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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 ( ω ) is as speciﬁed in Fig-ure P4.28(a). Let y ( t ) = x ( t )cos( t ). Find Y ( ω ). Hint 1: You should know the following equations very well: cos( t ) = 1 2 ( e jt + e-jt ) and F{ cos( t ) } = 1 2 (2 πδ ( ω-1) + 2 πδ ( ω + 1)). Hint 2: Use the property that multiplication in time equals the convolution in frequency. Compute the 1 2 π X ( ω ) * F{ cos( t ) } , which should be the Fourier transform of x ( t )cos( t ). • Use the previous sub-question, “guess” what type/shape of X ( ω ) can generate the given G ( jω ) based on the formula 1 2 π X ( ω ) * F{ cos( t ) } . • Once the correct X ( ω ) is “guessed,” then do the inverse Fourier transform to obtain x ( t )....

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- Fall '08
- GELFAND
- π π