wave profile time trace can be written as an infinite sum of sinusoids of amplitude *A*n, frequency *ω*n , and

relative phase *ε*n, that is

η(*t*) ' j *A*n cos (ωnt & εn)

4

(II-1-142)

' j *a*n cos *n*ω*t *% *b*nsin *n*ω*t*

4

(c) The coefficients *a*n and *b*n in the above equation may be determined explicitly from the orthogonality

properties of circular functions. Note that *a*0 is the mean of the record. Because real observations are of finite

length, the finite Fourier transform is used and the number of terms in the sum *n *is a finite value.

(d) The *covariance *of *η(t) *is related to the wave energy spectrum. This is defined in terms of the

squares of component amplitudes as

Water Wave Mechanics

II-1-81

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