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3.6 Fourier transform of periodic signals

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

x ( t ) = ∑ n = - ∞ ∞ c n e j Ω 0 n t

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 )

where F corresponds to the Fourier Transform of the signal within the brackets.
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Source:  OpenStax, Signals, systems, and society. OpenStax CNX. Oct 07, 2012 Download for free at http://cnx.org/content/col10965/1.15
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