# Lecture16 - EE313 Linear Systems and Signals Fall 2010 Initial conversion of content to PowerPoint by Dr Wade C Schwartzkopf Prof Brian L Evans

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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 Sampling Theorem 16 - 2 [ ] ( 29 s T n s n s = Sampling: Time Domain • Many signals originate as continuous-time signals, e.g. conventional music or voice • By sampling a continuous-time signal at isolated, equally-spaced points in time, we obtain a sequence of numbers n ∈ {…, -2, -1, 0, 1, 2,…} T s is the sampling period. Sampled analog waveform ( 29 ( 29 ∑ ∞-∞ =- = n s sampled T n t t s t s ) ( δ impulse train s ( t ) t T s T s ( 29 t s sampled 16 - 3 Sampling: Frequency Domain • Replicates spectrum of continuous-time signal At offsets that are integer multiples of sampling frequency • Fourier series of impulse train where ϖ s = 2 π f s • Example ( 29 ) (2 cos 2 ) ( cos 2 1 ) ( . . . + + + =- = ∑ ∞-∞ = t T t T T T n t t s s s s s n s T s ϖ ϖ...
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## This note was uploaded on 02/16/2011 for the course ECE 313 taught by Professor Evans during the Spring '11 term at University of Texas at Austin.

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Lecture16 - EE313 Linear Systems and Signals Fall 2010 Initial conversion of content to PowerPoint by Dr Wade C Schwartzkopf Prof Brian L Evans

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