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Learning path

Full curriculum

Full curriculum
  1. Continuous-time step and Dirac impulse signals
  2. Power spectral density of stationary random processes
  3. White noise
  4. Energy per bit and $E_b/N_0$
  5. Additive white Gaussian noise channels
  6. Shannon-Hartley capacity of an AWGN channel
  7. Matched filters and correlation receivers
  8. BPSK detection and bit error probability in AWGN

Unit content

White noise

White noise is an idealized stationary random process with constant power spectral density over frequency.

For two-sided PSD level $N_0/2$,

$$S_N(f)=\frac{N_0}{2}.$$

Its autocorrelation is concentrated at zero lag:

$$R_N(\tau)=\frac{N_0}{2}\delta(\tau).$$

The flat PSD means equal noise power is available per unit bandwidth throughout the idealized spectrum.

Ideal white noise has unlimited total power if its PSD is integrated over infinite bandwidth. Physical noise can therefore only be approximately white over a finite frequency range relevant to the system.

Whiteness is a statement about second-order statistics. It does not by itself specify the full probability distribution of the noise amplitudes; Gaussian white noise adds that separate assumption.