## Distributed Sampling for Sensor Networks

Animesh Kumar and Prakash Ishwar^{1}

(Professor Kannan Ramchandran)

(DARPA) F30602-00-2-0538 and (NSF) CCR-0219722

In the context of bandlimited signals, there are two ways to sample a signal. One is a PCM method, in which the sampling rate is slightly above the Nyquist rate, and each sample is quantized with a precise A/D converter. To reduce the cost there are schemes which use a 1 bit A/D converter with oversampling. Recently, it was shown [1,2] that one could achieve similar accuracy from the oversampling and PCM methods for the same rate. (PCM accuracy is so far the best known result.) This indicates that one should be able to trade off the oversampling with the A/D precision. We have some partial results in this area. At first the dither-based schemes [1] were generalized to trade off average oversampling with the accuracy of an A/D converter. Also, the one-bit dither method and the PCM method turned out to be a special case of our scheme, so it connects two completely separate looking schemes as well. We also have a distributed and energy efficient algorithm for sampling a one-dimensional bandlimited field.

A further related problem that we are pursuing is the distributed sampling of finite rate innovation signals [3]. It requires selection of suitable models, followed by schemes/algorithms and their analyses. Our main goals are good/best reconstruction and low energy consumption.

Figure 1: An example of conservation of bits principle

- [1]
- Z. Cvetkovic and I. Daubechies, "Single-Bit Oversampled A/D Conversion with Exponential Accuracy in the Bit-Rate,"
*Proc. Data Compression Conf.,* Snowbird, UT, March 2000.
- [2]
- Z. Cvetkovic, I. Daubechies, and B. F. Logan, "Interpolation of Bandlimited Functions from Quantized Irregular Samples,"
*Proc. Data Compression Conf.,* Snowbird, UT, April 2002.
- [3]
- M. Vetterli, P. Marziliano, and T. Blu, "Sampling Signals with Finite Rate of Innovation,"
*IEEE Trans. Signal Processing,* Vol. 50, No. 6, June 2002.

^{1}Postdoctoral Researcher

Send mail to the author : (animesh@eecs.berkeley.edu)

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