Polynomial Filters Research Articles

A block Chebyshev–Davidson method with inner–outer restart for large eigenvalue problems

We propose a block Davidson-type subspace iteration using Chebyshev polynomial filters for large symmetric/hermitian eigenvalue problem. The method consists of three essential components. The first is an adaptive procedure for constructing efficient block Chebyshev polynomial filters; the second is an inner–outer restart technique inside a Chebyshev–Davidson iteration that reduces the computational costs related to using a large dimension subspace; and the third is a progressive filtering technique, which can fully employ a large number of good initial vectors if they are available, without using a large block size. Numerical experiments on several Hamiltonian matrices from density functional theory calculations show the efficiency and robustness of the proposed method.

Discrete polynomial moments and the extraction of 3-D embossed digits for recognition

We extend the theory of polynomial moments by proving their spectral behavior with respect to Gaussian noise. This opens the door to doing computations on the signal-to-noise ratios of polynomial filters and with this, the comparability to classical filters is made possible. The compactness of the information in the polynomial and Fourier spectra can be compared to determine which solution will give the best performance and numerical efficiency. A general formalism for filtering with orthogonal basis functions is proposed. The frequency response of the polynomials is determined by analyzing the projection onto the basis functions. This reveals the tendency of polynomials to oscillate at the boundaries of the support; the resonant frequency of this oscillation can be determined. The new theory is applied to the extraction of 3-D embossed digits from cluttered surfaces. A three-component surface model is used consisting of a global component, corresponding to the surface; a Gaussian noise component, and local anomalies corresponding to the digits. The extraction of the geometric information associated with the digits is a preprocessing step for digit recognition. It is shown that the discrete polynomial basis functions are better suited than Fourier basis functions to fulfill this task.

LowModeMD—Implicit Low-Mode Velocity Filtering Applied to Conformational Search of Macrocycles and Protein Loops

We present a method for conformational search of complex molecular systems such as macrocycles and protein loops. The method is based on perturbing an existing conformation along a molecular dynamics trajectory using initial atomic velocities with kinetic energy concentrated on the low-frequency vibrational modes, followed by energy minimization. A novel Chebyshev polynomial filter is used to heavily dampen the high-frequency components of a randomly generated Maxwell-Boltzmann velocity vector. The method is very efficient, even for large systems; it is straightforward to implement and requires only standard force-field energy and gradient evaluations. The results of several computational experiments suggest that the method is capable of efficiently sampling low-strain energy conformations of complex systems with nontrivial nonbonded interaction networks.

Root and pre-constant signals of the 1D Teager-Kaiser operator

We give an input/output characterization of the Teager-Kaiser operator, then we classify the root signals (those that remain invariant) and the pre-constant signals (those that produce a constant output) of the operator. With the gained knowledge, a simple detector of sinusoidal signals and of their corresponding frequencies is designed. The methods used allow for a certain amount of generalization providing a paradigm of sorts for the design of quadratic and other polynomial filters.

Data validation of intelligent sensor using predictive filters and fuzzy logic

A new approach using polynomial predictive filters and fuzzy logic for the online validation of sensor measurements is proposed. Polynomial predictive filters are applied to measured data records during the fault free learning stage. Predictions derived from the predictive filters are compared with the actual measurements to generate an error sequence. Fuzzy rules are then derived from the error sequence together with the physical constraints of a sensor to classify the quality of measurements. Faulty measurements can then be picked up by the fuzzy detection rules to ensure the correctness of measurements. Experimental results for detecting the quality of measurements from a temperature sensor are presented.

Designing pareto optimal nonlinear filters for image processing

We consider a method of designing multidimensional polynomial filters characterized by an interval of a discrete functional Volterra series. This method allows designing Pareto optimal nonlinear filters by several criteria. We prove that finding a set of Pareto optimal alternatives is equivalent to minimizing a weighted target function. The designed nonlinear filter is characterized by the plane tangent to a convex optimal solving function, whose curvature is determined by how contradictory the given criteria are. We show examples of polynomial filter design for image processing and compare them with known filters of the same class.

Hybrid signal processing in voltammetric determination of chromium(VI)

This study presents different hybrid signal processing algorithms which are useful in the interpretation of voltammetric signals recorded on mercury film electrodes for the determination of Cr(VI). Because of the complex character of the distortions (random, fast increasing, nonlinear, background noise and other perturbations) the application of a complex numerical procedure is necessary. In this work different variants of hybrid algorithms are utilized: adaptive degree polynomial filter, baseline generation and subtraction, signals ratio method, orthogonal signal correction and continuous wavelet transformation with dedicated mother wavelet. The operation and effectiveness of proposed procedures were tested by the determination of very low concentrations of Cr(VI) in synthetic and river water samples.

