A#10 - Assignment #10 ECSE-2410 Signals & Systems -...

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Assignment #10 ECSE-2410 Signals & Systems - Spring 2009 Due Tue 02/24/09 Use the properties and transform Tables (no integrations of the definition) to solve the following: 1(14). Find the Fourier transform of and plot ω . ) ( vs X for 123 4 0 -1 x ( t ) t 1 5 < . 2(14). Find the Fourier transform of () ) ( sinc 2 ) 3 cos( t t t x = and sketch ( ) . vs X . 3(28). Perform the following steps: (a) Find the Fourier transform, H , of = t t h 2 3 sinc 3 . (b) Find the Fourier transform, X , of ( ) ( ) ( ) t t t x 3 cos cos + = . (c) Find the Fourier transform of () ( ) ( ) t x t h t y = , namely, ( ) ( )( ) X H Y = . (d) Finally take the inverse Fourier transform, ( ) ( ) { } Y F t y 1 = 4(28). Perform the following steps: (a) Use partial fraction expansion to find the inverse Fourier transform of ) 3 )( 1 ( 4 ) ( ωω j j X + + = . (b) To find the inverse Fourier transform, ( ) t w , of ) 3 )( 1 ( 1 ) ( 2 j j e
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