Optimum Inverse Filter Research Articles

A Signal Filtering Method for Magnetic Flux Leakage Detection of Rail Surface Defects Based on Minimum Entropy Deconvolution

Magnetic flux leakage (MFL) detection of rail surface defects is an important research field for railway traffic safety. Due to factors such as magnetization and material, it can generate background noise and reduce detection accuracy. To improve the detection signal strength and enhance the detection rate of more minor defects, a signal filtering method based on minimum entropy deconvolution is proposed to denoise. By using the objective function method, the optimal inverse filter parameters are calculated, which are applied to the filtering detection of MFL signals of the rail surface. The detection results show that the peak-to-peak ratio of the defect signal and noise signal detected by this algorithm is 2.01, which is about 1.5 times that of the wavelet transform method and median filtering method. The defect signal is significantly enhanced, and the detection rate of minor defects on the rail surface can be effectively improved.

Superior optimal inverse filtering of cutting forces in milling of thin-walled components

Measuring the cutting force when milling slender/thin-walled parts is difficult because of the large and long-lasting structural vibrations that cause inertial disturbances in the measured signals. Under these conditions, signal filtering is the only option to significantly extend the dynamic bandwidth of the device above 3 kHz. Non-parametric filters are typically preferred over parametric ones because they are more practical and easier to apply in industrial applications. Currently available parametric filters cannot address this problem because they are based on oversimplified transmissibility models or are affected by computational problems when the impulse responses of the device are excessively long. In this study, the novel non-parametric Superior Optimal Inverse Filter was developed to address the limitations of state-of-the-art filters. It is a non-trivial extension of the Optimal Inverse Filter to a higher dimensionality, and it can process long transients and generic (possibly aperiodic) signals. Thus, outstanding results were obtained both from modal analysis and from an actual case study, demonstrating the potential of the new filter for an effective and almost completely automatic cutting force dynamic compensation when milling thin-walled structures. The proposed filter was compared with parametric Kalman filters and with the existing non-parametric filters, and it offered a considerably better performance, particularly for compensating for cross disturbances and for input force position-dependent dynamics.

Application of a Novel Improved Adaptive CYCBD Method in Gearbox Compound Fault Diagnosis

Recently, cyclostationary blind deconvolution (CYCBD) is often used in gearbox fault feature extraction, and it is more effective in recovering single periodic pulse. However, in the engineering application of CYCBD, the filter length ( $L$ ) and cycle frequency ( $\alpha$ ) need to be verified and set through a large number of experiments, and the efficiency is very low; Moreover, the effect is not good when it is used to extract composite fault features under the background of strong noise. In order to overcome the above limitations, empirical mode decomposition (EEMD) is used to preprocess the composite fault. EEMD can remove the high-frequency noise and weak correlation components in the sampled signal. The strong correlation component is reconstructed to obtain the modal function closer to the fault frequency. The chimpanzee intelligent algorithm is applied to the determination of $L$ and $\alpha $ of CYCBD by optimization to form an adaptive CYCBD. Adaptive CYCBD takes the dispersion entropy of envelope spectrum as the fitness function of chimpanzee optimization algorithm (CHOA), and finds the optimal $L$ and $\alpha $ through iteration. The optimal parameter value is applied to CYCBD, and the reconstructed modal function is deconvoluted to obtain the optimal inverse filter, so as to accurately separate the fault characteristic components. Simulation and experimental results show that this method is effective for gearbox composite fault diagnosis and extraction under strong noise background.

