Two relations for generalized discrete Fourier transform coefficients

• Autorzy: Spałek D.

Identyfikatory

DOI

10.24425/123433

• Języki publikacji: EN

Abstrakty

EN

A new generalized discrete Fourier transform DFT that allows for sample shift δ 2 [0, T/N] in time-domain is defined. Two relations are proved for the sum of errors between generalized DFT coefficients and theirs theoretical values. The first is the equation for samples received for continuous and piecewise–smooth functions. The second relation is the inequality for samples generated by discontinuous functions. Moreover, the influence of samples shift on generalized DFT coefficients values, which leads to aliasing phenomenon, is presented.

Słowa kluczowe

EN

generalized discrete Fourier transform; coefficient errors; aliasing

PL

dyskretna transformata Fouriera; aliasing

• Wydawca: Polska Akademia Nauk, Wydział IV Nauk Technicznych
• Czasopismo: Bulletin of the Polish Academy of Sciences. Technical Sciences
• Rocznik: 2018
• Tom: Vol. 66, nr 3
• Strony: 275--281
• Opis fizyczny: Bibliogr. 11 poz., tab., wykr.

Twórcy

autor

Spałek D.

• Institute of Electrotechnics and Informatics, Silesian University of Technology, 10 Akademicka St., 44-100 Gliwice, Poland

Bibliografia

• [1] K. Kuratowski, Differential and Integral Calculus, PWN, Warsaw, 1978 (in Polish).
• [2] J. Klamka, M. Pawełczyk, and J. Wyrwał, Numerical Methods, Silesian University of Technology, Gliwice, 2001 (in Polish).
• [3] U. Meyer-Baese, Digital Signal Processing with Field Programmable Gate Arrays, Springer, 2007.
• [4] E. Majchrzak and B. Mochnacki, Numerical Methods. Theoretical Background, Practical Aspects and Algorithms, Silesian University of Technology, Gliwice, 2004 (in Polish).
• [5] D. Spałek, “Two feature of discrete Fourier transform for discontinuous functions”, 38th International Conference of Electrotechnics and Circuit Theory IC-SPETO, Gliwice Ustroń, 21‒22, (2015).
• [6] J. Hoła, J. Bień, Ł. Sadowski, and K. Schabowicz, “Non-destructive and semi-destructive diagnostics of concrete structures in assessment of their durability”, Bull. Pol. Ac.: Tech. 63 (1), 87‒96 (2015).
• [7] M. Zdanowski and R. Barlik, “Analytical and experimental determination of the parasitic parameters in high-frequency inductor”, Bull. Pol. Ac.: Tech. 65 (1), 107‒112 (2017).
• [8] D. Spałek, “Two features of discrete Fourier transform for discontinuous functions”, 39th International Conference of Electrotechnics and Circuit Theory, IC-SPETO Gliwice-Ustroń, 25‒26, (2016).
• [9] D. Spałek, “Proof of two features of generalized discrete Fourier transform”, 39th International Conference of Electrotechnics and Circuit Theory IC-SPETO, Gliwice-Ustroń, 27‒28, (2016).
• [10] D. Spałek, “Uogólniona dyskretna transformacja Fouriera – aliasing”, 39th International Conference of Electrotechnics and Circuit Theory IC-SPETO, Gliwice-Ustroń, 29‒30, (2016) [in Polish].
• [11] D. Spałek, “Dyskretna transformacja Fouriera dla N ¡ 3p próbek”, 39th International Conference of Electrotechnics and Circuit Theory IC-SPETO, Gliwice-Ustroń, 31‒32, (2016) [in Polish].

Uwagi

PL

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2018).