hw6 - HOMEWORK 6 ECE 220 Due May 3 2005 1 Use Fourier...

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HOMEWORK 6 ECE 220 Due May 3, 2005 1. Use Fourier transform pairs to find x ( t ) in each of the following cases. (a) X ( ) = 2 0 . 3+ e - 0 . 4 . (b) X ( ) = 3 - 2 cos ω . (c) X ( ) = 1 2+ - 1 5+ (d) X ( ) = ( ω - 17 π ) - ( ω + 17 π ). CD: “Inverse Fourier Transforms” 2. Find the Fourier transform H ( ) of h ( t ) = d dt sin(6 π ( t - 2)) π ( t - 2) Also, plot | H ( ) | versus ω . CD:“Forward Fourier Transforms” 3. Find the inverse Fourier transform of X ( ) = 4 (2 + ) 2 - 2 1 - (Hint: It might help to rewrite the first term as a product.) 4. Let x ( t ) be a triangular pulse defined by x ( t ) = 2 - 2 | t | | t | < 2 0 elsewhere (a) By taking the derivative of
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