Plate 
at the peak and rapid drop off of the sinusoid's energy in the neigh- 
bourhood of the peak, while a wide resolution bandwidth has the ten- 
dency of spreading the wave over a broader part of the spectrum, It 
follows that very sharply peaked spectra can be compared only if the 
resolution bandwidth for all spectra is defined asm. %m, where yy 
is the frequency of the peak and m is a constant for all spectra. For 
such an analysis, proportional bandwidth filters are very suitable, 
which is one reason why a former student of mine, Mr. P. Su (1970) 
has developed in his MS Thesis a new filtering technique for the ana- 
lysis of water surface data. It is one of the purposes of this paper to 
plead to future authors that they should present their wave spectra 
with all the information on resolution bandwidth,spacing of the data, 
and methods used for their spectral analysis. 
A second important consequency of the dominant wave not 
being purely sinusoidal is that there exists only one phase velocity 
for all harmonics of the dominant frequency. Instead of a phase velo- 
city of the component waves given to c# = g/k, where k is the wave 
number of the particular component wave, all components travel at 
the speed of the component at the spectral peak. As in the case of the 
Stokes wave in finite amplitude wave theory, this speed is larger than 
that calculated from c2 = g/ky . To prove that this is indeed so, 
Su (1970) has determined the phase speed of component waves filtered 
out of a wave record. He determined the wave records at two wave 
gages which were placed closely behind one another in a wind wave 
tank. For both records simultaneously,one particular wave compo- 
nent was filtered out and the cross correlation of the two filtered re- 
cords was determined. The distance between the wave gages divided 
by the time lag between the maximum correlation and zero yielded 
the phase velocity. Figure 7 shows a representative record. The fil- 
tering produces very high correlations even at long time lags (accor- 
ding to the uncertainty theorem of Fourier analysis) due to the narrow- 
ness of the filter, and the wave nature causes oscillation of the cross 
correlation function. These features are not important for the present 
purpose, Important is that the envelope to the cross correlation func- 
tion shows a maximum at the same time lag for all harmonics of wm 
and Su has shown that this time lag implies a phase speed of all com- 
ponents equal to that observed directly for the dominant wave. 
Waves on the sea surface and on laboratory channels may 
show important differences. This may be inferred from the average 
wave of Konda et.al. (1971) reproduced in figure 8. This wave also 
is nonsinusoidal, but in contrast to laboratory waves it appears to be 
much less skewed. Unfortunately, Konda et.al. do not give a wave 
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