ABSTRACT
As we have seen (in §2.4), RXX(τ) must be a real even function of τ . From the properties of the Fourier transform (Property 6, p. 113), we know that the power spectral density (PSD) must also be a real even function of f . Consider the output of a generic linear time-invariant filter whose impulse
response is h(t), and whose input is X(t). We find that the filter’s output is:
Y (t) = X ∗ h(t) = ∫ ∞ −∞
X(t− τ)h(τ)dτ.
