A single digital linear filter for computations in electrical methods—A unifying approach

Geophysics ◽  
1984 ◽  
Vol 49 (7) ◽  
pp. 1115-1118 ◽  
Author(s):  
U. C. Das
Keyword(s):  
Linear Filter ◽  
Linear Filtering ◽  
Electrical Measurements ◽  
Domain Integral ◽  
Electrical Methods ◽  
Single Formula

A major contribution to the interpretation of electrical measurements was made with the application of digital linear filtering introduced by Ghosh (1970, 1971a, b). This rendered the computations easy and fast. In a recent publication, I showed (Das, 1982) that the filters for computing responses for any electrode or coil configurations employed in electrical methods could be derived easily from stored basic spectra of the two filter functions, namely, [Formula: see text] and [Formula: see text]. One has to multiply the stored spectra by simple factors to arrive at the required spectra. I show here that a simple mathematical manipulation transforms a [Formula: see text] domain integral into its corresponding [Formula: see text] domain integral, thereby leading to the use of a single [Formula: see text] filter for a variety of computations in electrical methods.

scholarly journals Modular preprocessing pipelines can reintroduce artifacts into fMRI data

2018 ◽  
Author(s):  
Martin A. Lindquist ◽  
Stephan Geuter ◽  
Tor D. Wager ◽  
Brian S. Caffo
Keyword(s):  
Fmri Data ◽  
Linear Filter ◽  
Linear Filtering ◽  
Linear Filters ◽  
Data Set ◽  
Temporal Filtering ◽  
Global Signal ◽  
In Series ◽  
Band Pass ◽  
Fmri Analysis

AbstractThe preprocessing pipelines typically used in both task and restingstate fMRI (rs-fMRI) analysis are modular in nature: They are composed of a number of separate filtering/regression steps, including removal of head motion covariates and band-pass filtering, performed sequentially and in a flexible order. In this paper we illustrate the shortcomings of this approach, as we show how later preprocessing steps can reintroduce artifacts previously removed from the data in prior preprocessing steps. We show that each regression step is a geometric projection of data onto a subspace, and that performing a sequence of projections can move the data into subspaces no longer orthogonal to those previously removed, reintroducing signal related to nuisance covariates. Thus, linear filtering operations are not commutative, and the order in which the preprocessing steps are performed is critical. These issues can arise in practice when any combination of standard preprocessing steps—including motion regression, scrubbing, component-based correction, global signal regression, and temporal filtering—are performed sequentially. In this work we focus primarily on rs-fMRI. We illustrate the problem both theoretically and empirically through application to a test-retest rs-fMRI data set, and suggest remedies. These include (a) combining all steps into a single linear filter, or (b) sequential orthogonalization of covariates/linear filters performed in series.

Static and Dynamic Behavior of Ferronematics Under Magnetic Fields

1998 ◽  
Vol 12 (13) ◽  
pp. 529-540 ◽  
Author(s):  
Cornelia Motoc ◽  
Emil Petrescu
Keyword(s):  
Dynamic Behavior ◽  
Threshold Field ◽  
Relaxation Processes ◽  
Relaxation Phenomena ◽  
Electrical Measurements ◽  
Freedericksz Transition ◽  
Fréedericksz Transition ◽  
Electrical Methods ◽  
The Magnetic Field ◽  
Good Agreement

The static and dynamic behavior under magnetic elds of ferronematics obtained by adding an organomagnetic material to the nematic E3 is investigated. First, by using both optical and electrical measurements, an increase of the threshold field for magnetic Freedericksz transition was noticed. Second, we examined both theoretically and experimentally the relaxation phenomena occurring in these ferronematics when the magnetic field was suddenly varied. We found that for ferronematics the relaxation processes are delayed when compared to those occurring in pure nematics. The threshold fields for magnetic Freedericksz transition were determined by means of the relaxation time and the results are in good agreement with the ones obtained when using the optical and electrical methods reported before.

scholarly journals The Impact of Linear Filter Preprocessing in the Interpretation of Permutation Entropy

Entropy ◽  
2021 ◽  
Vol 23 (7) ◽  
pp. 787
Author(s):  
Antonio Dávalos ◽  
Meryem Jabloun ◽  
Philippe Ravier ◽  
Olivier Buttelli
Keyword(s):  
Moving Average ◽  
Permutation Entropy ◽  
Linear Filter ◽  
Type I ◽  
Linear Filtering ◽  
Linear Filters ◽  
Ordinal Information ◽  
Specific Frequency ◽  
The Impact ◽  
Specific Contribution

