An Irregular Sampling Theorem for Functions Bandlimited in a Generalized Sense

1987 ◽  
Vol 47 (5) ◽  
pp. 1112-1116 ◽  
Author(s):  
Kristian Seip
Keyword(s):  
Sampling Theorem ◽  
Irregular Sampling

Multivariate irregular sampling theorem

2009 ◽  
Vol 52 (11) ◽  
pp. 2469-2478 ◽  
Author(s):  
GuangGui Chen ◽  
GenSun Fang
Keyword(s):  
Sampling Theorem ◽  
Irregular Sampling

An Improved Nyquist–Shannon Irregular Sampling Theorem From Local Averages

2012 ◽  
Vol 58 (9) ◽  
pp. 6093-6100 ◽  
Author(s):  
Zhanjie Song ◽  
Bei Liu ◽  
Yanwei Pang ◽  
Chunping Hou ◽  
Xuelong Li
Keyword(s):  
Sampling Theorem ◽  
Irregular Sampling ◽  
Local Averages

scholarly journals Regular and Irregular Sampling Theorem for Multiwavelet Subspaces

2010 ◽  
Vol 2010 ◽  
pp. 1-18
Author(s):  
Liu Zhanwei ◽  
Hu Guoen ◽  
Wu Guochang
Keyword(s):  
Sampling Theorem ◽  
Irregular Sampling ◽  
Sufficient Condition ◽  
Regular Sampling ◽  
Shift Invariant Spaces ◽  
Invariant Spaces

We study the sampling theorem for frames in multiwavelet subspaces. Firstly, a sufficient condition under which the regular sampling theorem holds is established. Then, notice that irregular sampling is also useful in practice; we consider the general cases of the irregular sampling and establish a general irregular sampling theorem for multiwavelet subspaces. Finally, using this generalized irregular sampling theorem, we obtain an estimate for the perturbations of regular sampling in shift-invariant spaces.

FORMULATION AND SOLUTION OF OPTIMIZATION PROBLEM REDUNDANCY SYSTEM COMPRISING SITUATION CENTER

2019 ◽  
pp. 44-50
Author(s):  
A.V. Alekseev
Keyword(s):  
Analytical Model ◽  
Quality Indicators ◽  
Significant Influence ◽  
Optimization Problem ◽  
Sampling Theorem ◽  
Sampling Frequency ◽  
Generalized Sampling ◽  
Optimal Value ◽  
Situation Center ◽  
Situation Centers

The analysis of the concept, properties and features of heterogeneous redundancy in modern complex ergatic systems, including those included in the situation centers (SC). On the basis of the qualimetric paradigm, the generalized analytical model of quality and optimization of quality by private, group, summary and aggregated quality indicators is justified. Practical ways of realization of the model and methods of optimization of the objects which are a part of SC and them as a whole at the expense of reduction of structural, functional and other types of redundancy under the obligatory condition of non-reduction of the required value of quality are given. On the example of the generalized sampling theorem when choosing the optimal value of the sampling frequency of the real bandpass signal, the criticality and significant influence on the redundancy of data in their further processing in the SC is shown.

scholarly journals Bias correction for direct spectral estimation from irregularly sampled data including sampling schemes with correlation

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Nils Damaschke ◽  
Volker Kühn ◽  
Holger Nobach
Keyword(s):  
Spectral Estimation ◽  
Continuous Distribution ◽  
Discrete Distribution ◽  
Irregular Sampling ◽  
The Other ◽  
Sampled Data ◽  
Sampling Schemes ◽  
Other Hand ◽  
Sampling Intervals ◽  
Irregularly Sampled Data

AbstractThe prediction and correction of systematic errors in direct spectral estimation from irregularly sampled data taken from a stochastic process is investigated. Different sampling schemes are investigated, which lead to such an irregular sampling of the observed process. Both kinds of sampling schemes are considered, stochastic sampling with non-equidistant sampling intervals from a continuous distribution and, on the other hand, nominally equidistant sampling with missing individual samples yielding a discrete distribution of sampling intervals. For both distributions of sampling intervals, continuous and discrete, different sampling rules are investigated. On the one hand, purely random and independent sampling times are considered. This is given only in those cases, where the occurrence of one sample at a certain time has no influence on other samples in the sequence. This excludes any preferred delay intervals or external selection processes, which introduce correlations between the sampling instances. On the other hand, sampling schemes with interdependency and thus correlation between the individual sampling instances are investigated. This is given whenever the occurrence of one sample in any way influences further sampling instances, e.g., any recovery times after one instance, any preferences of sampling intervals including, e.g., sampling jitter or any external source with correlation influencing the validity of samples. A bias-free estimation of the spectral content of the observed random process from such irregularly sampled data is the goal of this investigation.

Regularization and datuming of seismic data by weighted, damped least squares

Geophysics ◽  
2006 ◽  
Vol 71 (5) ◽  
pp. U67-U76 ◽  
Author(s):  
Robert J. Ferguson
Keyword(s):  
Least Squares ◽  
Seismic Data ◽  
Synthetic Data ◽  
Real Data ◽  
Structural Data ◽  
Irregular Sampling ◽  
Data Set ◽  
Near Surface ◽  
Damped Least Squares ◽  
Wavefield Extrapolation

The possibility of improving regularization/datuming of seismic data is investigated by treating wavefield extrapolation as an inversion problem. Weighted, damped least squares is then used to produce the regularized/datumed wavefield. Regularization/datuming is extremely costly because of computing the Hessian, so an efficient approximation is introduced. Approximation is achieved by computing a limited number of diagonals in the operators involved. Real and synthetic data examples demonstrate the utility of this approach. For synthetic data, regularization/datuming is demonstrated for large extrapolation distances using a highly irregular recording array. Without approximation, regularization/datuming returns a regularized wavefield with reduced operator artifacts when compared to a nonregularizing method such as generalized phase shift plus interpolation (PSPI). Approximate regularization/datuming returns a regularized wavefield for approximately two orders of magnitude less in cost; but it is dip limited, though in a controllable way, compared to the full method. The Foothills structural data set, a freely available data set from the Rocky Mountains of Canada, demonstrates application to real data. The data have highly irregular sampling along the shot coordinate, and they suffer from significant near-surface effects. Approximate regularization/datuming returns common receiver data that are superior in appearance compared to conventional datuming.

Sign in / Sign up

Export Citation Format

Share Document