IEEE Solid-State Circuits Magazine - Summer 2015 - 68

These new devices demand a new approach
to analog-digital system partitioning with
the goal of significant overall reduction
in energy consumption.
account any heuristic or a priori side
information about the signal or its
information content other than the
physical bandwidth. While sampling at
or above Nyquist rate offers a classic
and straightforward approach, it can
compromise overall power efficiency.
Many emerging sensing applications, such as reactive user interfaces,
sensors for the IoT, medical monitoring systems, and radar applications,
evolve around sensing natural signals,
whose physical bandwidth is much
higher than their actual information
rate (Figure S1). In other words, a priori information on the sensed signal
can be exploited to reduce the information rate well below the physical
bandwidth. Examples include heartbeat signals and the reception of
reflected pulses in an ultrasound system (see "Bandwidth Versus Information and Feature Rates").

This a priori information can take
various forms, such as the shape,
periodicity, or sparseness of the
sensed signal. Taking this a priori
information into account reduces
the effective information rate of the
received signal well below the theoretical Nyquist rate. In theory, the signal can now be sampled at this lower
rate, while preserving full information
conversion into the digital domain.
Yet, in practice, it is not necessarily
straightforward to achieve sampling
rate reduction all the way down to the
information rate, as pursued by ADCs.

Alternative Sampling Techniques
Beyond Nyquist Through Analogto-Information Conversion
The term "analog-to-information" emerged
with the introduction of a subNyquist sampling technique called

compressed sensing (CS) for sparse
signals [2]-[4]. Sparsity means that
a signal is compressible and can be
represented with fewer samples on
an appropriate basis [5]. CS exploits
the fact that the information rate of a
waveform that is sparse in a particular domain (such as, e.g., in the time
domain, in the frequency domain, or
in a wavelet domain) is significantly
smaller than the Nyquist rate [6].
By correlating the signal with waveforms that are not coherent with the
sparse basis, the analog bandwidth
is narrowed down to near the information rate. Such projections can be
implemented in the analog domain
through nonuniform sampling, as
well as through various modulateand-integrate schemes.
Subsequently, the original waveform can be recovered in the digital
domain with signal processing of far
fewer samples through finding sparse
solutions to an underdetermined linear
system [5]. The resulting ADC architecture, as depicted in Figure S2(b) in
"Alternative Sampling Strategies," thus
uses a priori knowledge of the signal,
in terms of the signal sparcity. This
allows the ADC to trade off sampling

BANDWIDTH VERSUS INFORMATION AND FEATURE RATES
fore, their information rate is much smaller than their physical Nyquist
bandwidth (Figure S1).
In addition, some applications are not even concerned with the complete information rate but only interested in a selected subset of features that can be extracted from the signals. This can, for example, be
the amplitude of the pulses. As a result, the relevant feature rate of the
signal can again be smaller than its information rate.

Many emerging sensing applications, such as reactive user interfaces,
sensors for the IoT, medical monitoring systems, and radar applications, evolve around sensing natural signals, whose physical bandwidth is much higher than their actual information rate . For example,
a pulsed radar signal, which consists of sparse pulses in the time
domain with a known pulse shape, can be completely defined by
only characterizing the amplitude and position of the pulses. There-

Information Rate < Physical Bandwidth
All Signals with Physical Signal Bandwidth = W
a3
a1

a2
t1

Dimensionality = 2W * T
Information Rate = Physical Bandwidth

su m m e r 2 0 15

Dimensionality = 2 * 3

Information Rate << Physical Bandwidth

Figure S1: Physical bandwidth versus information rate versus feature rate.

IEEE SOLID-STATE CIRCUITS MAGAZINE

Dimensionality = 3
Feature Rate < Information Rate

Table of Contents for the Digital Edition of IEEE Solid-State Circuits Magazine - Summer 2015