Signals and Fourier Theory. Dr Costas Constantinou School of Electronic, Electrical & Computer Engineering University of Birmingham W: www.eee.bham.ac.uk/ConstantinouCC/ E: [email protected] Recommended textbook.
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Gibbs phenomenon: the Fourier series of a piecewise continuously differentiable periodic function exhibits an overshoot at a jump discontinuity that does not die out, but approaches a finite value in the limit of an infinite number of series terms (here approx. 9%)
(duration)∙(bandwidth) = constant
it can be shown that,
with the equality sign satisfied for a Gaussian pulse