scholarly journals Irregular sampling theorems for wavelet subspaces

1998 ◽  
Vol 44 (3) ◽  
pp. 1131-1142 ◽  
Author(s):  
Wen Chen ◽  
S. Itoh ◽  
J. Shiki
Keyword(s):  
Irregular Sampling ◽  
Sampling Theorems ◽  
Wavelet Subspaces

Irregular Sampling in Wavelet Subspaces

1995 ◽  
Vol 2 (2) ◽  
pp. 181-189 ◽  
Author(s):  
Y.M. Liu ◽  
G.G. Walter
Keyword(s):  
Irregular Sampling ◽  
Wavelet Subspaces

Sampling Theorems of Wavelet Subspaces with M Band in Higher Dimensions

2013 ◽  
Vol 709 ◽  
pp. 563-566
Author(s):  
Jin Zhou Li ◽  
Xin Cheng Zhang
Keyword(s):  
Image Processing ◽  
Signal Processing ◽  
Symmetry Property ◽  
Scaling Function ◽  
Higher Dimensions ◽  
Sampling Theorem ◽  
Scaling Functions ◽  
Sampling Theorems ◽  
Highpass Filter ◽  
Wavelet Subspaces

Sampling theorem has a key role in signal processing and image processing. In this paper, the scaling functions with cardinal property are discussed in the dimensions and their symmetry property is classified. Therefore, sampling theorems of wavelet subspaces are obtained. Then, the cardinal orthogonal scaling function with cardinal property is characterized in the dimensions and an equation between the highpass filter coefficients and wavelet samples are got. The existing results are generalized to the case of M band.

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.

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