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<math>b_k = a_{-k}</math> | <math>b_k = a_{-k}</math> | ||
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| + | <math>x(t)\Longleftrightarrow a_k</math> | ||
Revision as of 18:38, 8 July 2009
Continous - Time Fourier Series: Time Reversal
The period T of a periodic signal x(t) remains unchanged when it goes through time reversal
$ x(-t) = \sum_{k=-\infty}^\infty a_k e^{-jk2\pi t/T} $
Substitute k = -m
y(t) = $ x(-t) = \sum_{m=-\infty}^\infty a_{-m} e^{-jm2\pi t/T} $
Right-hand side of the equation has the form of a Fourier series synthesis equation for x(-t)
$ b_k = a_{-k} $
$ x(t)\Longleftrightarrow a_k $
