TY - GEN
T1 - Gaussian distortion-rate function under sub-nyquist nonuniform sampling
AU - Kipnis, Alon
AU - Goldsmith, Andrea J.
AU - Eldar, Yonina C.
N1 - Publisher Copyright:
© 2014 IEEE.
PY - 2014/1/30
Y1 - 2014/1/30
N2 - A bound on the amount of distortion in the reconstruction of a stationary Gaussian process from its rate-limited samples is derived. The bound is based on a combined sampling and source coding problem in which a Gaussian stationary process is described from a compressed version of its values on an infinite discrete set. We show that the distortion in reconstruction cannot be lower than the distortion-rate function based on optimal uniform filter-bank sampling using a sufficient number of sampling branches. This can be seen as an extension of Landau's theorem on a necessary condition for optimal recovery of a signal from its samples, in the sense that it describes both the error as a result of sub-sampling and the error incurred due to lossy compression of the samples.
AB - A bound on the amount of distortion in the reconstruction of a stationary Gaussian process from its rate-limited samples is derived. The bound is based on a combined sampling and source coding problem in which a Gaussian stationary process is described from a compressed version of its values on an infinite discrete set. We show that the distortion in reconstruction cannot be lower than the distortion-rate function based on optimal uniform filter-bank sampling using a sufficient number of sampling branches. This can be seen as an extension of Landau's theorem on a necessary condition for optimal recovery of a signal from its samples, in the sense that it describes both the error as a result of sub-sampling and the error incurred due to lossy compression of the samples.
UR - http://www.scopus.com/inward/record.url?scp=84938923048&partnerID=8YFLogxK
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U2 - 10.1109/ALLERTON.2014.7028546
DO - 10.1109/ALLERTON.2014.7028546
M3 - Conference contribution
AN - SCOPUS:84938923048
T3 - 2014 52nd Annual Allerton Conference on Communication, Control, and Computing, Allerton 2014
SP - 874
EP - 880
BT - 2014 52nd Annual Allerton Conference on Communication, Control, and Computing, Allerton 2014
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 2014 52nd Annual Allerton Conference on Communication, Control, and Computing, Allerton 2014
Y2 - 30 September 2014 through 3 October 2014
ER -