Circle the correct answer and explain your reasoning v

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Unformatted text preview: oints]: Let V (Ω) denote the DTFT of v [·]. Which of the following equations correctly shows how to obtain V (Ω) from X (Ω)? Note, incidentally, that X (−Ω) = X ∗ (Ω), where the latter quantity is the complex conjugate of X (Ω). (Circle the correct answer, and explain your reasoning.) • V (Ω) = X (Ω) • V (Ω) = 1/X (Ω) • V (Ω) = 1/X (−Ω) • V (Ω) = X (−Ω) • V (Ω) = −X (Ω) Define the signal r[·] as the convolution of x[·] and v [·], so r[n] = (x ∗ v )[n]. More explicitly, r[n] = ∞ 0 x[m]v [n − m] = m=−∞ ∞ 0 x[m]x[m − n] . (1) m=−∞ The signal r[·] is called the autocorrelation function of x[·], and r[n] is called the autocorrelation at lag n. 19. [4 points]: Denote the DTFT of r[·] by R(Ω). Write down an expression that shows how to obtain R(Ω) from X (Ω); the result of the previous problem is likely to be helpful. If you’ve done things correctly, you should find that R(Ω) is entirely determined by the magnitude of X (Ω). Please write your a...
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