Complex correction of data acquisition channels using FIR equalizerfilters

The common conviction about FIR (finite impulse response) digital filters is that the number of necessary taps, to reach the same performance as provided by IIR (infinite impulse response) digital filters, is usually too large. Moreover, the standard FIR filter design algorithm (Remez exchange) allows the design of linear-phase filters only. Therefore, IIR filters are often preferred over FIR ones, without any further investigations. This paper presents a case study of complex (amplitude and phase) equalization of the passband of a commercial anti-aliasing filter. The novelty is the usage of an FIR filter for this purpose (or an FIR one, combined with a low-order IIR filter), and a thorough discussion of the special design aspects. It turns out that for the given anti-aliasing filter (a Cauer filter of order 11) an FIR filter of length 60···100 can perform as well as a 26/26 (numerator order/denominator order) IIR one. The properties are even better if a low-order IIR filter is used in combination with an FIR one (orders, e.g., 1/1+40/0). Because of the absence of stability problems and the ease of implementation, the use of FIR filters is suggested     

Particle swarm optimization-based approach for optical finite impulse response filter design

This study presents what is to our knowledge a new and efficient method for the design of an optical finite impulse response (FIR) filter by employing a particle swarm optimization technique. With the method proposed, the design of an optical FIR filter, which is able to provide an arbitrary spectrum output based on crystal birefringence, could be implemented with good performance and high efficiency. The design procedure is discussed. A typical example of a green/magenta filter used in a liquid crystal on silicon projection display is included to demonstrate the feasibility and efficiency of this method in this design process as compared with simulated annealing.     

Design of linear phase FIR notch filters

This paper investigates some approaches for designing one-dimensional linear phase finite-duration impulse-responses (FIR) notch filters, which are based on the modification of several established design techniques of linear phase FIR band-selective filters. Based on extensive design examples and theoretical analysis, formulae have been developed for estimating the length of a linear phase FIR notch filter meeting the given specifications. In addition, the design of two-dimensional linear phase FIR notch filters is briefly considered. Illustrative examples are included. This work was supported in part by a University of California MICRO grant with matching supports from Rockwell International and CES Inc.     

The use of linear programming for the design of SAW filters andfilterbanks

A linear programming algorithm is proposed for designing surface acoustic wave (SAW) filters or filterbanks with arbitrary amplitude and phase responses. A modified sampling theorem representation is employed for the transducer frequency responses which allows the number of independent variables to be minimized without degrading the filter characteristics. The method can also be used as part of an iterative procedure to generate optimal corrections for second order effects such as diffraction and circuit loading. A simplified algorithm for this procedure is given, and the method is illustrated with theoretical and experimental data from a three channel contiguous SAW filterbank design. Although the method given in this paper is formulated primarily for SAW filters, it is equally applicable to FIR digital filter design     

Birefringent filter synthesis by use of a digital filter design algorithm

We present an efficient method for designing birefringent filters comprising a number of birefringent sections with equal length and arbitrary orientation between two polarizers and for producing a specified spectral response in transmission. The method uses a digital filter design algorithm (i.e., the Remez algorithm) to determine an optimal polynomial approximation to obtain a specified finite impulse response, and a layer-peeling algorithm to calculate the filter structure parameters. The design procedure is demonstrated for a 14-section bandpass filter with sidelobes below -40 dB. The influence of errors in length and orientation of the birefringent sections on the filter's spectral response is also discussed.     

Recursive Identification of Wiener-Hammerstein Systems with Nonparametric Nonlinearity

A recursive scheme is proposed for identifying a single input single output (SISO) Wiener-Hammerstein system, which consists of two linear dynamic subsystems and a sandwiched nonparametric static nonlinearity. The first linear block is assumed to be a finite impulse response (FIR) filter and the second an infinite impulse response (IIR) filter. By letting the input be a sequence of mutually independent Gaussian random variables, the recursive estimates for coefficients of the two linear blocks and the value of the static nonlinear function at any fixed given point are proven to converge to the true values, with probability one as the data size tends to infinity. The static nonlinearity is identified in a nonparametric way and no structural information is directly used. A numerical example is presented that illustrates the theoretical results.     

Elimination of zero-order diffraction and conjugate image in off-axis digital holography

The presence of zero-order diffraction and a conjugate image in digital holography essentially diminishes the quality of the reconstructed image. In this paper, a novel method that adopts numerical operation to eliminate the zero-order diffraction and conjugate image is presented. The whole process needs only one hologram and a complex finite impulse response (FIR) digital filter. The method of numerical elimination is simple; it filters the hologram directly in the spatial domain instead of in the frequency domain. The design of a complex finite impulse response filter is described in detail. The experimental results demonstrate that the operation can completely eliminate the zero-order diffraction and conjugate image and significantly enhance the quality of the reconstructed image.     

