On Derivation of Discrete Time Fourier Transform from Its Continuous Counterpart

• Autorzy: Borys Andrzej

Identyfikatory

DOI

10.24425/ijet.2020.131885

• Języki publikacji: EN

Abstrakty

EN

This paper is devoted to some problems that appear in derivations of the discrete time Fourier transform from a formula for its continuous time counterpart for transformation from the time into the frequency domain as well as to those regarding transformation in the inverse direction. In particular, the latter ones remained so far an unresolved problem. It is solved for the first time here. Many detailed explanations accompanying the solution found are presented. Finally, it is also worth noting that our derivations do not exploit any of such sophisticated mathematical tools as the so-called Dirac delta and Dirac comb.

Słowa kluczowe

EN

sampling of signals; discrete time; continuous time; Fourier transforms

• Wydawca: Polish Academy of Sciences, Committee of Electronics and Telecommunication
• Czasopismo: International Journal of Electronics and Telecommunications
• Rocznik: 2020
• Tom: Vol. 66, No. 2
• Strony: 355--360
• Opis fizyczny: Bibliogr. 11 poz.

Twórcy

autor

Borys Andrzej

• Department of Marine Telecommunications, Faculty of Electrical Engineering, Gdynia Maritime University, Gdynia, Poland

Bibliografia

• [1] Ch. A. Bouman, Digital Image Processing I - Lecture 11 - DTFT, DSFT, Sampling, and Reconstruction, https://cosmolearning.video-lectures/dtft-dsft-sampling-reconstruction/, accessed Dec. 2019.
• [2] H. C. So, Signals and Systems - Lecture 6 - Discrete-Time Fourier Transform, www.ee.cityu.edu.hk/~hcso/ee3210.html, accessed Dec. 2019.
• [3] J. H. McClellan, R. Schafer, and M. Yoder, DSP First, London: Pearson, 2015.
• [4] M. Vetterli, J. Kovacevic, and V. K. Goyal, Foundations of Signal Processing, Cambridge: Cambridge University Press, 2014.
• [5] R. Wang, Introduction to Orthogonal Transforms with Applications in Data Processing and Analysis, Cambridge: Cambridge University Press, 2010.
• [6] V. K. Ingle and J. G. Proakis, Digital Signal Processing Using Matlab, Stamford, USA: Cengage Learning, 2012.
• [7] A. V. Oppenhiem, S. Willsky, and S. H. Nawab, Signals and Systems, Upper Saddle River, USA: Prentice Hall, 1996.
• [8] R. Strichartz, A Guide to Distribution Theory and Fourier Transforms, Boca Raton, USA: CRC Press, 1994.
• [9] R. F. Hoskins, Delta Functions: An Introduction to Generalised Functions, Cambridge: Horwood Pub., 2009.
• [10] R. Brigola, Fourier-Analysis und Distributionen, Hamburg: edition swk, 2013.
• [11] A. Borys, “Under-sampling as a specific operation of filtering and signal shaping at the same time,” submitted to Electronics Letters, 4th January, 2020.

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2020).

PL

W artykule błędnie podano s. 355-368, faktycznie artykuł dot. s. 355-360.