Spectrum

Section: Random Signal

Spectrum of random signal

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

  • Fourier transform of a digital random signal is not meaningfull
  • The spectrum of a random signal is the Fourier transform of its autocorrelation function

$$ S[\nu] = \hat R_X[\nu] $$

  • Difficult to estimate

Spectrum estimation

  • Periodogram
  • Welch method