lecture12

# lecture12 - EE313 Linear Systems and Signals Fall 2010...

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Unformatted text preview: EE313 Linear Systems and Signals Fall 2010 Initial conversion of content to PowerPoint by Dr. Wade C. Schwartzkopf Prof. Brian L. Evans Dept. of Electrical and Computer Engineering The University of Texas at Austin Fourier Analysis 12 - 2 Periodic Signals • For all t , x ( t + T ) = x ( t ) x ( t ) is a periodic signal Smallest value of T is the fundamental period Fundamental frequency 1/ T • Periodic signals have a Fourier series representation Fourier series coefficient C m quantifies the strength of the component of x ( t ) at frequency m / T • Fourier transforms (defined next) are for both ( 29 ( 29 ∫ ∑- - ∞-∞ = = = 2 2 2 2 1 T T t T m j m m t T m j m dt e t x T C e C t x π π 12 - 3 Fourier Integral ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 Processing Signal Systems ion Communicat 2 1 2 2 ∫ ∫ ∫ ∫ ∞ ∞- ∞ ∞- ∞ ∞-- ∞ ∞-- = = = = ϖ ϖ π ϖ ϖ π ϖ π d e X t x df e f G t g dt e t x X dt e t g f G t j...
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lecture12 - EE313 Linear Systems and Signals Fall 2010...

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