Adaptive Filtered-x Algorithms for Room Equalization Based on Block-Based Combination Schemes

Room equalization has become essential for sound reproduction systems to provide the listener with the desired acoustical sensation. Recently, adaptive filters have been proposed as an effective tool in the core of these systems. In this context, this paper introduces different novel schemes based on the combination of adaptive filters idea: a versatile and flexible approach that permits obtaining adaptive schemes combining the capabilities of several independent adaptive filters. In this way, we have investigated the advantages of a scheme called combination of block-based adaptive filters which allows a blockwise combination splitting the adaptive filters into nonoverlapping blocks. This idea was previously applied to the plant identification problem, but has to be properly modified to obtain a suitable behavior in the equalization application. Moreover, we propose a scheme with the aim of further improving the equalization performance using the a priori knowledge of the energy distribution of the optimal inverse filter, where the block filters are chosen to fit with the coefficients energy distribution. Furthermore, the biased block-based filter is also introduced as a particular case of the combination scheme, especially suited for low signal-to-noise ratios (SNRs) or sparse scenarios. Although the combined schemes can be employed with any kind of adaptive filter, we employ the filtered-x improved proportionate normalized least mean square algorithm as basis of the proposed algorithms, allowing to introduce a novel combination scheme based on partitioned block schemes where different blocks of the adaptive filter use different parameter settings. Several experiments are included to evaluate the proposed algorithms in terms of convergence speed and steady-state behavior for different degrees of sparseness and SNRs.

High-frequency Compensation of Dynamic Distortions in Micromachining Force Measurements

In this paper, we present a comprehensive technique to obtain accurate three-dimensional (3D) micromachining forces for frequency bandwidths up to 25kHz. The capability to precisely measure cutting forces is central to gaining fundamental understanding on micromachining mechanics and dynamics. Multi-axis dynamometers are used to measure 3D machining forces. Forces experienced during micromachining involve very high frequencies due to the ultra-high spindle speeds used during the process. However, the specified bandwidths of the dynamometers do not meet high frequency requirements of micromachining forces; this limitation stems from the structural-dynamics response of the dynamometers. Therefore, it is important to develop approaches to compensate for the distortions arising from the dynamic effects of the dynamometer's structure in order to accurately measure micromachining forces. This paper presents a fully 3D compensation approach to enable accurate determination of 3D micromachining forces within a wide frequency range. The presented approach involves: (1) accurate identification of 3D force measurement characteristics of the dynamometer in the form of 3x3 force-to-force frequency response functions (F2F-FRFs) matrix within a 25kHz bandwidth, (2) design of an optimal inverse filter for post-processing the measured force data to remove the influence of structural dynamics of the dynamometer; and (3) validation of the compensation approach through impact testing where the actual applied force data acquired by the reference force sensor is compared with the corrected dynamometer measurements. Subsequently, the presented approach is demonstrated by obtaining 3D micromachining forces during micromilling of a brass workpiece. It is concluded that the presented approach is effective in high-frequency correction of dynamometer measurements for accurate measurement of 3D micromachining forces within the 0- 25kHz frequency range.

Inverse spiking filter based acquisition enhancement in software based global positioning system receiver

The lower visibility of the satellite in the acquisition stage of a GPS receiver under worst noisy situation leads to reacquisition of the data and thereby takes a longer time to obtain the first position fix. If the impulse noise affects the GPS signal, the conventional ways of acquiring the satellites do not guarantee to meet the minimum requirement of four satellites to find the user position. The performance of GPS receiver acquisition can be improved in the low SNR level using inverse spiking filtering technique. In the proposed method, the estimate of the desired GPS L1 signal corrupted by impulse noise (gn) is obtained by the prediction error filter (hopt), which is the optimum inverse filter that reshapes the noisy signal (yn) into a desired GPS signal (xn). In the proposed method, to detect the visible satellites under weak signal conditions the traditional differential coherent approach is combined with the inverse spiking filter method to increase the number of visible satellites and to avoid the reacquisition process. Montecarlo simulation is carried out to assess the performance of the proposed method for C/N0 of 20dB-Hz and results indicate that the modified differential coherent method effectively excises the noise with 90% probability of detection. Subsequently tracking operation is also tested to confirm the acquisition performance by demodulating the navigation data successfully.

EFFECTIVE VIBRATION ANALYSIS OF IC ENGINES USING CYCLOSTATIONARITY. PART II—NEW RESULTS ON THE RECONSTRUCTION OF THE CYLINDER PRESSURES

This part addresses the feasibility of reconstructing the pressure trace in IC engine from non-intrusive structural vibration measurements by means of an optimal inverse filter. The problem is formally phrased into the general framework of cyclostationary processes introduced in Part I of this paper. It is proved that the optimal inverse filter is periodically varying. A number of guidelines are given for efficiently applying the proposed deconvolution scheme.

