3015_Discussion_10_Solutions

3015_Discussion_10_Solutions - University of Minnesota Dept...

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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 0 > = π ω , and 4 / 1 / 0 = 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( ) ( 0 0 = ⎯→ The FT of p ( t ) is then given by −∞ = −∞ = = ⎯→ k k k FT k k T k k a t p ) ( ) sin( 2 ) ( 2 ) ( 0 0 0 0 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 0 T 0 2 T T 2 3 T 2T
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