Problems with Line Spectrum
The Ck2 is a “line spectrum” at a specific frequency and wavenumber
(k). We are not interested in these line spectra. Here are the reasons:
q Integer values of k have no specific meaning. They are determined
based on the length of the observation period T (=NDt):
      k = (0, 1, 2, 3,..N/2) cycles during the period T.
q Since we use N observations to determine a mean and N/2 line spectra,
each line spectrum has only about 2 degrees of freedom. With such
small dof, the line spectrum is not likely to be reproduced from one
sampling interval to the other.
q Also, most geophysical “signals” that we are interested in and wish to
study are not truly “periodic”. A lot of them are just “quasi-periodic”,
for example ENSO. So we are more interested in the spectrum over a
“band” of frequencies, not at a specific frequency.