Design of predictive IIR filters via feedback extension of FIRforward predictors

Finite impulse response (FIR) predictors for polynomial signals and sinusoids are easy to design because of the available closed-form design formulae. On the other hand, those FIR predictors have two major drawbacks: the passband gain peak is usually greater than +3 dB, and a long FIR structure is needed to attain high attenuation in the stopband. Both of these characteristics cause severe problems, particularly in control instrumentation when the predictor operates inside a closed control loop. In this paper, we present a novel feedback extension scheme for FIR forward predictors. This extension makes it possible to easily design infinite impulse response (IIR) predictors with low passband ripple and high stopband attenuation. The new approach is illustrated with design examples     

System identification application using Hammerstein model

Generally, memoryless polynomial nonlinear model for nonlinear part and finite impulse response (FIR) model or infinite impulse response model for linear part are preferred in Hammerstein models in literature. In this paper, system identification applications of Hammerstein model that is cascade of nonlinear second order volterra and linear FIR model are studied. Recursive least square algorithm is used to identify the proposed Hammerstein model parameters. Furthermore, the results are compared to identify the success of proposed Hammerstein model and different types of models.     

Comparative analysis of low-pass filters for the demodulation ofprojected gratings in 3-D adaptive profilometry

In 3-D adaptive profilometry based on structured light projection, the choice of the low-pass filter to he used in the deformed pattern demodulation is crucial. In this paper, we have studied the performance of a typical finite impulse response (FIR) and of an infinite impulse response (IIR) Butterworth low-pass filter. Adaptiveness of the filters to both coarse and small variations of the grating frequency has been investigated. The ability of the filters to adapt to coarse changes of the grating frequency has been quantified in terms of their speed of synthesis, while the ability of the filters to tolerate small variations of the grating frequency has been quantified by measuring the residual phase errors. The analysis shows that the IIR Butterworth filter performs better than the FIR filter both in the coarse and in the fine grating frequency variation cases     

Digital filtration of the signal from a moisture content sensor for flowing granular materials

We consider the design of a digital low-frequency FIR (finite impulse response) filter for a capacitive sensor measuring the moisture content of flowing granular materials. We have developed a technique for calculating the filter parameters, taking into account the requirements for ensuring that the amplitude—frequency characteristic is wideband and based on an approximation in the frequency domain. We propose a procedure for choosing the order of the filter. We have analyzed the filtration error and we present an example. Translated from Izmeritel'naya Tekhnika, No. 9, pp. 55–58, September, 1998.     

Optimal FIR and IIR Hilbert transformer design via LS and minimaxfitting

A method for the design of both finite impulse response (FIR) and infinite impulse resonant (IIR) digital Hilbert transformers, based on a parameter estimation method for linear systems, is presented. The first approximation is performed in a least-squares (LS) sense in the complex domain. An iterative extension of the algorithm is also presented. It results in an approximation in a minimax (Chebyshev) sense and is also in the complex domain. The procedures described can be used for the design of digital filters other than Hilbert transformers since the desired frequency response is given point by point     

First-order PMD compensation using optical FIR filter

We present a synthesis algorithm to design an optical finite impulse response (FIR) filter for compensating a first-order polarization mode dispersion (PMD) by minimizing the differential group delay (DGD). The desired frequency response was approximated using two widely used methods in designing digital FIR filters: the Fourier series expansion method and the frequency sampling method. A numerical simulation was performed for an eighth-order filter to demonstrate the difference between the two methods. The simulation results produced a sharper cutoff for the Fourier series expansion and higher stopband attenuation for the frequency sampling method. The Fourier series method produced better results in reducing the DGD.     

Digital filtering implementations for the detection of broad spectral features by direct analysis of passive Fourier transform infrared interferograms

Finite impulse response (FIR) filters and finite impulse response matrix (FIRM) filters are evaluated for use in the detection of volatile organic compounds with wide spectral bands by direct analysis of interferogram data obtained from passive Fourier transform infrared (FT-IR) measurements. Short segments of filtered interferogram points are classified by support vector machines (SVMs) to implement the automated detection of heated plumes of the target analyte, ethanol. The interferograms employed in this study were acquired with a downward-looking passive FT-IR spectrometer mounted on a fixed-wing aircraft. Classifiers are trained with data collected on the ground and subsequently used for the airborne detection. The success of the automated detection depends on the effective removal of background contributions from the interferogram segments. Removing the background signature is complicated when the analyte spectral bands are broad because there is significant overlap between the interferogram representations of the analyte and background. Methods to implement the FIR and FIRM filters while excluding background contributions are explored in this work. When properly optimized, both filtering procedures provide satisfactory classification results for the airborne data. Missed detection rates of 8% or smaller for ethanol and false positive rates of at most 0.8% are realized. The optimization of filter design parameters, the starting interferogram point for filtering, and the length of the interferogram segments used in the pattern recognition is discussed.     

Design considerations for narrow-band dielectric resonant grating reflection filters of finite length

An interference-waveguide approach is developed to predict the response of a resonant grating reflection filter and to provide a better understanding of the resonant process. An expression for the reflected field that accounts for all internal boundary reflections within the filter is developed. Under the assumption of an anti-reflective design, expressions characterizing the line shape of a filter of infinite length are first developed; then the effects of finite length on the response are determined. Expressions relating the length of the filter to the peak reflection efficiency and line width are developed. The degradation of the response as a function of filter length is evaluated. An equivalent waveguide representation is used to determine the location of the resonance as well as the spectral and angular linewidths of the filter. The minimum obtainable spectral linewidth for a filter of given length is determined to be on the order of deltalambda approximately lambda2/L. Rigorous analysis is used to verify the interference-waveguide approach.     

表面测量中抗混叠数字滤波器的设计与实现

在表面测量数据采集系统中,针对抗混叠滤波器设计问题,提出了“模拟滤波器＋数字滤波器”的设计方法．设计了具有线性相位的有限脉冲响应（FIR）型抗混叠数字滤波器,得出了幅频特性和相频特性,满足了表面测量信号处理的要求．与传统的单纯模拟抗混叠滤波器相比,该方法有效降低了对模拟滤波器的设计要求,使其易于实现,滤波效果好．把该方法应用于表面测量系统中,通过对实测数据的应用试验,验证了滤波器的性能．     

斜变滤波器时域加窗对图像重建的影响

提出了斜变滤波器的单位脉冲响应的时域加窗方法。 斜变滤波器的单位脉冲响应应取奇数个点并偶对称,以保证其严格零相位。可以用来截取单位脉冲响应的窗函数有矩形窗、三角窗、汉宁窗、海明窗、布莱克曼窗等。仿真实验表明,矩形窗精度最好,三角窗因过度地压低了第一旁瓣,精度最差,其余窗对应的CT图像的精度介于两者之间。在对斜变滤波器的单位脉冲响应截断时应该使用矩形窗。     

An unbiased FIR filter for TIE model of a local clock in applications to GPS-based timekeeping

An unbiased finite impulse response (FIR) filter is proposed to estimate the time-interval error (TIE) K-degree polynomial model of a local clock in global positioning system (GPS)-based timekeeping in the presence of noise that is not obligatory Gaussian. Generic coefficients for the unbiased FIRs are derived. The low-degree FIRs and noise power gains are given. An estimation algorithm is proposed and examined for the TIE measurements of a crystal clock in the presence of the uniformly distributed sawtooth noise induced by the multichannel GPS timing receiver. Based upon this algorithm, we show that the unbiased FIR estimates are consistent with the reference (rubidium) measurements and fit them better than the standard Kalman filter.     

Filtering of Randomly Sampled Time-Stamped Measurements

This paper concerns the filtering of measurements that are taken by networked sensors at nonuniform intervals but that are accurately time stamped. Traditional digital filtering methods are difficult or impossible to use due to nonuniform sampling. Two filtering methods are described. Both are based on making an assumption about the signal behavior between measurements, such as the signal being constant between measurements. In the first method, a filter is formulated as an ordinary differential equation that is incrementally solved as measurements arrive. Such filtering is general; nonlinear and nontime invariant filters may be constructed. In the second method, signal convolution with a continuous-time finite impulse response filter is efficiently performed using a spline representation for the filter response. Such filters are ldquoFIR likerdquo in the sense that they have frequency-domain performance similar to FIR filters and have only slightly worse asymptotic computation time and memory requirements compared to FIR filters, yet have the advantage of being able to deal with nonuniformly sampled measurements. Examples of the operation of both sorts of filters are shown on actual measured data.     

Fast Initial Response for CUSUM Quality-Control Schemes: Give Your CUSUM A Head Start

The fast initial response (FIR) feature for cumulative sum (CUSUM) quality-control schemes permits a more rapid response to an initial out-of-control situation than does a standard CUSUM quality-control scheme. This feature is especially valuable at start-up or after a CUSUM has given an out-of-control signal. This article presents the average run length and the distribution of run length for CUSUM schemes with the FIR feature and compares FIR CUSUM schemes to standard CUSUM schemes. The comparisons show that if the process starts out in control, the fast initial response feature has little effect; however, if the process mean is not at the desired level, an out-of-control signal will be given faster when the FIR feature is used.