I´m stuck in a deduction analysis of the variance of a gaussian white noise signal in a "integrate-and-dump detector" of a baseband data transmission receiver, where $n(t)$ is white noise with double-sided power spectral density $N_0/2$ [W/Hz]

first picture

second picture

I can understand all the steps except when they deduce third image

How do you get to this last expression? Thank you.


1 Answer 1


They say that $n(t)$ is white noise with a double-sided power spectral density (PSD) of $N_0/2$, i.e., the PSD is given by


The auto-correlation function is the inverse Fourier transform of $(1)$, which is


  • $\begingroup$ Thank you very much!! Now I understand $\endgroup$
    – Elias4l
    Nov 11, 2020 at 18:02

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