TY - JOUR
T1 - Sampling-reconstruction procedure of Gaussian processes with jitter characterized by the beta distribution
AU - Kazakov, Vladimir A.
AU - Rodríguez S., Daniel
N1 - Funding Information:
Manuscript received January 15, 2006; revised December 4, 2006. This work was supported in part by the Consejo Nacional de Ciencia y Tec-nología: National Council of Science and Technology (CONACYT), under Grant 31472-A.
PY - 2007/10
Y1 - 2007/10
N2 - The sampling-reconstruction procedure of different Gaussian processes with jitter and with a limited number of samples is investigated. We suggest a new model for the jitter effect; this is a continuous random variable with beta distribution. In this paper, the jitters of samples are assumed to be independent. The conditional mean rule is applied in order to describe the reconstruction procedure. We use multidimensional expressions of conditional expectation and conditional variance of Gaussian processes, and then, we carry out the operation of the statistical average of random times with respect to the corresponding types of beta distribution. The applied method provides a possibility of considering the variant when each sample has its own type of jitter probability density function. In particular, one or more samples can lack jitter. Error reconstruction functions and basic functions are investigated in detail in many examples.
AB - The sampling-reconstruction procedure of different Gaussian processes with jitter and with a limited number of samples is investigated. We suggest a new model for the jitter effect; this is a continuous random variable with beta distribution. In this paper, the jitters of samples are assumed to be independent. The conditional mean rule is applied in order to describe the reconstruction procedure. We use multidimensional expressions of conditional expectation and conditional variance of Gaussian processes, and then, we carry out the operation of the statistical average of random times with respect to the corresponding types of beta distribution. The applied method provides a possibility of considering the variant when each sample has its own type of jitter probability density function. In particular, one or more samples can lack jitter. Error reconstruction functions and basic functions are investigated in detail in many examples.
KW - Basic function
KW - Beta-distribution
KW - Gaussian process
KW - Jitter
KW - Mean-square reconstruction error
KW - Sampling-reconstruction procedure (SRP)
UR - http://www.scopus.com/inward/record.url?scp=34648836322&partnerID=8YFLogxK
U2 - 10.1109/TIM.2007.895607
DO - 10.1109/TIM.2007.895607
M3 - Artículo
SN - 0018-9456
VL - 56
SP - 1814
EP - 1824
JO - IEEE Transactions on Instrumentation and Measurement
JF - IEEE Transactions on Instrumentation and Measurement
IS - 5
ER -