PRINCIPLES OF DIGITAL MULTICHANNEL FILTERING

Geophysics ◽  
1970 ◽  
Vol 35 (5) ◽  
pp. 785-811 ◽  
Author(s):  
Sven Treitel
Keyword(s):  
Least Squares ◽  
Response Function ◽  
Channel Model ◽  
Single Channel ◽  
Correlation Coefficients ◽  
Sampled Data ◽  
Levinson Algorithm ◽  
Multichannel Filtering ◽  
The Stability ◽  
Weighting Coefficients

The transition from single‐channel to multichannel data processing systems requires substantial modifications of the simpler single‐channel model. While the response function of a single‐channel digital filter can be specified in terms of scalar‐valued weighting coefficients, the corresponding response function of a multichannel filter is more conveniently described by matrix‐valued weighting coefficients. Correlation coefficients, which are scalars in the single‐channel case, now become matrices. Multichannel sampled data are manipulated with greater ease by recourse to multichannel z‐transform theory. Exact inverse filters are calculable by a matrix inversion technique which is the counterpart to the computation of exact single‐channel inverse operators by polynomial division. The delay properties of the original filter govern the stability of its inverse. This inverse is expressible in the form of a two‐stage cascaded system, whose first stage is a single‐channel recursive filter. Optimum multichannel filtering systems result from a generalization of the single‐channel least squares error criterion. The corresponding correlation matrices are now functions of coefficients which are themselves matrices. The system of normal matrix‐valued equations that is obtained in this manner can be solved by means of Robinson’s generalization of the Wiener‐Levinson algorithm. Inverse multichannel filters are designed by specifying the desired output to be an identity matrix rather than a unit spike; if this matrix occurs at zero lag, the least squares filter is minimum‐delay. Simple numerical examples serve to illustrate the design principles involved and to indicate the types of problems that can be attacked with multichannel least squares processors.

Sparseness‐constrained least‐squares inversion: Application to seismic wave reconstruction

Geophysics ◽  
2003 ◽  
Vol 68 (5) ◽  
pp. 1633-1638 ◽  
Author(s):  
Yanghua Wang
Keyword(s):  
Least Squares ◽  
Seismic Data ◽  
Reconstruction Method ◽  
Sampled Data ◽  
Linear Inversion ◽  
Data Set ◽  
Least Squares Solution ◽  
Working Definition ◽  
The Stability ◽  
Irregularly Sampled Data

The spectrum of a discrete Fourier transform (DFT) is estimated by linear inversion, and used to produce desirable seismic traces with regular spatial sampling from an irregularly sampled data set. The essence of such a wavefield reconstruction method is to solve the DFT inverse problem with a particular constraint which imposes a sparseness criterion on the least‐squares solution. A working definition for the sparseness constraint is presented to improve the stability and efficiency. Then a sparseness measurement is used to measure the relative sparseness of the two DFT spectra obtained from inversion with or without sparseness constraint. It is a pragmatic indicator about the magnitude of sparseness needed for wavefield reconstruction. For seismic trace regularization, an antialiasing condition must be fulfilled for the regularizing trace interval, whereas optimal trace coordinates in the output can be obtained by minimizing the distances between the newly generated traces and the original traces in the input. Application to real seismic data reveals the effectiveness of the technique and the significance of the sparseness constraint in the least‐squares solution.

The use of the conjugate‐gradient algorithm in the computation of predictive deconvolution operators

Geophysics ◽  
1985 ◽  
Vol 50 (12) ◽  
pp. 2752-2758 ◽  
Author(s):  
Fulton Koehler ◽  
M. Turhan Taner
Keyword(s):  
Least Squares ◽  
Conjugate Gradient ◽  
Single Channel ◽  
Conjugate Gradient Algorithm ◽  
Gradient Algorithm ◽  
Time Varying ◽  
Simple Formulation ◽  
Deconvolution Problem ◽  
Levinson Algorithm ◽  
Multichannel Deconvolution

A number of excellent papers have been published since the introduction of deconvolution by Robinson in the middle 1950s. The application of the Wiener‐Levinson algorithm makes deconvolution a practical and vital part of today’s digital seismic data processing. We review the original formulation of deconvolution, develop the solution from another perspective, and demonstrate a general and rigorous solution that could be implemented. By “general” we mean a deterministic time‐varying and multichannel operator design, and by “rigorous” we mean the straightforward least‐squares error solution without simplifying to a Toeplitz matrix. Also we show that the conjugate‐gradient algorithm used in conjunction with the least‐squares problem leads to a satisfactory simplification; that in the computation of the operators, the square matrix involved in the normal equations need not be computed. Furthermore, the product of this matrix with a column matrix can be obtained directly from the data as a result of two cascaded simple convolutions. The time‐varying deconvolution problem is shown to be equivalent to the multichannel deconvolution problem. Hence, with one simple formulation and associated programming, the procedure can be utilized for time‐constant single‐channel and multichannel deconvolution and time‐varying single‐channel and multichannel deconvolution.