Mixed-phase deconvolution and wavelet estimation

The seismic convolutional model describes seismic wave propagation as a linear system. A seismic trace then consists of a wavelet or pulse convolved with the reflection response or reflectivity series plus additive noise. An important problem in seismic data processing is the removal of the effect of the wavelet (spiking deconvolution or inverse filtering) in order to estimate the reflectivity series. When the wavelet is known, designing an optimal spiking filter by a least-squares approach is straightforward. For a mixed-delay wavelet, we must delay the position of the desired output spike. This delay can later be removed so that the effective filter is no longer causal but operates on both past and future input data values with respect to the output position. When the wavelet is unknown, we must determine both the wavelet and the reflectivity series from the input data. Solving this ambiguous problem requires additional assumptions about the wavelet, the reflectivity series, and the noise. Common assumptions are that the reflectivity series is a stationary random process and that it is uncorrelated to the stationary random noise. Furthermore, if it is assumed that the signal-to-noise ratio is large, the autocorrelation function (ACF) of the seismic trace can be used as an estimate of the ACF of the wavelet. If, in addition, it is assumed (as it commonly is) that the wavelet is minimum delay, meaning that all roots of its associated polynomial have amplitude greater than 1, an optimal least-squares inverse filter can be computed by solving the normal equations using a Levinson algorithm. The normal equations are also called the Yule-Walker (YW) equations. However, problems can arise with minimum-phase inverse filtering when the wavelet is not minimum delay. In a tutorial on spiking deconvolution ( TLE , 1995), Leinbach showed that applying a minimum-phase filter to an air-gun …

H/sub 2/ optimal inverse of periodic FIR digital filters

The objective of this correspondence is to design a fixed-order H/sub 2/ optimal inverse filter of a given periodic FIR digital filter in the presence of measurement noise. The problem is solved by using a linear matrix inequality (LMI) approach to an equivalent time-invariant H/sub 2/ optimization problem constructed by applying the lifting technique to the original periodic problem. An example is given to demonstrate the effectiveness of the proposed design approach.

A new approach for the modelling of track geometry recording vehicles and the deconvolution of versine measurements

SUMMARYThis article deals with railway track geometry in horizontal and vertical directions, and its measurement by means of track recording vehicle. The first part of the article introduces the mathematics tools for describing planar curves, mainly the “transformed curve” defined as the double integration of the algebraic local curvature, function of the curvilinear abscissa. The complete non linear model of the non-centered versine apparatus has been calculated in this space, as well as its simplification in the case of low local angular values. The main contribution of this article lies in the choice of algebraic local curvature as system input for the further inversion of experimental data. The following part describes the deconvolution procedure using the Wiener approach; therefore the optimal inverse filter becomes the multiplication of the direct inversion by a regularization function linked to the signal-to-noise ratio. Then, the direct modelling of the French Mauzin measurement system and the adapted inverse numerical filtering (in horizontal and vertical directions) are calculated. It is shown that the inverse procedure allows the deconvolution of track irregularities of up to 150m wavelengths.

BLIND DECONVOLUTION OF IMPACTING SIGNALS USING HIGHER-ORDER STATISTICS

Experimental impacting signals with unknown measurement noise are examined using third-order statistics blind deconvolution. The impulse impact signals are recovered and the estimation of the time between impacts improved. The procedure for obtaining the optimal inverse filter is addressed using objective functions based onkth- (and second)-order statistics. The efficiency and robustness of the schemes based on a third-, fourth-, fifth- and sixth-order statistics are compared.

