EM 1110-2-1100 (Part II)
30 Apr 02
Figure II-1-33. A schematic for a two-dimensional wave spectrum E(f,θ)
wave profile time trace can be written as an infinite sum of sinusoids of amplitude An, frequency ωn , and
relative phase εn, that is
η(t) ' j An cos (ωnt & εn)
4
n'0
(II-1-142)
' j an cos nωt % bnsin nωt
4
n'0
(c) The coefficients an and bn in the above equation may be determined explicitly from the orthogonality
properties of circular functions. Note that a0 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