Short note: White noise and its PSDF

White noise is an idealised random noise whose power spectral density is constant at all frequencies, just as white light contains all colours equally. Its two-sided PSD is

$$S_n(f) = \frac{N_0}{2} \quad \text{for all } f$$

Its autocorrelation is the inverse Fourier transform, an impulse:

$$R_n(\tau) = \frac{N_0}{2}\,\delta(\tau)$$

so any two different samples are uncorrelated (and independent if Gaussian).

 Sn(f)                      Rn(tau)
   | N0/2                      ^ (N0/2) delta
 --+---------------- f   ------+------ tau

• Total power $\int S_n df$ is infinite, so it is only a model; real noise (thermal, shot) is flat up to very high frequencies ($\sim 10^{12}$ Hz), so it acts white in any practical bandwidth.
• For thermal noise $N_0 = kT$. Noise through a filter of bandwidth $B$ has power $N_0B$.
• Usually also assumed Gaussian: AWGN.