Impossibility of perfect recovering cosinusoidal signal of any phase sampled with nyquist rate

• Autorzy: Borys A , Korohoda P.

Identyfikatory

DOI

10.12716/1001.14.03.28

• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

nyquist rate; cosinusoidal sSignal; cosinusoidal signal amplitude; cosinusoidal signal phase; signal processing; critical sampling; analysis of critical signal; analysis of cosinusoidal signal

• Wydawca: Faculty of Navigation, Gdynia Maritime University
• Czasopismo: TransNav : International Journal on Marine Navigation and Safety of Sea Transportation
• Rocznik: 2020
• Tom: Vol. 14. no. 3
• Strony: 738--742
• Opis fizyczny: Bibliogr. 6 poz.

Twórcy

autor

Borys A

• Gdynia Maritime University, Gdynia, Poland

autor

Korohoda P.

• AGH University of Science and Technology, Kraków, Poland

Bibliografia

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• 3. Osgood B. 2014. The Fourier Transform and Its Applications, Lecture Notes EE261, Stanford University.
• 4. 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.
• 5. Dirac P. A. M. 1947. The Principles of Quantum Mechanics, 3rd Ed., Oxford Univ. Press, Oxford.
• 6. Hoskins R. F. 2009. Delta Functions: An Introduction to Generalised Functions, Horwood Pub., Oxford.