Chapter 10. METHODS FOR THE DETERMINATION 
OF POWER SPECTRA 
Introduction 
In Chapter 7, the sea surface as a function of time alone, 
at a fixed point was first studied. In Chapter 9, some properties 
of a short crested sea surface were derived. It is still necessary 
to show that a short crested sea surface observed at a fixed point 
is a Gaussian case of the Lebesgue Power Integral as a function 
of time. When this is accomplished it will also be possible to 
show that the functions, E(H), Ej(#,®), [aC 1° and [a5 (pm 6) 1° 
are interrelated. 
The techniques of Tukey [1949] and Tukey and Hamming [1949} 
will then be applied in order to obtain the relationships between 
the non-normalized auto-correlation function and the power spect- 
rum, and procedures for the estimation of the various power spectra 
will then be described. 
Other properties of a short crested sea surface will then be 
obtained. Finally methods for computing [ay (p 6) ]° will be pre- 
sented. 
Where and when the methods apply 
The methods to be presented in this chapter strictly speaking 
apply only when the sea surface is in a steady state. That is 
[a(n 1° or cay oh when determined by these methods should have 
the same value about any point of the sea surface at any time. It 
has already been pointed out that under these conditions wave fore- 
casts and methods of wave analysis would not be needed because the 
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