Question

The PSD of an ergodic random process $x(t)$ is $\mathcal{P}_x(f) = \begin{cases} \frac{1}{B}(B-|f|), & |f| \le B \\ 0, & f \text{ elsewhere} \end{cases}$ where $B > 0$. Find (a) The RMS value of $x(t)$. (b) $R_x(\tau)$.

          The PSD of an ergodic random process $x(t)$ is
$\mathcal{P}_x(f) = \begin{cases} \frac{1}{B}(B-|f|), & |f| \le B \\ 0, & f \text{ elsewhere} \end{cases}$
where $B > 0$. Find
(a) The RMS value of $x(t)$.
(b) $R_x(\tau)$.

The PSD of an ergodic random process x(t) is
𝒫x(f) = (1)/(B)(B-|f|), |f| ≤ B
0, f elsewhere
where B > 0. Find
(a) The RMS value of x(t).
(b) Rx(τ).

Added by Ashley A.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Narayan Hari

Step 1

In this case, the random process x(t) has a power spectral density (PSD) of 1 B-VVB (Band-limited white noise with a bandwidth of B), and is zero elsewhere. Show more…

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