(Semi‐)automatic pitch‐synchronous computation of glottal flow

Large‐scale investigations of the aerodynamics of voice production are most easily performed using noninvasive measurement methods. Glottal airflow can be estimated by inverse filtering the mouth flow, measured with a pneumotachograph mask. A semi‐automatic pitch‐synchronous inverse filtering method was developed that combines the advantages of interactive inverse filtering and inverse filtering with fixed‐filter settings: Our method yields accurate and calibrated estimates of glottal flow during VC and CV transitions, which are amenable for parametrization and can be used for bulk processing. Using glottal dosing and opening moments derived from the electroglottogram, covariance LPC analysis on the closed glottis interval is employed to compute the optimal inverse filter for each period. For male speakers, the method yields quite stable waveforms. These will be parametrized in order to develop rules for a physiologically interpretable, time‐varying synthetic voice source. The control parameters used are F0, duty cycle, top‐top flow amplitude, glottal leak area, and vertical phasing. A number of these parameters can be derived from both the EGG and the glottal flow. Comparison of parameter values from the two signals will give an indication of their reliability. The results will be discussed.

A comprehensive solution to the linear deconvolution problem

Summary Linear inverse theory is used to deconvolve a data set when the blurring function or source wavelet is (approximately) known. Rather than attempting to find one of infinitely many models which fits the data this paper uses the methods of Backus and Gilbert to generate localized averages of the model which are unique except for a statistical uncertainty caused by errors in the data. The averages, their statistical error and the associated averaging window completely codify our knowledge about the model. Averages with lower standard deviations can be had by sacrificing resolution and the investigator is free to choose those results which are most meaningful. Moreover, this method is optimum in the sense that no other averaging window can be constructed which has greater resolving power and yet produces averages with the same statistical accuracy. Our deconvolution method in the time domain is shown to be very similar to finding the inverse filter of the source wavelet, and indeed the averaging window is simply the convolution of these two functions. However, by investigating the trade-off between resolution and accuracy we have shown that the data errors can be much more important than the parameters of the Wiener optimum inverse filter such as the length of that filter and the desired location of the output spike. In the frequency domain the equations for trading off accuracy and resolution have been developed and the computations are seen particularly to be simple because no matrix inversion is required. Sufficient examples will be presented to show the importance of incorporating the observational errors into the deconvolution procedure. Additionally, we have shown how to reduce the sidelobes of the averaging windows by shaping them into Gaussian functions of a predetermined width, have looked at the effects of using a zero area source function characteristic of seismic problems, and have attempted a deconvolution when the wavelet was only approximately known. The frequency domain deconvolution filter derived here is also compared quantitatively with those derived intuitively by Helmberger and Wiggins and Deregoiwski. Lastly, we show how information in the averages and averaging windows can be used to construct a parametric model, composed of a series of delta functions, which fits the data. Such a model is of importance in seismological and spectroscopic studies.

Some experiments with an area function dyad synthesizer

An area function dyad synthesis procedure is described which is based on an area function model representing the vocal tract as a set of 14 cross‐sectional areas. Area functions representing phoneme steady states (nuclei) and transitions between any ordered pair of phonemes (dyads) are stored in a dyad table. Given an input phoneme string, the synthesizer selects the corresponding sequence of nuclei and transitions and interpolates between each of the 14 cross‐sectional areas, producing a model of the shape of the vocal tract changing in time. The filtering process of this vocal tract model is identical to the optimum inverse filter of linear prediction analysis, allowing direct conversion to linear predictive coding (LPC) synthesis. Experiments were performed which tested the effect of varying certain attributes of the synthesizer, viz., linear versus spline interpolation, one point versus three point transitions, nucleus versus no nucleus, and different gain roles. Results will be discussed and a tape played. [Work supported by Rome Air Development Center under Contract No. F30602‐77‐C‐0056.]

On the use of linear prediction error energy for speech and speaker recognition

The error energy of the linear prediction inverse filter seems to give an effective triter ion for speech and speaker recognition. In this task, reference sounds are stored in terms of their filter coefficients and the error energy of their optimal inverse filters. The error energy of an unknown sound from each reference filter is compared with the reference error energy (Method A). Alternately, the error energy of the optimal inverse filter for an unknown sound is compared with the error energy of the same sound from the reference filters (Method B). Method A has its advantage in requiring only the autocorrelation function of unknown sounds. The recognition task was conducted with ten American vowels in the context of “hVd” produced by nine male and seven female speakers. A single speaker system averaged 99% recognition, whereas a multispeaker system in which one of the speakers was chosen as the reference averaged 46%. A proper threshold for the criterion suggested that the method is effective for speaker recognition. In general, Method A was slightly inferior to Method B. This work is part of a study of the effectiveness of inter‐speaker normalization. [The work was supported by the Office of Naval Research.]

