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Minimum number of possibly non-contiguous samples to distinguish two periods

Tenneti, Srikanth V. and Vaidyanathan, P. P. (2017) Minimum number of possibly non-contiguous samples to distinguish two periods. In: 2017 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). IEEE , Piscataway, NJ, pp. 3824-3828. ISBN 978-1-5090-4117-6 . https://resolver.caltech.edu/CaltechAUTHORS:20170621-163606697

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Abstract

Given that a sequence x(n) is periodic with period P belonging to a known integer set {P_1, P_2, … P_L}, what is the minimum number of samples of x(n) required to find the period? For the special case where the samples of x(n) are constrained to be contiguous in time, this problem has recently been solved. More generally, when the samples are allowed to be non-contiguous, the problem is quite difficult. This paper provides the answer for the restricted situation where P ∈ {P_1, P_2}. With P_1 < P_2, the necessary and sufficient number of (possibly noncontiguous) samples for period estimation turns out to be (a) P_1, if P_1 is not a divisor of P_2, and (b) P_2 otherwise. While the proof is quite involved even in this restricted case, it is likely to form the basis for addressing the more general situation where P ∈ {P_1, P_2, … P_L}.


Item Type:Book Section
Related URLs:
URLURL TypeDescription
https://doi.org/10.1109/ICASSP.2017.7952872DOIArticle
http://ieeexplore.ieee.org/document/7952872/PublisherArticle
Additional Information:© 2017 IEEE. This work was supported by the ONR grant N00014-15-1-2118, and the California Institute of Technology.
Funders:
Funding AgencyGrant Number
Office of Naval Research (ONR)N00014-15-1-2118
CaltechUNSPECIFIED
Subject Keywords:Period Estimation, Minimum Samples, Ramanujan Sums, Nested Periodic Matrices
Record Number:CaltechAUTHORS:20170621-163606697
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20170621-163606697
Official Citation:S. V. Tenneti and P. P. Vaidyanathan, "Minimum number of possibly non-contiguous samples to distinguish two periods," 2017 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), New Orleans, LA, USA, 2017, pp. 3824-3828. doi: 10.1109/ICASSP.2017.7952872
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:78443
Collection:CaltechAUTHORS
Deposited By: Kristin Buxton
Deposited On:22 Jun 2017 01:20
Last Modified:03 Oct 2019 18:08

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