IEEE Signal Processing - May 2018 - 16
Alon Kipnis, Yonina C. Eldar, and Andrea J. Goldsmith
Analog-to-Digital
Compression
A new paradigm for converting signals to bits
P
rocessing, storing, and communicating information that
originates as an analog signal involves converting this
information to bits. This conversion can be described by
the combined effect of sampling and quantization, as
shown in Figure 1. The digital representation is achieved by first
sampling the analog signal to represent it by a set of discretetime 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 the information
loss due to sampling based on characteristics of the continuoustime input. The quantizer is designed to represent the samples
as accurately as possible, subject to a constraint on the number
Digital Object Identifier 10.1109/MSP.2017.2774249
Date of publication: 26 April 2018
16
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 of the sampling system subject to the constraints
on the available number of bits for storing, communicating, or
processing the analog information.
Motivation
As a motivation for optimizing sampling and quantization
together, consider the minimal sampling rate that arises in
classical sampling theory due to Whittaker, Kotelnikov,
Shannon, and Landau [1]-[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,
IEEE Signal Processing Magazine
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May 2018
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1053-5888/18©2018IEEE
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