Noise

Section: Random Signal

Gaussian White noise

Let $\boldsymbol{X} = (X[0],X[1],\ldots,X[N-1])$ be a random signal

  • All the random variables $X[n]$ are i.i.d. from a centered gaussian distribution with variance $\sigma^2$
  • Autocorrelation function : $R_X[t] = \sigma^2\delta[t]$
  • Spectrum : $S[\nu] = \sigma^2$

Gaussian colored noise

  • A colored noise is a filtered white noise

Spectrum estimation

Mains non parametric methods:

  • Periodogram: power spectrum of the observed random signal
  • Modified Periodogram: power spectrum of the observed random signal weighted by a window
  • Welch’s method: average of several smaller modified Periodogram