Question

7.49 Given $x[n] = \{1, 4, 3, 2, 5, 7, -45, 7, 5, 2, 3, 4, 1\}$, compute the following: (a) $X(e^{j\pi})$ (b) $|X(e^{j\Omega})|$ (c) $\int_{-\pi}^{\pi} X(e^{j\Omega}) \,d\Omega$ (d) $\int_{-\pi}^{\pi} |X(e^{j\Omega})|^2 \,d\Omega$

          7.49 Given $x[n] = \{1, 4, 3, 2, 5, 7, -45, 7, 5, 2, 3, 4, 1\}$, compute the following:
(a) $X(e^{j\pi})$
(b) $|X(e^{j\Omega})|$
(c) $\int_{-\pi}^{\pi} X(e^{j\Omega}) \,d\Omega$
(d) $\int_{-\pi}^{\pi} |X(e^{j\Omega})|^2 \,d\Omega$

$7.49 Given x[n] = {1, 4, 3, 2, 5, 7, -45, 7, 5, 2, 3, 4, 1}, compute the following: (a) X(e^jπ) (b) |X(e^jΩ)| (c) ∫-π^π X(e^jΩ) dΩ (d) ∫-π^π |X(e^jΩ)|^2 dΩ$

Added by Charles S.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Ivan Kochetkov

Step 1

In this case, N = 13. So, for each value of k, we substitute e^jr and compute X(k): X(0) = Σ x(n) * e^(-j2π(0)n/13) = Σ x(n) * e^0 = Σ x(n) X(1) = Σ x(n) * e^(-j2π(1)n/13) X(2) = Σ x(n) * e^(-j2π(2)n/13) ... X(12) = Σ x(n) * e^(-j2π(12)n/13) Substituting Show more…

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