Permutation Entropy (PE) is a powerful tool for measuring the amount of information contained within a time series. However, this technique is rarely applied directly on raw signals. Instead, a preprocessing step, such as linear filtering, is applied in order to remove noise or to isolate specific frequency bands. In the current work, we aimed at outlining the effect of linear filter preprocessing in the final PE values. By means of the Wiener–Khinchin theorem, we theoretically characterize the linear filter’s intrinsic PE and separated its contribution from the signal’s ordinal information. We tested these results by means of simulated signals, subject to a variety of linear filters such as the moving average, Butterworth, and Chebyshev type I. The PE results from simulations closely resembled our predicted results for all tested filters, which validated our theoretical propositions. More importantly, when we applied linear filters to signals with inner correlations, we were able to theoretically decouple the signal-specific contribution from that induced by the linear filter. Therefore, by providing a proper framework of PE linear filter characterization, we improved the PE interpretation by identifying possible artifact information introduced by the preprocessing steps.

DEPTH FACTORS AND RESOLVING POWER OF ELECTRICAL MEASUREMENTS

Geophysics ◽  
1938 ◽  
Vol 3 (2) ◽  
pp. 78-95 ◽  
Author(s):  
H. M. Evjen
Keyword(s):  
Potential Drop ◽  
Point Of View ◽  
Resolving Power ◽  
Ratio Method ◽  
Electrical Measurements ◽  
New Approach ◽  
Resistivity Method ◽  
Electrical Methods ◽  
Electrical Prospecting ◽  
Interpretation Problem

The use of depth factors in electrical prospecting is critically reviewed. The use of depth factors is placed on a rational foundation. This is accomplished by assigning new physical significance to the so‐called apparent resistivities and potential drop ratios measured by electrical methods. It is shown that these measurables may be considered as broadly averaged representations of the distribution of electric images with depth. As a result, universal depth factors exist which may be calculated once for all for any given electrode arrangement. The depth factors are calculated for a number of commonly used electrode arrangements and are found to be smaller than generally assumed. The potential drop ratio method is shown to be superior to the apparent resistivity method in regard to depth of reference as well as to resolving power. The resolution by either method, however, is found to be entirely inadequate to give anywhere near the detail obtained with well logs. The new approach adopted in this paper leads to quite simple and practical methods of analysis and direct solution of the interpretation problem which are illustrated. These methods are shown to have a useful field of application also in gravitational interpretation. The extent to which a detailed analysis justifiably may be carried is briefly examined. From the point of view of practicability it is reaffirmed that the best field of application of the electrical methods is the investigation of horizontal changes such as the mapping of faults and salt dome flanks.

scholarly journals Algorithms of distortion compensation for broadband signals propagated through satellite ionospheric channels.

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
V.V. Batanov ◽  
◽  
L.E. Nazarov ◽  
◽  
Keyword(s):  
Computer Simulations ◽  
Frequency Band ◽  
Digital Signal ◽  
Computational Procedure ◽  
Linear Filter ◽  
Linear Filtering ◽  
Digital Signals ◽  
Distortion Compensation ◽  
Complex Envelope ◽  
Wideband Signals

Methods for describing of digital signal complex envelope distortions due to influence of satellite ionosphere radiolines based on linear filtering methods are presented. Distortions of the phase-frequency characteristics of the digital signal envelopes due to the dispersion properties of the ionosphere cause time scattering and the occurrence of intersymbol interference, which reduce the reliability of communication. This determines the relevance of the development of the computational procedure for processing digital signals that reduce the effectiveness of this type of interferences. The descriptions of the algorithms for compensation of these distortions based on the use of the broadband pilot-signals and the formation of an inverse linear filter are given. A useful property of the considered pilot-signals is the coincidence of their structure (frequency band, envelope type, manipulation law) with the structure of information digital signals. By means of computer simulations of this algorithms, the possibility of almost complete compensation of the considered distortions of wideband signals is shown.

scholarly journals G-Filtering Nonstationary Time Series

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
Mengyuan Xu ◽  
Krista B. Cohlmia ◽  
Wayne A. Woodward ◽  
Henry L. Gray
Keyword(s):  
Time Series ◽  
Stationary Process ◽  
Nonstationary Time Series ◽  
Linear Filter ◽  
Time Varying ◽  
Linear Filtering ◽  
Original Process ◽  
Filtering Method ◽  
Time Deformation ◽  
Time Varying Frequency

The classical linear filter can successfully filter the components from a time series for which the frequency content does not change with time, and those nonstationary time series with time-varying frequency (TVF) components that do not overlap. However, for many types of nonstationary time series, the TVF components often overlap in time. In such a situation, the classical linear filtering method fails to extract components from the original process. In this paper, we introduce and theoretically develop the G-filter based on a time-deformation technique. Simulation examples and a real bat echolocation example illustrate that the G-filter can successfully filter a G-stationary process whose TVF components overlap with time.

