# What is the difference between the PSD of a deterministic and stochastic signal?

I am learning about stochastic processes and I don't get one thing:

• What is the advantage of calculating the PSD of a signal using the Wiener-Khinchin theorem $\Phi(\omega) =\mathcal{F}\{R_{xx}\}$ and calculating its PSD with $\Phi(\omega) =X(\omega) X^*(\omega)$.

I mean, if I record some random signal and I want to get its spectrum then I do $\mathcal{F}\{x(t)\}$.

• What's wrong about using this way?
• Why should I deal with autocorrelation and Wiener-Khinchin-Theorem?

I've created in MATLAB a cosine with random amplitude, so in my understanding this is a stochastic signal

t = 0:0.1:1000
x = rand() * cos(t)
plot(abs(fft(xcorr(x,x))))
plot(abs(fft(x)).^2)


Both plots seem to be very equal, I can't see the difference.