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Unformatted text preview: x ( t ) = sin4 t t sin(50 t ) X ( j ) = (d) x ( t ) = X ( j ) = ( sin(200 ) ) 2 (e) x ( t ) = X ( j ) = cos 2 ( ) 1 4. (20 Points) Determine the inverse Fourier transform of X ( j ) = 5 (3 + j ) 2 Although there is no table entry for this case, the convolution property can be applied if X ( j ) is written as a product. 5. (20 Points) Prove that the Fourier transform of the unit-step signal, u ( t ), is U ( j ) = 1 j + K ( ) where K = . At rst glance, it might seem that the impulse term K ( ) should be zero, but show that K 6 = 0 because the following signal s ( t ) is an odd symmetric signal. s ( t ) = ( u ( t )-1 2 if t 6 = 0; if t = 0; Note: Even though s ( t ) and u ( t )-1 2 dier at one isolated point, t = 0; they still have the same Fourier transform. 2...
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This note was uploaded on 10/25/2011 for the course ELCT 321 taught by Professor Shin during the Spring '08 term at South Carolina.
- Spring '08