Analog-to-Digital Compression: A New Paradigm for Converting Signals to Bits

Processing, storing and communicating information that originates as an analog signal involves conversion of this information to bits. This conversion can be described by the combined effect of sampling and quantization, as illustrated in Fig. 1. The digital representation is achieved by first sampling the analog signal so as to represent it by a set of discrete-time samples and then quantizing these samples to a finite number of bits. Traditionally, these two operations are considered separately. The sampler is designed to minimize information loss due to sampling based on characteristics of the continuous-time input. The quantizer is designed to represent the samples as accurately as possible, subject to a constraint on the number of bits that can be used in the representation. The goal of this article is to revisit this paradigm by illuminating the dependency between these two operations. In particular, we explore the requirements on the sampling system subject to constraints on the available number of bits for storing, communicating or processing the analog information. As motivation for jointly optimizing sampling and quantization, consider the minimal sampling rate that arises in classical sampling theory due to Whittaker, Kotelnikov, Shannon and Landau [1], [2], [3]. These works establish the Nyquist rate or the spectral occupancy of the signal as the critical sampling rate above which the signal can be perfectly reconstructed from its samples. This statement, however, focuses only on the critical sampling rate required to perfectly reconstruct a bandlimited signal from its discrete samples; it does not incorporate the quantization precision of the samples