38,558 research outputs found
Sampling and Reconstruction of Spatial Fields using Mobile Sensors
Spatial sampling is traditionally studied in a static setting where static
sensors scattered around space take measurements of the spatial field at their
locations. In this paper we study the emerging paradigm of sampling and
reconstructing spatial fields using sensors that move through space. We show
that mobile sensing offers some unique advantages over static sensing in
sensing time-invariant bandlimited spatial fields. Since a moving sensor
encounters such a spatial field along its path as a time-domain signal, a
time-domain anti-aliasing filter can be employed prior to sampling the signal
received at the sensor. Such a filtering procedure, when used by a
configuration of sensors moving at constant speeds along equispaced parallel
lines, leads to a complete suppression of spatial aliasing in the direction of
motion of the sensors. We analytically quantify the advantage of using such a
sampling scheme over a static sampling scheme by computing the reduction in
sampling noise due to the filter. We also analyze the effects of non-uniform
sensor speeds on the reconstruction accuracy. Using simulation examples we
demonstrate the advantages of mobile sampling over static sampling in practical
problems.
We extend our analysis to sampling and reconstruction schemes for monitoring
time-varying bandlimited fields using mobile sensors. We demonstrate that in
some situations we require a lower density of sensors when using a mobile
sensing scheme instead of the conventional static sensing scheme. The exact
advantage is quantified for a problem of sampling and reconstructing an audio
field.Comment: Submitted to IEEE Transactions on Signal Processing May 2012; revised
Oct 201
Sub-Nyquist Sampling: Bridging Theory and Practice
Sampling theory encompasses all aspects related to the conversion of
continuous-time signals to discrete streams of numbers. The famous
Shannon-Nyquist theorem has become a landmark in the development of digital
signal processing. In modern applications, an increasingly number of functions
is being pushed forward to sophisticated software algorithms, leaving only
those delicate finely-tuned tasks for the circuit level.
In this paper, we review sampling strategies which target reduction of the
ADC rate below Nyquist. Our survey covers classic works from the early 50's of
the previous century through recent publications from the past several years.
The prime focus is bridging theory and practice, that is to pinpoint the
potential of sub-Nyquist strategies to emerge from the math to the hardware. In
that spirit, we integrate contemporary theoretical viewpoints, which study
signal modeling in a union of subspaces, together with a taste of practical
aspects, namely how the avant-garde modalities boil down to concrete signal
processing systems. Our hope is that this presentation style will attract the
interest of both researchers and engineers in the hope of promoting the
sub-Nyquist premise into practical applications, and encouraging further
research into this exciting new frontier.Comment: 48 pages, 18 figures, to appear in IEEE Signal Processing Magazin
Oversampling PCM techniques and optimum noise shapers for quantizing a class of nonbandlimited signals
We consider the efficient quantization of a class of nonbandlimited signals, namely, the class of discrete-time signals that can be recovered from their decimated version. The signals are modeled as the output of a single FIR interpolation filter (single band model) or, more generally, as the sum of the outputs of L FIR interpolation filters (multiband model). These nonbandlimited signals are oversampled, and it is therefore reasonable to expect that we can reap the same benefits of well-known efficient A/D techniques that apply only to bandlimited signals. We first show that we can obtain a great reduction in the quantization noise variance due to the oversampled nature of the signals. We can achieve a substantial decrease in bit rate by appropriately decimating the signals and then quantizing them. To further increase the effective quantizer resolution, noise shaping is introduced by optimizing prefilters and postfilters around the quantizer. We start with a scalar time-invariant quantizer and study two important cases of linear time invariant (LTI) filters, namely, the case where the postfilter is the inverse of the prefilter and the more general case where the postfilter is independent from the prefilter. Closed form expressions for the optimum filters and average minimum mean square error are derived in each case for both the single band and multiband models. The class of noise shaping filters and quantizers is then enlarged to include linear periodically time varying (LPTV)M filters and periodically time-varying quantizers of period M. We study two special cases in great detail
Fractional biorthogonal partners in channel equalization and signal interpolation
The concept of biorthogonal partners has been introduced recently by the authors. The work presented here is an extension of some of these results to the case where the upsampling and downsampling ratios are not integers but rational numbers, hence, the name fractional biorthogonal partners. The conditions for the existence of stable and of finite impulse response (FIR) fractional biorthogonal partners are derived. It is also shown that the FIR solutions (when they exist) are not unique. This property is further explored in one of the applications of fractional biorthogonal partners, namely, the fractionally spaced equalization in digital communications. The goal is to construct zero-forcing equalizers (ZFEs) that also combat the channel noise. The performance of these equalizers is assessed through computer simulations. Another application considered is the all-FIR interpolation technique with the minimum amount of oversampling required in the input signal. We also consider the extension of the least squares approximation problem to the setting of fractional biorthogonal partners
Compressed Sensing of Analog Signals in Shift-Invariant Spaces
A traditional assumption underlying most data converters is that the signal
should be sampled at a rate exceeding twice the highest frequency. This
statement is based on a worst-case scenario in which the signal occupies the
entire available bandwidth. In practice, many signals are sparse so that only
part of the bandwidth is used. In this paper, we develop methods for low-rate
sampling of continuous-time sparse signals in shift-invariant (SI) spaces,
generated by m kernels with period T. We model sparsity by treating the case in
which only k out of the m generators are active, however, we do not know which
k are chosen. We show how to sample such signals at a rate much lower than m/T,
which is the minimal sampling rate without exploiting sparsity. Our approach
combines ideas from analog sampling in a subspace with a recently developed
block diagram that converts an infinite set of sparse equations to a finite
counterpart. Using these two components we formulate our problem within the
framework of finite compressed sensing (CS) and then rely on algorithms
developed in that context. The distinguishing feature of our results is that in
contrast to standard CS, which treats finite-length vectors, we consider
sampling of analog signals for which no underlying finite-dimensional model
exists. The proposed framework allows to extend much of the recent literature
on CS to the analog domain.Comment: to appear in IEEE Trans. on Signal Processin
Xampling: Signal Acquisition and Processing in Union of Subspaces
We introduce Xampling, a unified framework for signal acquisition and
processing of signals in a union of subspaces. The main functions of this
framework are two. Analog compression that narrows down the input bandwidth
prior to sampling with commercial devices. A nonlinear algorithm then detects
the input subspace prior to conventional signal processing. A representative
union model of spectrally-sparse signals serves as a test-case to study these
Xampling functions. We adopt three metrics for the choice of analog
compression: robustness to model mismatch, required hardware accuracy and
software complexities. We conduct a comprehensive comparison between two
sub-Nyquist acquisition strategies for spectrally-sparse signals, the random
demodulator and the modulated wideband converter (MWC), in terms of these
metrics and draw operative conclusions regarding the choice of analog
compression. We then address lowrate signal processing and develop an algorithm
for that purpose that enables convenient signal processing at sub-Nyquist rates
from samples obtained by the MWC. We conclude by showing that a variety of
other sampling approaches for different union classes fit nicely into our
framework.Comment: 16 pages, 9 figures, submitted to IEEE for possible publicatio
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