Personality differences affect brainstem autonomic responses to visceral pain

Brainstem autonomic nuclei integrate interoceptive inputs including pain, with descending modulation, to produce homeostatic and defence outputs. Cardiac Vagal Control is especially implicated in psychophysiological processes for both health and disease and is indexed non-invasively by heart rate variability. The study aim was to determine the nature of psychophysiological response profiles for visceral pain. Nineteen healthy subjects had electrocardiographic recordings at rest and during 10 painful oesophageal balloon distensions. Cardiac Vagal Control originating from nucleus ambiguus (CVC(NA)) was determined by polynomial filter application to the electrocardiogram inter-beat interval series. Heart rate and 'Cardiac Sympathetic Index (CSI)' were also determined. Psychological state and trait, including neuroticism and extroversion, were assessed. Subjects who increased CVC(NA) to pain were more neurotic, anxious and sensory sensitive than those who decreased CVC(NA.) Cluster analysis identified two psychophysiological groups: Group 1 (n = 11) demonstrated lower baseline CVC(NA) (P = 0.0001), higher heart rate (P = 0.02) and CSI (P = 0.015), pain tolerance at lower balloon volumes (P = 0.04), but attenuated heart rate response to pain (P = 0.01). Group 2 (n = 8) had the converse profile. Neuroticism scores were higher (P = 0.0004) and extroversion lower (P = 0.01) for group 1 than group 2. Two distinct psychophysiological response profiles to visceral pain exist that are influenced by personality. These may reflect different psychobiological bases for active and passive defence repertoires. Prevalence and clinical relevance of these endophenotypes as vulnerability factors for pain and emotion disorders warrant further exploration.

Rotational-oscillational motions of the nonrigid Earth about the center of mass

We use the model of a nearly axisymmetric viscoelastic rigid body to study perturbed rotational-oscillational motions of the Earth’s pole. We point out that the Chandler component of oscillations is of celestial-mechanics nature and is caused by the gravitational-tidal actions of the Sun and the Moon. We analyze the pole oscillation excitation mechanism at a frequency close to the Chandler frequency and show that the undamped pole oscillations are caused by the resonance harmonic of the external perturbation at a frequency close to the free nutation frequency. We discuss whether it is possible to solve the problem of constructing a short-term forecast of the pole motion on the basis of a polynomial filter obtained by the least-squares method without taking into account small-scale oscillations caused by wide-band random factors of arbitrary physical nature. In the present paper, we perform numerical simulation of tidal inhomogeneities in the Earth’s axial rotation. Attention is mainly paid to the analysis of day length variations on short time intervals with periods less than or equal to one year (interannual oscillations) and to their forecast.

Effect of Bandpass Filters for TA Suppression in Perpendicular Recording System

Thermal asperities (TAs) cause a crucial problem in magnetic recording systems because they can distort the readback signal to the extent of causing possible sector read failure. This problem becomes even more severe in perpendicular recording channels because these channels contain a d.c. component. This paper presents a novel TA suppression method by use of a bandpass ¯lter to mitigate the TA effect. We also investigate the effect of different bandpass filters for TA suppression. Results indicate that the proposed TA suppression method using a bandpass filter polynomial G(D) = (1+D)2(1-D) yields lower bit-error rate than the existing ones at the expense of increased complexity, and is also robust to large peak TA amplitudes.

A novel adaptive bilinear filter based on pipelined architecture

To overcome the computational complexity of the Volterra filter, a novel adaptive joint process filter using pipelined bilinear polynomial architecture (JPBPF) is proposed in this paper. The proposed architecture consists of two subsections: nonlinear subsection performing a nonlinear mapping from the input space to an intermediate space by the bilinear polynomial filter (BPF), and a linear filter performing a linear mapping from the intermediate space to the output space. The corresponding adaptive algorithms are deduced for the nonlinear subsection and linear filter subsection, respectively. To evaluate the performance of the JPBPF, a series of simulations are presented including nonlinear system identification, predicting of speech signals and nonlinear channel equalization. Compared with the conventional second-order Volterra (SOV) filter and BPF, the JPBPF exhibits a slightly better convergence performance in terms of convergence speed and steady-state error. Moreover, since those modules of a JPBPF can be performed simultaneously in a pipelined parallelism fashion, this would lead to a significant improvement in its total computational efficiency.

