433 research outputs found
Encoding and Decoding Mixed Bandlimited Signals using Spiking Integrate-and-Fire Neurons
Conventional sampling focuses on encoding and decoding bandlimited signals by
recording signal amplitudes at known time points. Alternately, sampling can be
approached using biologically-inspired schemes. Among these are
integrate-and-fire time encoding machines (IF-TEMs). They behave like
simplified versions of spiking neurons and encode their input using spike times
rather than amplitudes.
Moreover, when multiple of these neurons jointly process a set of mixed
signals, they form one layer in a feedforward spiking neural network. In this
paper, we investigate the encoding and decoding potential of such a layer.
We propose a setup to sample a set of bandlimited signals, by mixing them and
sampling the result using different IF-TEMs. We provide conditions for perfect
recovery of the set of signals from the samples in the noiseless case, and
suggest an algorithm to perform the reconstruction.Comment: To appear in ICASSP 2020. Code is available at
https://github.com/karenadam/Multi-Channel-Time-Encodin
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
Consistent Recovery of Sensory Stimuli Encoded with MIMO Neural Circuits
We consider the problem of reconstructing finite energy stimuli encoded with a population of spiking leaky integrate-and-fire neurons. The reconstructed signal satisfies a consistency condition: when passed through the same neuron, it triggers the same spike train as the original stimulus. The recovered stimulus has to also minimize a quadratic smoothness optimality criterion. We formulate the reconstruction as a spline interpolation problem for scalar as well as vector valued stimuli and show that the recovery has a unique solution. We provide explicit reconstruction algorithms for stimuli encoded with single as well as a population of integrate-and-fire neurons. We demonstrate how our reconstruction algorithms can be applied to stimuli encoded with ON-OFF neural circuits with feedback. Finally, we extend the formalism to multi-input multi-output neural circuits and demonstrate that vector-valued finite energy signals can be efficiently encoded by a neural population provided that its size is beyond a threshold value. Examples are given that demonstrate the potential applications of our methodology to systems neuroscience and neuromorphic engineering
Neuromorphic Sampling of Signals in Shift-Invariant Spaces
Neuromorphic sampling is a paradigm shift in analog-to-digital conversion
where the acquisition strategy is opportunistic and measurements are recorded
only when there is a significant change in the signal. Neuromorphic sampling
has given rise to a new class of event-based sensors called dynamic vision
sensors or neuromorphic cameras. The neuromorphic sampling mechanism utilizes
low power and provides high-dynamic range sensing with low latency and high
temporal resolution. The measurements are sparse and have low redundancy making
it convenient for downstream tasks. In this paper, we present a
sampling-theoretic perspective to neuromorphic sensing of continuous-time
signals. We establish a close connection between neuromorphic sampling and
time-based sampling - where signals are encoded temporally. We analyse
neuromorphic sampling of signals in shift-invariant spaces, in particular,
bandlimited signals and polynomial splines. We present an iterative technique
for perfect reconstruction subject to the events satisfying a density
criterion. We also provide necessary and sufficient conditions for perfect
reconstruction. Owing to practical limitations in meeting the sufficient
conditions for perfect reconstruction, we extend the analysis to approximate
reconstruction from sparse events. In the latter setting, we pose signal
reconstruction as a continuous-domain linear inverse problem whose solution can
be obtained by solving an equivalent finite-dimensional convex optimization
program using a variable-splitting approach. We demonstrate the performance of
the proposed algorithm and validate our claims via experiments on synthetic
signals
Time Encoding Sampling of Bandpass Signals
This paper investigates the problem of sampling and reconstructing bandpass
signals using time encoding machine(TEM). It is shown that the sampling in
principle is equivalent to periodic non-uniform sampling (PNS). Then the TEM
parameters can be set according to the signal bandwidth and amplitude instead
of upper-edge frequency and amplitude as in the case of bandlimited/lowpass
signals. For a bandpass signal of a single information band, it can be
perfectly reconstructed if the TEM parameters are such that the difference
between any consecutive values of the time sequence in each channel is bounded
by the inverse of the signal bandwidth. A reconstruction method incorporating
the interpolation functions of PNS is proposed. Numerical experiments validate
the feasibility and effectiveness of the proposed TEM scheme.Comment: 5 pages, 6 figure
Neuromorphic Sampling of Sparse Signals
Neuromorphic sampling is a bioinspired and opportunistic analog-to-digital
conversion technique, where the measurements are recorded only when there is a
significant change in the signal amplitude. Neuromorphic sampling has paved the
way for a new class of vision sensors called event cameras or dynamic vision
sensors (DVS), which consume low power, accommodate a high-dynamic range, and
provide sparse measurements with high temporal resolution making it convenient
for downstream inference tasks. In this paper, we consider neuromorphic sensing
of signals with a finite rate of innovation (FRI), including a stream of Dirac
impulses, sum of weighted and time-shifted pulses, and piecewise-polynomial
functions. We consider a sampling-theoretic approach and leverage the close
connection between neuromorphic sensing and time-based sampling, where the
measurements are encoded temporally. Using Fourier-domain analysis, we show
that perfect signal reconstruction is possible via parameter estimation using
high-resolution spectral estimation methods. We develop a kernel-based sampling
approach, which allows for perfect reconstruction with a sample complexity
equal to the rate of innovation of the signal. We provide sufficient conditions
on the parameters of the neuromorphic encoder for perfect reconstruction.
