Abstract
We investigate the possibility of data recovery for finite sequences with constraints on their spectrum defined by a special discretization of the spectrum range. These sequences are dense in the space of all sequences. We show that uniqueness sets for them can be singletons.
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Candés, E., Romberg, J., and Tao, T., Robust Uncertainty Principles: Exact Signal Reconstruction from Highly Incomplete Frequency Information, IEEE Trans. Inform. Theory, 2006, vol. 52, no. 2, pp. 489–509. https://doi.org/10.1109/TIT.2005.862083
Candés, E. and Tao, T., Near Optimal Signal Recovery from Random Projections: Universal Encoding Strategies?, IEEE Trans. Inform. Theory, 2006, vol. 52, no. 12, pp. 5406–5425. https://doi.org/10.1109/TIT.2006.885507
Dokuchaev, N., On Recovery of Discrete Time Signals from Their Periodic Subsequences, Signal Process., 2019, vol. 162, pp. 180–188. https://doi.org/10.1016/j.sigpro.2019.04.008
Dokuchaev, N., On Linear Weak Predictability with Single Point Spectrum Degeneracy, Appl. Comput. Harmon. Anal., 2021, vol. 53, pp. 116–131. https://doi.org/10.1016/j.acha.2021.01.005
Olevskii, A.M. and Ulanovskii, A., Functions with Disconnected Spectrum: Sampling, Interpolation, Translates, Providence, RI: Amer. Math. Soc., 2016.
Venkataramani, R. and Bresler, Y., Sub-Nyquist Sampling of Multiband Signals: Perfect Reconstruction and Bounds on Aliasing Error, in Proc. 1998 IEEE Int. Conf. on Acoustics, Speech and Signal Processing (ICASSP’98), May 12–15, 1998, Seattle, WA, USA, vol. 3, pp. 1633–1636. https://doi.org/10.1109/ICASSP.1998.681767
Baker, A., Transcendental Number Theory, London/New York: Cambridge Univ. Press, 1975.
Smart, N.P., The Algorithmic Resolution of Diophantine Equations, New York: Cambridge Univ. Press, 1998.
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Translated from Problemy Peredachi Informatsii, 2021, Vol. 57, No. 4, pp. 74–78 https://doi.org/10.31857/S0555292321040069.
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Dokuchaev, N. On Data Compression and Recovery for Sequences Using Constraints on the Spectrum Range. Probl Inf Transm 57, 368–372 (2021). https://doi.org/10.1134/S0032946021040062
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DOI: https://doi.org/10.1134/S0032946021040062