Optimal linear combination of order statistics filters and their relationship to the Delta-operator

1999 ◽  
Author(s):  
Ali K. Hocaoglu ◽  
Paul D. Gader ◽  
Erol Gelenbe ◽  
Taskin Kocak
Keyword(s):  
Order Statistics ◽  
Linear Combination ◽  
Delta Operator ◽  
Optimal Linear Combination ◽  
Optimal Linear

scholarly journals Combining different ECG derived respiration tracking methods to create an optimal reconstruction of the breathing pattern

2015 ◽  
Vol 1 (1) ◽  
pp. 54-57 ◽  
Author(s):  
Gustavo Lenis ◽  
Felix Conz ◽  
Olaf Dössel
Keyword(s):  
Linear Combination ◽  
Breathing Pattern ◽  
Accurate Estimation ◽  
The Past ◽  
Optimal Linear Combination ◽  
Fixed Set ◽  
Optimal Linear ◽  
Respiration Signal ◽  
Electrocardiogram Ecg ◽  
Ecg Derived Respiration

AbstractECG derived respiration (EDR) is a technique applied to estimate the respiration signal using only the electrocardiogram (ECG). Different approaches have been proposed in the past on how respiration could be gained from the ECG. However, in many applications only one of them is used while the others are not considered at all. In this paper, we propose a new algorithm for the optimal linear combination of different EDR methods in order to create a more accurate estimation. Using two well known databases, it was statistically shown that an optimally chosen fixed set of coefficients for the linear combination delivers a better estimation than each of the methods used solely.

scholarly journals Calm Multi-Baryon Operators

2018 ◽  
Vol 175 ◽  
pp. 05029
Author(s):  
Evan Berkowitz ◽  
Amy Nicholson ◽  
Chia Cheng Chang ◽  
Enrico Rinaldi ◽  
M.A. Clark ◽  
...  
Keyword(s):  
Correlation Function ◽  
Excited State ◽  
Variational Method ◽  
Linear Combination ◽  
Correlation Functions ◽  
Nuclear Physics ◽  
Physical Point ◽  
Euclidean Time ◽  
Optimal Linear Combination ◽  
Optimal Linear

There are many outstanding problems in nuclear physics which require input and guidance from lattice QCD calculations of few baryons systems. However, these calculations suffer from an exponentially bad signal-to-noise problem which has prevented a controlled extrapolation to the physical point. The variational method has been applied very successfully to two-meson systems, allowing for the extraction of the two-meson states very early in Euclidean time through the use of improved single hadron operators. The sheer numerical cost of using the same techniques in two-baryon systems has so far been prohibitive. We present an alternate strategy which offers some of the same advantages as the variational method while being significantly less numerically expensive. We first use the Matrix Prony method to form an optimal linear combination of single baryon interpolating fields generated from the same source and different sink interpolating fields. Very early in Euclidean time this optimal linear combination is numerically free of excited state contamination, so we coin it a calm baryon. This calm baryon operator is then used in the construction of the two-baryon correlation functions.To test this method, we perform calculations on the WM/JLab iso-clover gauge configurations at the SU(3) flavor symmetric point with mπ~ 800 MeV — the same configurations we have previously used for the calculation of two-nucleon correlation functions. We observe the calm baryon significantly removes the excited state contamination from the two-nucleon correlation function to as early a time as the single-nucleon is improved, provided non-local (displaced nucleon) sources are used. For the local two-nucleon correlation function (where both nucleons are created from the same space-time location) there is still improvement, but there is significant excited state contamination in the region the single calm baryon displays no excited state contamination.

Component-scaled signal reconstruction for enhanced noise filtration

2022 ◽  
pp. 107754632110514
Author(s):  
Aryan Singh ◽  
Keegan J Moore
Keyword(s):  
Linear Combination ◽  
Signal Reconstruction ◽  
Gaussian White Noise ◽  
Three Dimensional ◽  
Noise Removal ◽  
Noise Signal ◽  
Image Correlation ◽  
Intrinsic Mode Functions ◽  
Optimal Linear Combination ◽  
Optimal Linear

This research introduces a procedure for signal denoising based on linear combinations of intrinsic mode functions (IMFs) extracted using empirical mode decomposition (EMD). The method, termed component-scaled signal reconstruction, employs the standard EMD algorithm, with no enhancements to decompose the signal into a set of IMFs. The problem of mode mixing is leveraged for noise removal by constructing an optimal linear combination of the potentially mixed IMFs. The optimal linear combination is determined using an optimization routine with an objective function that maximizes and minimizes the information and noise, respectively, in the denoised signal. The method is demonstrated by applying it to a computer-generated voice sample and the displacement response of a cantilever beam with local stiffness nonlinearity. In the first application, the noise is introduced into the sample manually by adding a Gaussian white-noise signal to the signal. In the second application, the response of the entire beam is filmed using two 1-megapixel cameras, and the three-dimensional displacement field is extracted using digital image correlation. The noise in this application arises entirely from the images captured. The proposed method is compared to existing EMD, ensemble EMD, and LMD based denoising approaches and is found to perform better.

scholarly journals The Total Score With Maximal Reliability and Maximal Criterion Validity: An Illustration Using a Career Satisfaction Measure

2017 ◽  
Vol 78 (6) ◽  
pp. 1108-1122
Author(s):  
Yuanshu Fu ◽  
Zhonglin Wen ◽  
Yang Wang
Keyword(s):  
Linear Combination ◽  
Measurement Errors ◽  
Career Satisfaction ◽  
Reliability And Validity ◽  
Criterion Validity ◽  
Satisfaction Measure ◽  
Optimal Linear Combination ◽  
Optimal Linear ◽  
Item Scores ◽  
Composite Reliability

The maximal reliability of a congeneric measure is achieved by weighting item scores to form the optimal linear combination as the total score; it is never lower than the composite reliability of the measure when measurement errors are uncorrelated. The statistical method that renders maximal reliability would also lead to maximal criterion validity. Using a career satisfaction measure as an example, the present article calculated the maximal reliability and maximal criterion validity and compared them with the composite reliability and the scale criterion validity, respectively. The improvement of reliability and validity indicated that the optimal linear combination is preferred when forming a total score of a measure. The Mplus codes for analyzing maximal reliability, maximal criterion validity, and related parameters are provided.

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