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Textbook by: Carlos E. Davila. E-mail the author

# Fourier Transform of Periodic Signals

Module by: Carlos E. Davila. E-mail the author

If the signal of interest is periodic with period TT, then it has a Fourier Series:

x ( t ) = n = - c n e j Ω 0 n t x ( t ) = n = - c n e j Ω 0 n t
(1)

Using the linearity of the Fourier Transform, we have

X ( j Ω ) = n = - c n F e j Ω 0 n t = 2 π n = - c n δ ( Ω - n Ω 0 ) X ( j Ω ) = n = - c n F e j Ω 0 n t = 2 π n = - c n δ ( Ω - n Ω 0 )
(2)

where FF corresponds to the Fourier Transform of the signal within the brackets.

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