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A Time-Based Sampling Framework for Finite-Rate-of-Innovation Signals

Abstract: 

Time-based sampling of continuous-time signals is an alternate sampling paradigm in which the signal is encoded using a sequence of non-uniform instants time. The standard methods for reconstructing bandlimited and shift-invariant signals from their time-encoded measurements employ alternating projections type methods. In this paper, we consider the problem of sampling and perfect reconstruction of periodic finite-rate-of-innovation (FRI) signals using crossing time-encoding machine (C-TEM) and integrate-and-fire TEM (IF-TEM). We formulate the reconstruction problem in the frequency domain and propose techniques to compute the Fourier coefficients, which contain the unknown parameters of the signal in the form of a sum of weighted complex exponentials. The parameters are then estimated using high-resolution spectral estimation techniques. The proposed method is generalized to incorporate reconstruction of periodic FRI signals consisting of weighted and shifted versions of an arbitrary pulse with arbitrarily close delays, and is compatible with a large class of sampling kernels. We provide sufficient conditions for sampling and perfect reconstruction using C-TEM and IF-TEM. We present simulation results to support our claims. We also discuss an extension to sampling of aperiodic FRI signals.

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Paper Details

Authors:
Submitted On:
14 May 2020 - 12:45pm
Short Link:
Type:
Presentation Slides
Event:
Presenter's Name:
Abijith J Kamath
Paper Code:
SPTM-P2.2
Document Year:
2020
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Document Files

TEM FRI ICASSP20.pdf

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[1] , "A Time-Based Sampling Framework for Finite-Rate-of-Innovation Signals", IEEE SigPort, 2020. [Online]. Available: http://sigport.org/5316. Accessed: Jul. 13, 2020.
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publisher = {IEEE SigPort},
title = {A Time-Based Sampling Framework for Finite-Rate-of-Innovation Signals},
year = {2020} }
TY - EJOUR
T1 - A Time-Based Sampling Framework for Finite-Rate-of-Innovation Signals
AU -
PY - 2020
PB - IEEE SigPort
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. (2020). A Time-Based Sampling Framework for Finite-Rate-of-Innovation Signals. IEEE SigPort. http://sigport.org/5316
, 2020. A Time-Based Sampling Framework for Finite-Rate-of-Innovation Signals. Available at: http://sigport.org/5316.
. (2020). "A Time-Based Sampling Framework for Finite-Rate-of-Innovation Signals." Web.
1. . A Time-Based Sampling Framework for Finite-Rate-of-Innovation Signals [Internet]. IEEE SigPort; 2020. Available from : http://sigport.org/5316