data points to sets of interpolated values. Since these matrices are characterized by low norms, they permit reduced-word implementations, and are suitable for real-time processing with array processors and massively parallel machines. The design of the interpolation operators uses windows that, unlike traditional approaches, extend beyond the data interval up to the length permitted by the dimensionality theorem. A new form of the dimensionality theorem is used to minimize the minimax interpolation error within a predetermined frequency range, which may be either the passband of the antialiasing filter or the passband of an analog prototype filter. The main application presented in the paper is the design of combined digital filters and interpolators, which will be referred to as interpolating filters. The frequency responses of such filters, as well as the interpolated time responses, almost coincide with those of the corresponding analog prototypes     

Design of stable IIR digital filter based on least P-power error criterion

In this paper, the least p-power error criterion is presented to design digital infinite impulse response (IIR) filters to have an arbitrarily prescribed frequency response. First, an iterative quadratic programming (QP) method is used to design a stable unconstrained one-dimensional IIR filter whose optimal filter coefficients are obtained by solving the QP problem in each iteration. Then, the proposed method is extended to design constrained IIR filters and two-dimensional IIR filters with a separable denominator polynomial. Finally, design examples of the low-pass filter are demonstrated to illustrate the effectiveness of the proposed iterative QP method.     

Implementation of Digital Unbiased FIR Filters with Polynomial Impulse Responses

This paper addresses the design and implementation of digital unbiased finite impulse response (FIR) filters with polynomial impulse response functions. The transfer function, its fundamental properties, and a general block-diagram are discussed for the impulse response represented with the l-degree Taylor series expansion. As a particular results, we show a fundamental identity uniquely featured to such filters in the transform domain. For low-degree impulse responses, the transfer functions are found in simple closed forms and represented in compact block-diagrams. The magnitude and phase responses are also analyzed along with the group delays. A comparison with predictive FIR filters is given. As examples of applications, filtering of time errors of local clocks is discussed along with the low-pass filter design employing a cascade of the unbiased FIR filters.     

An improved design method based on polyphase components for digital FIR filters

This paper presents an efficient design of digital finite impulse response (FIR) filter, based on polyphase components and swarm optimisation techniques (SOTs). For this purpose, the design problem is formulated as mean square error between the actual response and ideal response in frequency domain using polyphase components of a prototype filter. To achieve more precise frequency response at some specified frequency, fractional derivative constraints (FDCs) have been applied, and optimal FDCs are computed using SOTs such as cuckoo search and modified cuckoo search algorithms. A comparative study of well-proved swarm optimisation, called particle swarm optimisation and artificial bee colony algorithm is made. The excellence of proposed method is evaluated using several important attributes of a filter. Comparative study evidences the excellence of proposed method for effective design of FIR filter.