Question

9. The following four facts are given about a particular signal $x[n]$ with \\ DTFT $X(e^{j\omega})$. \\ a. $x[n] = 0$ for $n > 0$. \\ b. $\frac{1}{2\pi} \int_{-\pi}^{\pi} X(e^{j\omega}) d\omega = \delta[n]$ \\ c. $Im(X(e^{j\omega})) = X_I(e^{j\omega}) = \sin(\omega) - a\sin(2\omega)$, $a > 0$ \\ d. $\int_{-\pi}^{\pi} |X(e^{j\omega})|^2 d\omega = 6\pi$ \\ Determine $x[n]$.

          9. The following four facts are given about a particular signal $x[n]$ with \\
DTFT $X(e^{j\omega})$. \\
a. $x[n] = 0$ for $n > 0$. \\
b. $\frac{1}{2\pi} \int_{-\pi}^{\pi} X(e^{j\omega}) d\omega = \delta[n]$ \\
c. $Im(X(e^{j\omega})) = X_I(e^{j\omega}) = \sin(\omega) - a\sin(2\omega)$, $a > 0$ \\
d. $\int_{-\pi}^{\pi} |X(e^{j\omega})|^2 d\omega = 6\pi$ \\
Determine $x[n]$.

9. The following four facts are given about a particular signal x[n] with

DTFT X(e^jω).

a. x[n] = 0 for n > 0.

b. (1)/(2π)∫-π^π X(e^jω) dω = δ[n]

c. Im(X(e^jω)) = XI(e^jω) = sin(ω) - asin(2ω), a > 0

d. ∫-π^π |X(e^jω)|^2 dω = 6π

Determine x[n].

Added by Alexander A.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Adi S

07/22/2022

Step 1

Step 1: Using the given fact a, x[n] = 0 for n < 0, we can infer that the signal x[n] is a right-sided signal. Show more…

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9. The following four facts are given about a particular signal with DTFT X(e^jω): a. x[n] = 0 for n < 0 b. 2πf = X(e^jω) c. Im{X(e^jω)} = -X(e^-jω) sin(ω) = -a sin(2ω) d. f = 1, X(e^j6)