Sampling of Band-Limited Signals with Nonuniform Sampling-Time and Bit-Depth

To reproduce a band-limited continuous-time signal with optimal fidelity, usually it is sampled at the Nyquist sampling rate and then the sample values are quantized. In nonuniform sampling, the total number of samples are reduced in expense of adding some reconstruction complexity and assuming prior information about the signal. In this paper we propose nonuniform sampling-time with nonuniform bit resolution per sample (bit-depth) to reduce the total required bit budget (i.e. the number of samples timed the bit-depth) even further. This idea is based on the fact that the maximum local variation of band-limited signals is bounded in a given time horizon. Therefore, it is not necessary to allocate a fixed bit-depth proportional to the signal´s dynamic range to each sample. Instead, we try to allocate adaptively only the needed number of bits to represent the next sample considering the physical characteristics of the signal. Both sampling and reconstruction entities can generate the next sampling-times and bit-depths locally by observing the current and previous samples only. We propose different techniques in our generalized sampling framework that share a common sampling architecture. Here we only consider ECG signals for evaluation purpose. Based on the simulation results, the total number of required bits to reconstruct the signal with negligible distortion can be reduced up to 88% without imposing any form of transform coding compression.