Figure 1: An example of conservation of bits principle
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