98,396 research outputs found
Quantum effects in linguistic endeavors
Classifying the information content of neural spike trains in a linguistic
endeavor, an uncertainty relation emerges between the bit size of a word and
its duration. This uncertainty is associated with the task of synchronizing the
spike trains of different duration representing different words. The
uncertainty involves peculiar quantum features, so that word comparison amounts
to measurement-based-quantum computation. Such a quantum behavior explains the
onset and decay of the memory window connecting successive pieces of a
linguistic text. The behavior here discussed is applicable to other reported
evidences of quantum effects in human linguistic processes, so far lacking a
plausible framework, since either no efforts to assign an appropriate quantum
constant had been associated or speculating on microscopic processes dependent
on Planck's constant resulted in unrealistic decoherence times
Uncertainty Relations for Shift-Invariant Analog Signals
The past several years have witnessed a surge of research investigating
various aspects of sparse representations and compressed sensing. Most of this
work has focused on the finite-dimensional setting in which the goal is to
decompose a finite-length vector into a given finite dictionary. Underlying
many of these results is the conceptual notion of an uncertainty principle: a
signal cannot be sparsely represented in two different bases. Here, we extend
these ideas and results to the analog, infinite-dimensional setting by
considering signals that lie in a finitely-generated shift-invariant (SI)
space. This class of signals is rich enough to include many interesting special
cases such as multiband signals and splines. By adapting the notion of
coherence defined for finite dictionaries to infinite SI representations, we
develop an uncertainty principle similar in spirit to its finite counterpart.
We demonstrate tightness of our bound by considering a bandlimited lowpass
train that achieves the uncertainty principle. Building upon these results and
similar work in the finite setting, we show how to find a sparse decomposition
in an overcomplete dictionary by solving a convex optimization problem. The
distinguishing feature of our approach is the fact that even though the problem
is defined over an infinite domain with infinitely many variables and
constraints, under certain conditions on the dictionary spectrum our algorithm
can find the sparsest representation by solving a finite-dimensional problem.Comment: Accepted to IEEE Trans. on Inform. Theor
From Theory to Practice: Sub-Nyquist Sampling of Sparse Wideband Analog Signals
Conventional sub-Nyquist sampling methods for analog signals exploit prior
information about the spectral support. In this paper, we consider the
challenging problem of blind sub-Nyquist sampling of multiband signals, whose
unknown frequency support occupies only a small portion of a wide spectrum. Our
primary design goals are efficient hardware implementation and low
computational load on the supporting digital processing. We propose a system,
named the modulated wideband converter, which first multiplies the analog
signal by a bank of periodic waveforms. The product is then lowpass filtered
and sampled uniformly at a low rate, which is orders of magnitude smaller than
Nyquist. Perfect recovery from the proposed samples is achieved under certain
necessary and sufficient conditions. We also develop a digital architecture,
which allows either reconstruction of the analog input, or processing of any
band of interest at a low rate, that is, without interpolating to the high
Nyquist rate. Numerical simulations demonstrate many engineering aspects:
robustness to noise and mismodeling, potential hardware simplifications,
realtime performance for signals with time-varying support and stability to
quantization effects. We compare our system with two previous approaches:
periodic nonuniform sampling, which is bandwidth limited by existing hardware
devices, and the random demodulator, which is restricted to discrete multitone
signals and has a high computational load. In the broader context of Nyquist
sampling, our scheme has the potential to break through the bandwidth barrier
of state-of-the-art analog conversion technologies such as interleaved
converters.Comment: 17 pages, 12 figures, to appear in IEEE Journal of Selected Topics in
Signal Processing, the special issue on Compressed Sensin
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