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Unformatted text preview: [There is one more question on the back.] Question 10: We will solve p. 344, Problem 4.30 step by step. Consider a test signal x ( t ), whose Fourier transform X ( ) is as specied in Figure P4.28(a). Let y ( t ) = x ( t )cos( t ). Find Y ( ). Hint 1: You should know the following equations very well: cos( t ) = 1 2 ( e jt + ejt ) and F{ cos( t ) } = 1 2 (2 ( 1) + 2 ( + 1)). Hint 2: Use the property that multiplication in time equals the convolution in frequency. Compute the 1 2 X ( ) * F{ cos( t ) } , which should be the Fourier transform of x ( t )cos( t ). Use the previous subquestion, guess what type/shape of X ( ) can generate the given G ( j ) based on the formula 1 2 X ( ) * F{ cos( t ) } . Once the correct X ( ) is guessed, then do the inverse Fourier transform to obtain x ( t )....
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 Spring '08
 GELFAND
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