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Unformatted text preview: University of Minnesota Dept. of Electrical and Computer Engineering EE3015 – Signals and Systems Discussion Session #10: Applications of Fourier representations 1. Consider the system depicted below. The input signal x ( t ) has a Fourier Transform (FT) X ( j ω ) also shown below. Signal ) ( t x is multiplied by ) ( t p , which is a periodic signal with period T , fundamental frequency W T 2 / 2 > = π ω , and 4 / 1 / = T T . a. Find and sketch P ( j ω ), the FT of p ( t ) In class, we showed that the FS coefficients of p ( t ) are given by π ω k T k a t p k FS ) sin( ) ( = ⎯→ ← The FT of p ( t ) is then given by ∑ ∑ ∞ −∞ = ∞ −∞ = − = − ⎯ ⎯→ ← k k k FT k k T k k a t p ) ( ) sin( 2 ) ( 2 ) ( ω ω δ ω ω ω δ π Which results in x ( t ) p ( t ) h ( t ) v ( t ) y ( t ) ω 1 X ( j ω ) -W W t 1 p ( t ) … … -2T 2 3 T −-T 2 T −-T T 2 T T 2 3 T 2T b. Sketch V ( j ω ), the FT of v ( t ) Using the multiplication property: ) ) ( ( ) sin( ) (...
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This note was uploaded on 12/20/2009 for the course EE 3015 taught by Professor Staff during the Fall '08 term at Minnesota.
- Fall '08