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I was given a WSS ergodic process $x(t)$ with power spectrum :

$$ \begin{array}{rcl} G_x(f) &=&1−\left|\frac{f}{B}\right| &\mbox{for } |f|<B\\ G_x(f) &=& 0 & \mbox{ elsewhere} \end{array} $$ and first order probability density function is uniform in the range $[−A, A]$. How do I evaluate $A$?

It's not a home work but it was a question asked in my exam which I failed. Any help will be appreciated.

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You can compute the power of the process from its power spectrum as well as from its PDF. Equating the two gives you a relation between the constants $A$ and $B$. More specifically you get

$$\int_{-B}^BG_x(f)df=\frac{1}{2A}\int_{-A}^Ax^2dx$$

If I'm not mistaken this should give $A=\sqrt{3B}$.

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