REMOVAL OF HEAVY METAL Cr (II), Ni (II), Cu (II), Zn (II), Cd (II), Pb (II) IONS FROM AQUEOUS SOLUTION BY MENTHA PIPERITA EXTRACT

2020 ◽  
pp. 15-20
Author(s):  
Ersin Yucel ◽  
Mine Yucel
Keyword(s):  
Aqueous Solution ◽  
Metal Ions ◽  
High Efficiency ◽  
Correlation Coefficients ◽  
Langmuir Model ◽  
Mentha Piperita ◽  
Freundlich Model ◽  
Biosorption Capacity ◽  
Peppermint Extract ◽  
The Stability

In this study, the usage of the peppermint (Mentha piperita) for extracting the metal ions [Mg (II), Cr (II), Ni (II), Cu (II), Zn (II), Cd (II), Pb (II)] that exist at water was investigated. In order to analyze the stability properties, Langmuir, Freundlich, Temkin and Dubinin-Radushkevich isotherms were used at removing the metal ions and the highest correlation coefficients (R2) were obtained at Langmuir isotherm. Therefore, it is seen that the Langmuir model is more proper than the Freundlich model. However, it was found that the correlation coefficients of removing Ni and Cd is higher at Freundlich model than Langmuir and low at Dubinin-Radushkevich isotherm. It is established that the biosorption amount increase depends on the increase of biosorbent and it can be achieved high efficiency (95%) even with small amount (0.6 mg, peppermint extract) at lead ions. It is also determined that the peppermint extracted that is used at this study shows high biosorption capacity for metal ions and can be used for immobilization of metals from polluted areas.

scholarly journals Explicit parallel co-simulation approach: analysis and improved coupling method based on H-infinity synthesis

2021 ◽  
Author(s):  
Weitao Chen ◽  
Shenhai Ran ◽  
Canhui Wu ◽  
Bengt Jacobson
Keyword(s):  
Frequency Domain ◽  
Wide Frequency Range ◽  
Coupling Method ◽  
Sampled Data ◽  
H Infinity ◽  
First Case ◽  
Communication Step ◽  
Coupling Variables ◽  
The Stability ◽  
Stability And Accuracy

AbstractCo-simulation is widely used in the industry for the simulation of multidomain systems. Because the coupling variables cannot be communicated continuously, the co-simulation results can be unstable and inaccurate, especially when an explicit parallel approach is applied. To address this issue, new coupling methods to improve the stability and accuracy have been developed in recent years. However, the assessment of their performance is sometimes not straightforward or is even impossible owing to the case-dependent effect. The selection of the coupling method and its tuning cannot be performed before running the co-simulation, especially with a time-varying system.In this work, the co-simulation system is analyzed in the frequency domain as a sampled-data interconnection. Then a new coupling method based on the H-infinity synthesis is developed. The method intends to reconstruct the coupling variable by adding a compensator and smoother at the interface and to minimize the error from the sample-hold process. A convergence analysis in the frequency domain shows that the coupling error can be reduced in a wide frequency range, which implies good robustness. The new method is verified using two co-simulation cases. The first case is a dual mass–spring–damper system with random parameters and the second case is a co-simulation of a multibody dynamic (MBD) vehicle model and an electric power-assisted steering (EPAS) system model. Experimental results show that the method can improve the stability and accuracy, which enables a larger communication step to speed up the explicit parallel co-simulation.

Thermal Hydraulic Studies of a Fluoride Salt Cooled High Temperature Test Reactor With Different CFD Methods

2014 ◽  
Author(s):  
Chenglong Wang ◽  
Yao Xiao ◽  
Jianjun Zhou ◽  
Dalin Zhang ◽  
Suizheng Qiu ◽  
...  
Keyword(s):  
High Temperature ◽  
Channel Model ◽  
Single Channel ◽  
Fluoride Salt ◽  
Applied Physics ◽  
Local Flow ◽  
Single Channel Analysis ◽  
Test Reactor ◽  
Safety Operation ◽  
Temperature Test