Signal Resolution via Digital Inverse Filtering

Research in numerous areas is directed toward the resolution of multiple overlapping signals in a noisy environment. These areas include radar, sonar, speech, seismology, and electrophysiology. Sometimes matched filters are used; other times inverse filters are employed. This paper discusses one approach to the analysis of the resolution of inverse filters. Our method is to compromise the trade-off between signal resolution and the output signal-to-noise ratio (SNR). A performance measure for the inverse or deconvolution filter is defined as a quantity proportional to the harmonic mean of the resolution and the SNR. An optimum output pulse duration is obtained using this criterion, where the pulse shape has been previously selected and the input signal waveform is known. In addition, upper and lower bounds for the output pulse duration are presented. Graphs are given which allow the designer to select the optimum inverse filter output pulse duration for a desired signal resolution and an estimated SNR.

Estimation of the Vocal-Tract Shape by Optimum Inverse Filter Processing of Speech

It is shown that the filtering process of the optimum inverse filter [J. D. Markel, SCRL Monogr. No. 7, 111 (Oct. 1971)] is identical to the filtering process of the nonuniform acoustic tube model [B. S. Atal and S. L. Hanauer, J. Acoust. Soc. Amer. 50, 637 (1971)] in which the vocal tract is divided into a finite number of sections with equal lengths. The common factor between the two processes is shown to be a set of reflection coefficients. These reflection coefficients are obtained as intermediate results of a recursive solution to the inverse filter equations. Both area functions and filter coefficients can be easily determined from this set of reflection coefficients. The procedure can be realized by recursive digital filters, thus making possible an efficient implementation as a computer program to obtain the time variation of the vocal-tract shape together with the spectral envelope of the speech sample. This procedure simplifies finding the relationships between the vocal-tract shape and its acoustic features, e.g., from the vocal-tract shape to the filter coefficients, from which formant frequencies and bandwidths can be determined, and vice versa. Applications and limitations of this procedure to connected speech are discussed. [The work was supported by the Office of Naval Research.]

An Iterative Technique for Determining Inverse Filters

It is the objective of much geophysical research to increase the resolution of signals recorded on a sluggish measuring device. The approach genreally followed is to use inverse digital filters. This treatment presents an iterative technique for obtaining "stable inverse digital filters." A stable inverse filter is one whose impulse response decays to zero with increasing time. An optimum inverse filter R() is defined here as R()=1/H(), where H()0; R()=0, where H()=0. It is shown that one can converge to this solution by operating in the time domain using the method of successive substitution. This approach to inverse filtering is unique in that the inverse filter is obtained by an iterative technique, thereby eliminating the dependence on computer limitations, as indicated in some reported techniques. In addition, a method of handling the zero crossings of H() is posed. A smoothing technique to modify these filters for inverse filtering in the presence of noise is also presented.

OPTIMUM INVERSE FILTERS WHICH SHORTEN THE SPACING OF VELOCITY LOGS

A long‐spacing velocity log contains almost the same information as an ideal short‐spacing log, but in a distorted form with added noise. The distortion can be thought of as a moving average or smoothing filter. Its inverse, called a “sharpening” filter by astronomers, amplifies noise. If the inverse is to be useful, it must be designed with a balance between errors due to noise amplification and those due to incomplete sharpening. The Wiener optimum filter theory gives a prescription for achieving this balance. The result is called an optimum inverse filter. We have calculated finite‐memory optimum inverse filters using the IBM 704. We have applied them to actual data, digitized in the field, to produce synthetic short‐spacing velocity logs. These we have compared with their field counterparts. The synthetic logs have less calibration error and are free from noise spikes. The general agreement is good.