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Wavelet-Based Reconstruction for Unlimited Sampling

Abstract: 

Self-reset analog-to-digital converters (ADCs) allow for digitization of a signal with a high dynamic range. The reset action is equivalent to a modulo operation performed on the signal. We consider the problem of recovering the original signal from the measured modulo-operated signal. In our formulation, we assume that the underlying signal is Lipschitz continuous. The modulo-operated signal can be expressed as the sum of the original signal and a piecewise-constant signal that captures the transitions. The reconstruction requires estimating the piecewise-constant signal. We rely on local smoothness of the modulo-operated signal and employ wavelets with sufficient vanishing moments to suppress the polynomial component. We employ Daubechies wavelets, which are most compact for a given number of vanishing moments. The wavelet filtering provides a sequence consisting of a sum of scaled and shifted versions of a kernel derived from the wavelet filter. The transition locations are estimated from the sequence using a sparse recovery technique. We derive a sufficient condition on the sampling frequency for ensuring perfect reconstruction of the smooth signal. We validate our reconstruction technique on a signal consisting of sinusoids in both clean and noisy conditions and compare the reconstruction quality with the recently developed repeated finite-difference method.

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Paper Details

Authors:
Aniruddha Adiga, Basty Ajay Shenoy, Chandra Sekhar Seelamantula
Submitted On:
12 April 2018 - 2:06pm
Short Link:
Type:
Poster
Event:
Presenter's Name:
Sunil Rudresh
Paper Code:
ICASSP18001
Document Year:
2018
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Document Files

ICASSP_2018_Sunil.pdf

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[1] Aniruddha Adiga, Basty Ajay Shenoy, Chandra Sekhar Seelamantula, "Wavelet-Based Reconstruction for Unlimited Sampling", IEEE SigPort, 2018. [Online]. Available: http://sigport.org/2460. Accessed: Jul. 16, 2019.
@article{2460-18,
url = {http://sigport.org/2460},
author = {Aniruddha Adiga; Basty Ajay Shenoy; Chandra Sekhar Seelamantula },
publisher = {IEEE SigPort},
title = {Wavelet-Based Reconstruction for Unlimited Sampling},
year = {2018} }
TY - EJOUR
T1 - Wavelet-Based Reconstruction for Unlimited Sampling
AU - Aniruddha Adiga; Basty Ajay Shenoy; Chandra Sekhar Seelamantula
PY - 2018
PB - IEEE SigPort
UR - http://sigport.org/2460
ER -
Aniruddha Adiga, Basty Ajay Shenoy, Chandra Sekhar Seelamantula. (2018). Wavelet-Based Reconstruction for Unlimited Sampling. IEEE SigPort. http://sigport.org/2460
Aniruddha Adiga, Basty Ajay Shenoy, Chandra Sekhar Seelamantula, 2018. Wavelet-Based Reconstruction for Unlimited Sampling. Available at: http://sigport.org/2460.
Aniruddha Adiga, Basty Ajay Shenoy, Chandra Sekhar Seelamantula. (2018). "Wavelet-Based Reconstruction for Unlimited Sampling." Web.
1. Aniruddha Adiga, Basty Ajay Shenoy, Chandra Sekhar Seelamantula. Wavelet-Based Reconstruction for Unlimited Sampling [Internet]. IEEE SigPort; 2018. Available from : http://sigport.org/2460