A comparative study on several algorithms for denoising of thin layer densitograms

This paper compares classical filtering techniques (Savitzky–Golay, Adaptive Degree Polynomial Filter, Fourier denoising, Butterworth and Chebyshev IIR filters) and the wavelet shrinkage (31 mother wavelets, 3 thresholding techniques and 11 decomposition levels). These techniques were compared with the original noisy signal and the reference signal, denoised experimentally by the averaging of 64 measurements. The best similarity to reference signal was observed in the case of filters, but they slightly oversmoothed the signal. The wavelet shrinkage gave less denoised signals. The significant influence of the thresholding technique and decomposition level was observed (the best conditions—the level 2 or 3 and soft thresholding). Changing of the mother wavelet almost does not change the result, which is similar to the earlier literature findings. The presented results can be used as general recommendations for denoising of the densitometric fingerprints before applying further chemometric algorithms. The best choices are: Savitzky–Golay filter of appropriate (optimized against the autocorrelation) window width or wavelet shrinkage with Haar wavelet, soft thresholding and high decomposition level.

State estimation of stochastic systems with switching measurements: A polynomial approach

AbstractThe state estimation problem is here investigated for a class of stochastic linear switching‐output systems, in which the output matrix switches in a finite set of possible values according to a not directly measured discrete Markov sequence. This note presents a real‐time algorithm, based on the optimal polynomial filtering approach, which achieves the simultaneous estimation of both the continuous system state and the switching parameter. The state and observation noises do not need to be Gaussian. It is shown that the optimal filter of degree one (best affine filter) does not solve the parameter estimation problem, due to a structural first‐order unobservability property, and therefore the use of higher‐order filters becomes necessary. As an application of the proposed filter, the problem of the online simultaneous estimation of the transmitted signal and of the impulse response samples of a multipath fast‐fading digital communication channel is considered in this paper. Differently from other approaches, the polynomial filter solves the problem without the use of training sequences (preambles) in the transmitted data, so that the information flow through the channel is not interrupted. Copyright © 2009 John Wiley & Sons, Ltd.

Suppressing the charged coupled device noise in univariate thin-layer videoscans: A comparison of several algorithms

The digital processing of chromatographic thin-layer plate images has increasing popularity among last years. When using a camera instead of flatbed scanner, the charged coupled device (CCD) noise is a well-known problem—especially when scanning dark plates with weakly fluorescing spots. Various techniques are proposed to denoise (smooth) univariate signals in chemometric processing, but the choice could be difficult. In the current paper the classical filters (Savitzky–Golay, adaptive degree polynomial filter, Fourier denoising, Butterworth and Chebyshev infinite impulse response filters) were compared with the wavelet shrinkage (31 mother wavelets, 3 thresholding techniques and 8 decomposition levels). The signal obtained from 256 averaged videoscans was treated as the reference signal (with noise naturally suppressed, which was found to be almost white one). The best choice for denoising was the Haar mother wavelet with soft denoising and any decomposition level larger than 1. Satisfying similarity to reference signal was also observed in the case of Butterworth filter, Savitzky–Golay smoothing, ADPF filter, Fourier denoising and soft-thresholded wavelet shrinkage with any mother wavelet and middle to high decomposition level. The Chebyshev filters, Whittaker smoother and wavelet shrinkage with hard thresholding were found to be less efficient. The results obtained can be used as general recommendations for univariate denoising of such signals.

Contribution of Light Scattering to near Infrared Absorption in Milk

The presence of milk fat globule emulsion produces scattering phenomena on near infrared (NIR) radiation through the raw milk. Numerically, 80% of milk fat globules have a diameter of less than 3μm interfering with the radiation having a wavelength from 1 μm to 2.5 μm with a radiation dispersion in all directions. Consequently, the NIR transmitted radiation does not behave in accordance with Lambert–Beer's law: the NIR spectra of milk samples with high fat content have high offset values and lower specific absorptions than those of samples with lower fat levels. Usually, this problem is reduced by acting at the level of sample preparation (homogenisation), of optical geometry (transflectance mode coupled with the use of an integrating sphere to collect the widespread radiation) and using chemometric regression models able to optimise non-linear spectral responses. Transmittance measurements have already been exploited for the determination of macro-composition in the agro-food and in the dairy fields. In this work, a set of 150 individual milk samples, collected over three days from a single farm with 49 milking cows, was analysed with Fourier transform-NIR apparatus in order to study the effects of scattering on partial least squares predictors for casein. The spectra of non-homogenised raw whole milk and the respective skimmed samples were collected in transmission mode. Using the true scattering curves obtained by subtraction from the raw milk spectra of skimmed milk spectra the extended multiplicative scatter correction (EMSC) estimate of scattering effects was optimised. EMSC uses polynomial filters in modelling the aspecific absorptions due to the scattering effects. The correct scatter elimination can help in the individuation and interpretation of the true predictors in calibration procedures.

