About Fourier series in study of periodic signals

Authors:
Mioara Boncut;Amelia Bucur
Affiliations:
University Lucian Blaga of Sibiu, Romania;University Lucian Blaga of Sibiu, Romania
Venue:
NN'08 Proceedings of the 9th WSEAS International Conference on Neural Networks
Year:
2008

Citing 3
Cited 0

The Gibbs phenomenon for piecewise-linear approximation

American Mathematical Monthly
Electronic devices and circuit theory (6th ed.)

Electronic devices and circuit theory (6th ed.)
Modern Digital and Analog Communication Systems

Modern Digital and Analog Communication Systems

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Abstract

This work is about Fourier Series in study of Periodic Signals. A periodic function can be represented by means of Fourier series, which contains all the information about the harmonic structure. The Fourier series is an infinite sum of sinusoidal and cosenoidal terms, however, when the series is truncated, a high frequency phenomenon appears superimposed to the resulting finite Fourier expansion, referred as Gibbs oscillations. In this paper, such a phenomenon is analyzed for a function which is m times differentiable. The case m = 0 is studied in a discontinuous functions.