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ISSN 2083-6473
ISSN 2083-6481 (electronic version)
 

 

 

Editor-in-Chief

Associate Editor
Prof. Tomasz Neumann
 

Published by
TransNav, Faculty of Navigation
Gdynia Maritime University
3, John Paul II Avenue
81-345 Gdynia, POLAND
www http://www.transnav.eu
e-mail transnav@umg.edu.pl
Impossibility of Perfect Recovering Cosinusoidal Signal of Any Phase Sampled with Nyquist Rate
ABSTRACT: In this paper, a problem of a perfect recovering cosinusoidal signal of any phase being sampled critically is considered. It is shown that there is no general solution to this problem. Its detailed analysis presented here shows that recovering both the original cosinusoidal signal amplitude and its phase is not possible at all. Only one of this quantities can be recovered under the assumption that the second one is known. And even then, performing some additional calculations is needed. As a byproduct, it is shown here that a transfer function of the recovering filter that must be used in the case of the critical sampling differs from the one which is used when a cosinusoidal signal is sampled with the use of a sampling frequency greater than the Nyquist rate. All the results achieved in this paper are soundly justified by thorough derivations.
REFERENCES
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Korohoda P., Borgosz J. 1999. Explanation of sampling and reconstruction at critical rate, Proceedings of the 6th International Conference on Systems, Signals, and Image Processing (IWSSIP), Bratislava, Slovakia, 157-160.
Osgood B. 2014. The Fourier Transform and Its Applications, Lecture Notes EE261, Stanford University.
Borys A., Korohoda P. 2017. Analysis of critical sampling effects revisited, Proceedings of the 21st International Conference Signal Processing: Algorithms, Architectures, Arrangements, and Applications SPA2017, Poznań, Poland, 131 – 136. - doi:10.23919/SPA.2017.8166852
Dirac P. A. M. 1947. The Principles of Quantum Mechanics, 3rd Ed., Oxford Univ. Press, Oxford.
Hoskins R. F. 2009. Delta Functions: An Introduction to Generalised Functions, Horwood Pub., Oxford - doi:10.1533/9780857099358
Citation note:
Borys A., Korohoda P.: Impossibility of Perfect Recovering Cosinusoidal Signal of Any Phase Sampled with Nyquist Rate. TransNav, the International Journal on Marine Navigation and Safety of Sea Transportation, Vol. 14, No. 3, doi:10.12716/1001.14.03.28, pp. 737-742, 2020

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