(11) |

The crosscorrelation process produces the autocorrelation of equation ():

(12) |

Firstly, also contains the additional terms and . We can discard the first of these terms, since it is anti-causal, and the second term contains so will be much smaller than the signal of interest.

The second difference between equations () and () is the wavelet. The Kolmogorov wavelet is minimum phase, whereas the crosscorrelation wavelet is zero-phase. The amplitude spectrum of the crosscorrelation wavelet will also be the square of the Kolmogorov wavelet.

Thus the principal advantage of the Kolmogorov result is that it
has a broader bandwidth than the crosscorrelation. Whereas the
Kolmogorov result has the same amplitude spectrum as the original
data, the amplitude spectrum of the crosscorrelation impulse response
is equal to the *power* spectrum of the original data.

5/27/2001