The Arnoldi Eigenvalue Iteration with Exact Shifts Can Fail

The restarted Arnoldi algorithm, implemented in the ARPACK software library and MATLAB's eigs command, is among the most common means of computing select eigenvalues and eigenvectors of a large, sparse matrix. To assist convergence, a starting vector is repeatedly refined via the application of automatically constructed polynomial filters whose roots are known as “exact shifts.” Though Sorensen proved the success of this procedure under mild hypotheses for Hermitian matrices, a convergence proof for the non-Hermitian case has remained elusive. The present note describes a class of examples for which the algorithm fails in the strongest possible sense; that is, the polynomial filter used to restart the iteration deflates the eigenspace one is attempting to compute.

Real time estimation in local polynomial regression, with application to trend-cycle analysis

The paper focuses on the adaptation of local polynomial filters at the end of the sample period. We show that for real time estimation of signals (i.e., exactly at the boundary of the time support) we cannot rely on the automatic adaptation of the local polynomial smoothers, since the direct real time filter turns out to be strongly localized, and thereby yields extremely volatile estimates. As an alternative, we evaluate a general family of asymmetric filters that minimizes the mean square revision error subject to polynomial reproduction constraints; in the case of the Henderson filter it nests the well-known Musgrave’s surrogate filters. The class of filters depends on unknown features of the series such as the slope and the curvature of the underlying signal, which can be estimated from the data. Several empirical examples illustrate the effectiveness of our proposal.

Synthesis of neural pulse interference filters for image restoration

The synthesis of nonlinear pulse interference filters in the form of three-layer and polynomial perceptrons has been considered in this study. Neural filters were used for removing the “salt and pepper“-type pulse interference from half-tone images. It was shown that a three-layer perceptron filter in terms of the filtration accuracy is not inferior to its polynomial analogues and its mathematical model is mush simpler than the Volterra model. Neural and polynomial filters ensure a higher level of pulse interference suppression as compared with median filters.

Efficient predictive estimator for holdover in GPS-based clock synchronization

This paper addresses an unbiased p-step predictive finite impulse response (FIR) filter of the local clock K-degree time interval error (TIE) polynomial model with applications to the global positioning system (GPS)-based clock synchronization. Generic coefficients are derived for a 2-parameter family of the polynomial filter gains. A generalization is provided for the p-step linear (ramp) gain allowing for close to optimal predictive filtering of the TIE. Basic holdover algorithms are discussed along with their most critical properties. Efficiency of the proposed filter in holdover is demonstrated by simulation and in real applications to GPS-based (sawtooth and sawtoothless) measurements of the TIE of a crystal clock.

Analysis and Identification of Wiener-Hammerstein System in Frequency Domain Using Two-Tone Measurements for Nonlinear RF Transmitters

This paper presents analysis and identification method of Wiener-Hammerstein system to characterize a nonlinear RF transmitter in fundamental frequency zone. A two-tone signal is used to analyze and identify a Wiener-Hammerstein model. A RF signal is converted to baseband-equivalent complex signal, and Wiener-Hammerstein model is considered to have a baseband equivalent complex polynomial and linear filters. For a two-tone input signal, closed form descriptions of the output signal in the time domain and frequency domain are developed using a newly suggested nonlinearly modulated two-tone phasors (NMTP). The relationship between frequency terms of input and output signals in RF transmitters are represented with linear matrix-vector equation based on NMTP analysis. An advantage of the proposed method is its simplicity using closed form analysis and linear approximation. In addition, we can model a wideband system with relatively narrowband measurements by sweeping two-tone signal. The prediction of spectral regrowth and the predistortion performance for WiBro 1FA signal demonstrate the validity of the proposed approach in identifying the nonlinear RF transmitters.