ESS210B
Prof. Jin-Yi Yu
Problems with Line Spectrum
qInteger 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.
qSince 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.
qAlso, 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.
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: