ABSTRACT
The Fourier series for z(t) is given by Equation 2:
z z a f t
b f t av
( )t cos( )
i )
= +
2π (2)
where
a bn n n ni ( )) s= n (3)
Many time varying processes, z(t), in nature (such as wind turbulence, and gravity waves in deep water), exhibit “well behaved” spectral density variations but no defined characteristics in phase angle φ(f), which appears to be completely random from one frequency ordinate (Fourier wave component) to the next, so that:
φ πn RAND( ) (4)
Equations 4 and 3 can be used to set up a set of Fourier coefficient pairs (an, bn) in a series format required by the appropriate software available to the user to then be able to generate a simulated time series from an IFFT on this Fourier set. The process is then completed by adding the mean value of z, zav, to the resultant series.
