True false we know from the inverse dtft that rn 1 2

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Unformatted text preview: nswer in terms of |X (Ω)|. In terms of |X (Ω)| we can write R(Ω) = Page 13 of 17 6.02 Fall 2012, Quiz 2 20. [3 points]: State whether each of the following statements is True or False, with a very short explanation in each case. – R(Ω) is real. True / False – R(Ω) is an even function of Ω. True / False – R(Ω) is nonnegative at all Ω. True / False We know from the inverse DTFT that r[n] = 1 2π from which r[0] = 1 2π π R(Ω)ej Ωn dΩ , −π π R(Ω) dΩ . −π 21. [2 points]: In the latter equation, express r[0] in terms of x[·] using Eq. (1), and express R(Ω) in terms of |X (Ω)| using the result of Problem 19. Write down the resulting equation; this equality is known as Parseval’s theorem for a discrete-time signal. Parseval’s theorem: (From what you’ve proved above, the following chain of reasoning is justified: |r[n]| = ≤ = = = π 1 R(Ω)ej Ωn dΩ 2π −π π 1 |R(Ω)ej Ωn |dΩ 2π −π π 1 |R(Ω)| dΩ 2π −π π 1 R(Ω) dΩ 2π −π r[0] . This establishes that the autocorrelation function has its maximum magnitude when the lag is 0. You’ve used similar ideas for preamble detection.) Page 14 of 17 6.02 Fall 2012, Quiz 2 V Q to the Rescue James Bond at the casino in Macau wants ur...
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This document was uploaded on 03/17/2014 for the course ELECTRICAL 6.02 at MIT.

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