DIRECT INTERPRETATION OF GEOELECTRIC MEASUREMENTS BY THE USE OF LINEAR FILTER THEORY

Geophysics ◽  
1975 ◽  
Vol 40 (1) ◽  
pp. 121-122 ◽  
Author(s):  
Sri Niwas
Keyword(s):  
Kernel Function ◽  
Apparent Resistivity ◽  
Linear Filter ◽  
Intermediate Step ◽  
Electrical Measurements ◽  
Filter Theory ◽  
Direct Interpretation ◽  
Order Of Magnitude ◽  
Electrical Soundings

In a recent paper Lee and Green (1973) worked out a method for direct interpretation of electrical soundings made over a fault or dike (see Figure 1). They computed the kernel function using the method developed by Meinardus (1970). However, Koefoed (1968), while dealing with direct interpretation of electrical measurements made over a horizontally layered earth, showed that the relative variations in the apparent resistivity were not of the same order of magnitude in the corresponding kernel curve; thus, any method based on the determination of this function as the intermediate step would lead to a loss of information and hence to incorrect interpretation. Koefoed (1970) introduced a function T(λ) called the resistivity transform (a function related to the kernel function) as an intermediate step. Ghosh (1971) used linear filter theory and gave a simple and quick procedure to obtain the T(λ) function from the apparent resistivity field curve. He cited the properties of the T function as, (1) it is solely determined by the layer distribution; (2) it is an unambiguous representation of the [Formula: see text] function; and (3) for small and large values of 1/λ it approaches the [Formula: see text] curves.

Identification of maneuvering objects during structural and system control of airspace

2021 ◽  
pp. 16-26
Author(s):  
Георгий Борисович Гуров ◽  
Валерий Юрьевич Поздышев ◽  
Александр Васильевич Тимошенко ◽  
Ольга Эдуардовна Разинькова
Keyword(s):  
Ideal Observer ◽  
Linear Filter ◽  
System Control ◽  
Correct Identification ◽  
Linear Filtering ◽  
Monitoring Tools ◽  
Accuracy Of Measurements ◽  
Angular Coordinates ◽  
Mean Square Errors ◽  
The Ideal

Работа посвящена построению процедуры идентификации маневрирующих объектов с использованием критерия идеального наблюдателя и фильтрации параметров трасс при сопровождении средствами мониторинга в интересах структурносистемного контроля воздушного пространства. Для минимизации среднеквадратических ошибок оценок координат и скоростей движения объектов разработаны алгоритмы экстраполяции параметров траекторий путем задания корректирующего шумового ускорения и замены результатов фильтрации оценок координат на измеренные значения при распознавании маневра. Обоснованы параметры фильтрации с шумовым ускорением в зависимости от точности измерений пространственных характеристик и идентификации при группировании однотипных признаков с наибольшими значениями условных вероятностей ситуаций отождествления объектов Purpose. This work addresses construction of the procedure for identifying maneuvering air objects in the process of tracking their routes. Monitoring tools during structural and system air space control are employed. The study is aimed to establish the abilities of correct identification of objects and false alarm at various standard errors of measurements of angular coordinates and to determine ways to increase efficiency of identifications performed due to selection of filtering options during trace tracking. Methodology. Identification of objects was performed according to the ideal observer criterion by comparing estimates of angular coordinates of objects subjected to linear filtering with corrective noise acceleration. In order to minimize root-mean-square errors of coordinates and motion velocity estimates of objects, route parameter extrapolation algorithms are obtained by setting correcting noise acceleration and replacing the results of filtering coordinate estimates with measured values during manoeuvre recognition. Due to a priori uncertainty of route parameters, target tracking was initially performed using recurring linear filtering while maintaining the priority of straight uniform movement. The recognition of the maneuver was carried out as a result of exceeding the difference between the measured and filtered values of the target coordinates of the threshold value. Findings. Filtering parameters with noise acceleration are justified depending on the accuracy of measurements of spatial characteristics and identification when grouping identification features with the highest values of conditional probabilities of situations for the objects under identification. As a result of replacing filtered parameters of alignments containing areas with rotations of 10 and 20, measured values for standard bearing errors (1 ... 2), the maximum error in determining directions for objects reaches 0.8 and 0.9, respectively. When replacing the estimates of the parameters of the alignments obtained using a recurring linear filter without taking into account noise acceleration, the coordinate values measured at the bearing error (0 . 5 ... 2), the errors of the filtered bearing of the targets at the angles of rotation of 10are (0 . 2 ... 1). When maneuvering objects with turns by 20, the largest value of the standard bearing error increases to 1.2. By increasing the accuracy of the diaper from 2 to 0.5, the probability of correct identification of objects in monitoring tools performing noise correction acceleration filtering increases by about 3 times and reaches a value of 0.9. As a result of replacing the estimates of the parameters of the alignments filtered taking into account the corrective noise acceleration with the results of measurements, the probability of correct identification of objects with standard bearing errors of not more than 0.5decreases from 0.9 to 0.85. Originality/value. The identification of maneuvering air objects is performed using filtering of route parameters calculated with the help of the ideal observer criterion. For the most efficient identification, the identification features belonging to the same object must be established according to the highest conditional probability of the identification situation. To minimize errors in estimation of the angular coordinates of objects, a procedure for filtering motion parameters with corrective noise acceleration is implemented

