Fróðskaparrit - 01.01.1975, Side 74

82
Sea Level Fluctuations in Tórshavn, Preliminary Results
cited). Hence c; can be calculated from the area under the
peak. The width Af is ambiguous, but for an harmonic disting-
uishable from the noise, the peak is so narrow and pronounced
that this makes no problem as long as it is clearly separated
from other peaks. In practise it is not very feasible determining
the integral by numerical quadrature, rather one may employ
the fact, mentioned by Burg (ref. 6) that a significant peak at
a frequency f; will have a definite shape given by the formula
p(f •)
P(f) = -------^5---5- (5)
i + (f-f^r/ (>
Integration then yields
j cT = n-P(f.)-6 (6)
which permits c; to be determined from b, P(f;) and <5. Compu-
tational methods which, from a given set of filter coefficients,
find the f/s by binary search, evaluate P(fj) and determine b
by fitting the peak to equation (5) have been developed and
programmed to the computer; details will be given elsewhere
In common with the Autocorrelation function the filter
coefficients contain no information on the phase of harmonic
constituents of the series. The cp^’s of eq(l) may however be
found using the MEM in the followihg way. Assume the f/s
and Cj ’s to be known, then construct the two new time series
h1(k),| rcos (2 • tt • f. *At' k)
1 h(k) - I c.I 1 (7)
h2(k)i i 1 vsin(2 • tt* f. • At'k)
By analyzing these two series as described above, one gets
peaks in the PDS at the same frequencies as for the original
series h and the ratios of the new amplitudes to the c/s will
yield the (pj’s-
The MEM is very demanding both in computing time and
in storage and the demand increases with length of data series
and length of filter. Therefore even on a large computer like
the one used, it may be necessary to split the data series into
separate parts for analysis. If the series is to be split into n