Real-time integration and differentiation of analog signals bymeans of digital filtering

A novel filter design method for broadband recursive digital integrators and differentiators is presented. The performance of the digital infinite-impulse response (IIR) filters designed with the method is compared with that of finite-impulse response (FIR) filters and that of classical numerical integration and differentiation. The common conviction that IIR filters with excellent amplitude characteristics always have poor phase behavior is refuted. It is shown that it is possible to design easily realizable IIR integrators and differentiators with an arbitrarily small amplitude and phase error. While there is no FIR alternative for IIR integrators, both FIR and IIR methods give competitive results for differentiators     

Energy-based effective length of the impulse response of arecursive filter

A measure for the effective length of the impulse response of a stable recursive digital filter based on accumulated energy is proposed. The new measure finds applications in several fields of digital signal processing, including estimation of the extent of attack transients for filters with dynamically varying inputs, elimination of transients in variable recursive filters, and design and implementation of linear-phase IIR systems. A general definition and a simple algorithm to evaluate it are introduced, and closed-form expressions are derived for first and second-order all-pole filters. The effect of zeros on the effective length is analyzed. An upper bound for the effective length of higher-order filters is derived using results for low-order filters, which is illustrated for classical digital lowpass filters. The use of the measure is demonstrated with examples of implementation of linear-phase IIR systems and estimation of transients in variable IIR filters     

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     

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．     

Clutter filter design for ultrasound color flow imaging

For ultrasound color flow images with high quality, it is important to suppress the clutter signals originating from stationary and slowly moving tissue sufficiently. Without sufficient clutter rejection, low velocity blood flow cannot be measured, and estimates of higher velocities will have a large bias. The small number of samples available (8 to 16) makes clutter filtering in color flow imaging a challenging problem. In this paper, we review and analyze three classes of filters: finite impulse response (FIR), infinite impulse response (IIR), and regression filters. The quality of the filters was assessed based on the frequency response, as well as on the bias and variance of a mean blood velocity estimator using an autocorrelation technique. For FIR filters, the frequency response was improved by allowing a non-linear phase response. By estimating the mean blood flow velocity from two vectors filtered in the forward and backward direction, respectively, the standard deviation was significantly lower with a minimum phase filter than with a linear phase filter. For IIR filters applied to short signals, the transient part of the output signal is important. We analyzed zero, step, and projection initialization, and found that projection initialization gave the best filters. For regression filters, polynomial basis functions provide effective clutter suppression. The best filters from each of the three classes gave comparable bias and variance of the mean blood velocity estimates. However, polynomial regression filters and projection-initialized IIR filters had a slightly better frequency response than could be obtained with FIR filters     

A Novel Single-Multiplier Implementation of IIR and FIR Digital Filters Using Tri-State Logic

A new implementation of digital FIR and IIR filters which takes advantage of the availability of tri-state logic for modularity and extensibility is outlined. The filter is a time-based design and uses a single multiplier. The sequence of operations for a second-order IIR filter with such an implementation is illustrated with the aid of a block diagram.     

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.     

Finite impulse response utilizing the principle of superposition

A critical parameter in any finite impulse response (FIR) design is the impulse response length, which must be optimized for the given design specifications in order to reduce the size of the filter. To this end, many design algorithms have been introduced, such as Remez exchange, linear programming, and least mean squares. A new algorithm has been derived that is simple, efficient, and accurate for the design of arbitrary filter specifications and requires fewer computations than many other FIR approaches. This paper provides the definition of the basic functions used for the design process. An overview of the design process is given and the design technique used to design filters with tailored passband and stopband responses to yield a near-optimum time length is presented. This design can be very useful when compensating for the effects of a second transducer or other second order effects in surface acoustic wave (SAW) devices. The effects of monotonically increasing sidelobes on the impulse response length are discussed and illustrated. The addition of arbitrary phase response to the filter design process is discussed. The results of the current FIR approach are discussed and compared with other design techniques.     

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.     

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     

Signal processor implementation of variable digital filters

The implementation of two recently introduced variable digital filter schemes using a TMS320-series digital signal processor is presented. One is a method for updating the coefficients of an FIR (finite-impulse response) filter in a simple manner such that the cutoff frequencies can be controlled through a single parameter. The other is a method for tuning the cutoff frequency of an IIR (infinite-impulse response) filter with one parameter using a series expansion of the low-pass-low-pass frequency transformation. The measured frequency responses compare well with the theory     

Multiple delay line shaping: a new class of weighting functions suitable for digital signal processing

We introduce a whole class of weighting functions, that can be implemented with an analog prefilter, an analog-to-digital converter and a FIR or IIR digital filter. These weighting functions feature a finite duration and can have a flat top within less than 1%. General rules are given about the design of such general class of filters. The shape of the obtained weighting function is strictly related to the chosen prefilter, and its duration may be effectively shrinked by the digital processing. However the number of samples required in order to keep a finite duration of the weighting function is shown to increase with the complexity of the prefilter. The developed class of weighting functions can be alternatively implemented with analog delay lines or switched-capacitor filters.     

Recursive implementation of FIR differentiators with optimum noiseattenuation

We introduce a computationally efficient recursive implementation of digital finite impulse response (FIR) filters for estimating the rate of change or slope of digitized signals. The proposed FIR differentiator is characterized by the optimal attenuation of white noise and an efficient suppression of upper-band frequencies. The basic structure needs only one multiplier, which becomes a power of two with an appropriate selection of the length of the impulse response. The structure does not need resetting and recovers from any bit errors. For long filters, sampling rate reduction by decimation gives further computational savings     

Adaptive IIR filter design for single sensor applications

The goal of this research was to investigate the theoretical design and physical implementation of a digital adaptive IIR filter to serve as an enhancement to the traditional active RC or passive RLC anti-aliasing filter. This all-digital filter will reside directly on the DSP engine. As explained in the paper, the adaptive IIR filter is designed to process an oversampled signal coming from a single sensor to reject noise in an acquisition system. Differentiation between the noise and the signal is obtained by exploiting the different auto-correlation functions of the two signals. In contrast to oversampling techniques employed in sampled data systems that are designed to relax the requirements of an analog anti-aliasing filter, this filter will track a signal in the frequency domain. Several power spectral density plots are given to illustrate the performance of the new filter. The results also indicate that the new filter performs well as compared to the Wiener filter in the stationary case     

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.     

Design and efficient implementations of predictive FIR filters

Two new approaches to the design of predictive FIR filters are presented. First, we discuss the design of predictors and estimators for narrow-band signals based on the interpolated FIR (IFIR) filter approach. The transfer function of the IFIR predictor is of the form H(z)=P(z^L)G(z) where P(z) is a predictor and G(z) is an interpolating estimator. The general-purpose design procedure for efficient IFIR predictors is described, and demonstrated for polynomial predictors. The resulting predictors, optimized for white noise attenuation, have much lower computational complexity than the corresponding direct-form FIR predictors. Secondly, an IIR filter-based implementation of sinusoidal FIR predictors is presented. As an application, a zero-crossing detector for 50 Hz thyristor drives is designed     

The effect of accumulation of cathodic decomposition on the anodic conversion of sulfide ions to sulfur in a continuous extractive electrochemical reactor

Abstract

This paper presents an intelligent digital filter synthesis system which consists of a user‐friendly graphic I/O interface, a synthesis program designing filter coefficients, an intelligent hardware generation system and a simulator including time and frequency domain simulation. Users need only to specify the filter type, filter specifications, sampling rate requirement and some parameters through the graphic interface. The filter response and the simulation results can be immediately shown on the screen. The graphic interface is based on the X Window System and therefore provides a network‐transparent and vendor‐independent operating environment for the system. The synthesis system is targeted for two main types of digital filter: FIR and IIR. An automatic partition algorithm on FIR is developed to meet the user's sampling rate requirement. The optimal cascade architecture of biquad‐based IIR with programmable coefficients is also derived. The final circuit designs under economic bitwidth are generated by the GDT system and further layouts can be generated.     

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.     

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     

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.