TY - GEN
T1 - Distortion rate function of sub-Nyquist sampled Gaussian sources corrupted by noise
AU - Kipnis, Alon
AU - Goldsmith, Andrea J.
AU - Weissman, Tsachy
AU - Eldar, Yonina C.
AU - Kipnis, Alan
N1 - We thank I. E. Aguerri and D. Gündüz for valuable discussions regarding the problem formulation, and S. Rini for helpful remarks and suggestions. This work was supported in part by the NSF Center for Science of Information (CSol) under grant CCF-0939370 and BSF Transformative Science Grant 2010505.
PY - 2013/1/1
Y1 - 2013/1/1
N2 - The amount of information lost in sub-Nyquist uniform sampling of a continuous-time Gaussian stationary process is quantified. We first derive an expression for the mean square error in reconstruction of the process for a given sampling structure as a function of the sampling frequency and the average number of bits describing each sample. We define this function as the distortion-rate-frequency function. It is obtained by reverse water-filling over spectral density associated with the minimum variance reconstruction of an undersampled Gaussian process, plus the error in this reconstruction. Further optimization is then performed over the sampling structure, and an optimal pre-sampling filter associated with the statistic of the input signal and the sampling frequency is found. This results in an expression for the minimal possible distortion achievable under any uniform sampling scheme. This expression is calculated for several examples to illustrate the fundamental tradeoff between rate distortion and sampling frequency derived in this work that lies at the intersection of information theory and signal processing.
AB - The amount of information lost in sub-Nyquist uniform sampling of a continuous-time Gaussian stationary process is quantified. We first derive an expression for the mean square error in reconstruction of the process for a given sampling structure as a function of the sampling frequency and the average number of bits describing each sample. We define this function as the distortion-rate-frequency function. It is obtained by reverse water-filling over spectral density associated with the minimum variance reconstruction of an undersampled Gaussian process, plus the error in this reconstruction. Further optimization is then performed over the sampling structure, and an optimal pre-sampling filter associated with the statistic of the input signal and the sampling frequency is found. This results in an expression for the minimal possible distortion achievable under any uniform sampling scheme. This expression is calculated for several examples to illustrate the fundamental tradeoff between rate distortion and sampling frequency derived in this work that lies at the intersection of information theory and signal processing.
UR - http://www.scopus.com/inward/record.url?scp=84897677392&partnerID=8YFLogxK
U2 - 10.1109/Allerton.2013.6736621
DO - 10.1109/Allerton.2013.6736621
M3 - Conference contribution
SN - 9781479934096
T3 - 2013 51st Annual Allerton Conference on Communication, Control, and Computing, Allerton 2013
SP - 901
EP - 908
BT - 2013 51st Annual Allerton Conference on Communication, Control, and Computing, Allerton 2013
T2 - 51st Annual Allerton Conference on Communication, Control, and Computing, Allerton 2013
Y2 - 2 October 2013 through 4 October 2013
ER -