CBED study of low-temperature InP grown by gas source MBE

1993 ◽  
Vol 51 ◽  
pp. 810-811
Author(s):  
R. Rajesh ◽  
M.J. Kim ◽  
J.S. Bow ◽  
R.W. Carpenter ◽  
G.N. Maracas
Keyword(s):  
Low Temperature ◽  
Second Phase ◽  
Material System ◽  
Ion Milling ◽  
Electrical Measurements ◽  
Gas Source ◽  
Structural And Electrical Properties ◽  
The One ◽  
Lt Inp ◽  
Gas Source Mbe

In our previous work on MBE grown low temperature (LT) InP, attempts had been made to understand the relationships between the structural and electrical properties of this material system. Electrical measurements had established an enhancement of the resistivity of the phosphorus-rich LT InP layers with annealing under a P2 flux, which was directly correlated with the presence of second-phase particles. Further investigations, however, have revealed the presence of two fundamentally different types of precipitates. The first type are the surface particles, essentially an artefact of argon ion milling and containing mostly pure indium. The second type and the one more important to the study are the dense precipitates in the bulk of the annealed layers. These are phosphorus-rich and are believed to contribute to the improvement in the resistivity of the material.The observation of metallic indium islands solely in the annealed LT layers warranted further study in order to better understand the exact reasons for their formation.

Recent Progress and Plans in Computer-Controlled High Resolution Electron Microscopy

1990 ◽  
Vol 48 (1) ◽  
pp. 154-155
Author(s):  
W.J. de Ruijter ◽  
Peter Rez ◽  
David J. Smith
Keyword(s):  
Electron Microscopy ◽  
Digital Processing ◽  
High Resolution Electron Microscopy ◽  
Objective Lens ◽  
Linear Filter ◽  
Contrast Transfer Function ◽  
Image Displacement ◽  
Spatially Resolved ◽  
Wide Range ◽  
On Line

Digital computers are becoming widely recognized as standard accessories for electron microscopy. Due to instrumental innovations the emphasis in digital processing is shifting from off-line manipulation of electron micrographs to on-line image acquisition, analysis and microscope control. An on-line computer leads to better utilization of the instrument and, moreover, the flexibility of software control creates the possibility of a wide range of novel experiments, for example, based on temporal and spatially resolved acquisition of images or microdiffraction patterns. The instrumental resolution in electron microscopy is often restricted by a combination of specimen movement, radiation damage and improper microscope adjustment (where the settings of focus, objective lens stigmatism and especially beam alignment are most critical). We are investigating the possibility of proper microscope alignment based on computer induced tilt of the electron beam. Image details corresponding to specimen spacings larger than ∼20Å are produced mainly through amplitude contrast; an analysis based on geometric optics indicates that beam tilt causes a simple image displacement. Higher resolution detail is characterized by wave propagation through the optical system of the microscope and we find that beam tilt results in a dispersive image displacement, i.e. the displacement varies with spacing. This approach is valid for weak phase objects (such as amorphous thin films), where transfer is simply described by a linear filter (phase contrast transfer function) and for crystalline materials, where imaging is described in terms of dynamical scattering and non-linear imaging theory. In both cases beam tilt introduces image artefacts.

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