finalv3_f04

# finalv3_f04 - GEORGIA INSTITUTE OF TECHNOLOGY SCHOOL of...

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PROBLEM Fall-04-F.1: In each of the following cases, simplify the expression as much as possible. (a) ( t 2 - 5 t + 1) δ ( t - 4) = (b) u ( t + 3) * δ ( t - 4) = (c) 5 - 5 sin( πτ/ 4) δ ( τ + 3) = (d) x [ n ] = 5 cos(0 . 3 πn - π/ 4) + 5 2 cos(0 . 3 πn + π/ 2) =
PROBLEM Fall-04-F.2: Continuous-Time LTI System h ( t ) and H ( ) x ( t ) y ( t ) The periodic input to the above LTI system has the Fourier transform X ( ) drawn below: -5 ω 0 -4 ω 0 -2 ω 0 - ω 0 0 ω 0 2 ω 0 4 ω 0 5 ω 0 ω -3 ω 0 3 ω 0 X ( j ω ) (2 π / 5 π ) (2 π / π ) (2 π / 2) (2 π / π ) (2 π / 5 π ) (-2 π / 3 π ) (-2 π / 3 π ) where the dark arrows denote impulses.

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