Furthermore, we extend the analysis to multichannel neuromorphic sampling of
FRI signals, in the single-input multi-output (SIMO) and multi-input
multi-output (MIMO) configurations. We show that the signal parameters can be
jointly estimated using multichannel measurements. Experimental results are
provided to substantiate the theoretical claims
Real-Time Decoding of an Integrate and Fire Encoder
Neuronal encoding models range from the detailed biophysically-based Hodgkin Huxley model, to the statistical linear time invariant model specifying firing rates in terms of the extrinsic signal. Decoding the former becomes intractable, while the latter does not adequately capture the nonlinearities present in the neuronal encoding system. For use in practical applications, we wish to record the output of neurons, namely spikes, and decode this signal fast in order to act on this signal, for example to drive a prosthetic device. Here, we introduce a causal, real-time decoder of the biophysically-based Integrate and Fire encoding neuron model. We show that the upper bound of the real-time reconstruction error decreases polynomially in time, and that the L[subscript 2] norm of the error is bounded by a constant that depends on the density of the spikes, as well as the bandwidth and the decay of the input signal. We numerically validate the effect of these parameters on the reconstruction error.National Science Foundation (U.S.) (Emerging Frontiers in Research and Innovation Grant 1137237
Shuttle Ku-band signal design study
Carrier synchronization and data demodulation of Unbalanced Quadriphase Shift Keyed (UQPSK) Shuttle communications' signals by optimum and suboptimum methods are discussed. The problem of analyzing carrier reconstruction techniques for unbalanced QPSK signal formats is addressed. An evaluation of the demodulation approach of the Ku-Band Shuttle return link for UQPSK when the I-Q channel power ratio is large is carried out. The effects that Shuttle rocket motor plumes have on the RF communications are determined also. The effect of data asymmetry on bit error probability is discussed
Time Encoding via Unlimited Sampling: Theory, Algorithms and Hardware Validation
An alternative to conventional uniform sampling is that of time encoding,
which converts continuous-time signals into streams of trigger times. This
gives rise to Event-Driven Sampling (EDS) models. The data-driven nature of EDS
acquisition is advantageous in terms of power consumption and time resolution
and is inspired by the information representation in biological nervous
systems. If an analog signal is outside a predefined dynamic range, then EDS
generates a low density of trigger times, which in turn leads to recovery
distortion due to aliasing. In this paper, inspired by the Unlimited Sensing
Framework (USF), we propose a new EDS architecture that incorporates a modulo
nonlinearity prior to acquisition that we refer to as the modulo EDS or MEDS.
In MEDS, the modulo nonlinearity folds high dynamic range inputs into low
dynamic range amplitudes, thus avoiding recovery distortion. In particular, we
consider the asynchronous sigma-delta modulator (ASDM), previously used for low
power analog-to-digital conversion. This novel MEDS based acquisition is
enabled by a recent generalization of the modulo nonlinearity called
modulo-hysteresis. We design a mathematically guaranteed recovery algorithm for
bandlimited inputs based on a sampling rate criterion and provide
reconstruction error bounds. We go beyond numerical experiments and also
provide a first hardware validation of our approach, thus bridging the gap
between theory and practice, while corroborating the conceptual underpinnings
of our work.Comment: 27 pgs, 11 figures, IEEE Trans. Sig. Proc., accepted with minor
revision
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