On distributed sampling of bandlimited and non-bandlimited sensor fields
Distributed sampling and reconstruction of a physical field using an array of sensors is a problem of increasing interest in environmental monitoring applications of sensor networks. We show, using a dither-based scheme, that it is possible to reconstruct non-bandlimited fields with a reconstruction accuracy that depends on the available bitrate R and the spectral decay characteristics of the sensor field - we study exponentially decaying spectra as an illustration. For bandlimited fields f(t), the maximum pointwise error D/sub f/ decays as D/sub f/ /spl sim/ 2/sup -a1R/, i.e. exponentially with rate R. For the non-bandlimited case, we show that for fields u(t) with exponentially decaying spectral tails, i.e., |U(/spl omega/)|/spl sim/e/sup -a|/spl omega/|/, the maximum pointwise error D/sub u/ decays as D/sub u//spl sim/e/sup -a2/spl radic/R/(1+o(R)) with spatial bit rate R bits/metre. We also show that it is possible to trade off the number of sensors with their precision, while maintaining a similar reconstruction accuracy - a phenomenon that may be dubbed as a "bit-conservation" principle underlying the sampling framework.