The Fluoride-salt-cooled High temperature Reactor (FHR) is new reactor concept-about a decade old which is mainly on going in China and U.S. The preliminary thermal-hydraulic studies of the Fluoride salt cooled High temperature Test Reactor (FHTR) is necessary for the development of the FHR technology. In this paper, the thermal-hydraulics of FHTR (also called TMSR-SF) designed by Shanghai Instituted of Applied Physics (SINAP) is studied in different power modes. The temperature distributions of the coolant and the fuel pebble are obtained using a steady-state thermal-hydraulic analysis code for FHR. The comprehensive local flow and heat transfer are investigated by computational fluid dynamics (CFD) for the locations where may have the maximum pebble temperature based on the results from single channel analysis. The profiles of temperature, velocity, pressure and Nu of the coolant on the surface of the pebble as well as the temperature distribution of a fuel pebble are obtained and analyzed. Numerical results showed that the results of 3-D simulation are in reasonable agreement with that of single channel model and also illustrated safety operation of the preliminary designed TMSR-SF in different power mode.

A trait of mind: stability and robustness of sleep across sleep opportunity manipulations during simulated military operational stress

SLEEP ◽  
2021 ◽  
Author(s):  
Alice D LaGoy ◽  
J David Cashmere ◽  
Meaghan E Beckner ◽  
Shawn R Eagle ◽  
Aaron M Sinnott ◽  
...  
Keyword(s):  
Military Personnel ◽  
Correlation Coefficients ◽  
Sleep Architecture ◽  
Sleep Restriction ◽  
Spectral Parameters ◽  
Intra Class Correlation ◽  
Operational Stress ◽  
Spectral Activity ◽  
Sleep Parameters ◽  
The Stability

Abstract Study Objectives Within-subject stability of certain sleep features across multiple nights is thought to reflect the trait-like behavior of sleep. However, to be considered a trait, a parameter must be both stable and robust. Here, we examined the stability (i.e., across the same sleep opportunity periods) and robustness (i.e., across sleep opportunity periods that varied in duration and timing) of different sleep parameters. Methods Sixty-eight military personnel (14 W) spent 5 nights in the sleep laboratory during a simulated military operational stress protocol. After an adaptation night, participants had an 8-hour sleep opportunity (23:00–07:00) followed by 2 consecutive nights of sleep restriction and disruption which included two 2-hour sleep opportunities (01:00–03:00; 05:00–07:00) and, lastly, another 8-hour sleep opportunity (23:00–07:00). Intra-class correlation coefficients were calculated to examine differences in stability and robustness across different sleep parameters. Results Sleep architecture parameters were less stable and robust than absolute and relative spectral activity parameters. Further, relative spectral activity parameters were less robust than absolute spectral activity. Absolute alpha and sigma activity demonstrated the highest levels of stability that were also robust across sleep opportunities of varying duration and timing. Conclusions Stability and robustness varied across different sleep parameters, but absolute NREM alpha and sigma activity demonstrated robust trait-like behavior across variable sleep opportunities. Reduced stability of other sleep architecture and spectral parameters during shorter sleep episodes as well as across different sleep opportunities has important implications for study design and interpretation.

scholarly journals A Method of Implementing a 4 × 4 Correlation Matrix for Evaluating the Uplink Channel Properties of MIMO Over-the-Air Apparatus

Sensors ◽  
2021 ◽  
Vol 21 (18) ◽  
pp. 6184
Author(s):  
Kazuhiro Honda
Keyword(s):  
Correlation Matrix ◽  
Channel Model ◽  
Multiple Input Multiple Output ◽  
Correlation Coefficients ◽  
Base Station ◽  
Theoretical Formula ◽  
Secondary Wave ◽  
Two Dimensional ◽  
Mimo Antenna ◽  
Channel Properties

This paper presents a method of implementing a 4 × 4 correlation matrix for evaluating the uplink channel properties of multiple-input multiple-output (MIMO) antennas using an over-the-air measurement system. First, the implementation model used to determine the correlation coefficients between the signals received at the base station (BS) antennas via the uplink channel is described. Then, a methodology is introduced to achieve a 4 × 4 correlation matrix for a BS MIMO antenna based on Jakes’ model by setting the initial phases of the secondary wave sources in the two-dimensional channel model. The performance of the uplink channel for a four-element MIMO terminal array antenna is evaluated using a two-dimensional bidirectional fading emulator. The results show that the measured correlation coefficients between the signals received via the uplink channel at the BS antennas using the proposed method are in good agreement with the BS correlation characteristics calculated using Monte Carlo simulation and the theoretical formula, thereby confirming the effectiveness of the proposed method.

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