Unformatted text preview: R 12 ( τ )] = G 1 ( w ) G * 2 ( w ) 6. We know that e t  FT ↔ 2 1 + ω 2 Now use an appropriate property of FT to ﬁnd the FT of te t  . 7. Let y ( t ) = ( x ( t ) cos 2 ( t )) ⊗ sin ( t ) πt Assume that X( ω ) = 0 for  ω ≥ 1. Show that ∃ a linear time invariant system h ( t ), such that y ( t ) = x ( t ) ⊗ h ( t ). Find h ( t ). (Here ⊗ stands for convolution operator). 8. Let x(t) FT ↔ X( ω ). Show that Z t∞ x ( τ ) dτ FT ↔ X ( ω ) jω + X (0) δ ( ω ) ....
View
Full Document
 Spring '07
 Prof.H.Narayanan
 LTI system theory, Home Work Set, signal systems, Let R12

Click to edit the document details