HarmonicSeries.m

Space-Time series (1D, 2D, or 3D) as the sum of cosines.

Syntax:

Z = harmonicseries(AMP, PER, PHA, LEN, DIR, T, X, Y);
Performs the sum of harmonics:

z(t,y,x) = sum [ a*cos(k*x + l*y - w*t + theta) ]

where:

a = AMP (amplitude)

k = K*cos(rdir) (x-component of wavenumber vector)

l = K*sin(rdir) (y-component of wavenumber vector)

K = sqrt(k^2+l^2) = (2*pi)./LEN (magnitude of wavenumber vector)

rdir = DIR*(pi/180) (direction of wavenumber vector in radians)

w = (2*pi)./PER (Temporal angular frequency)

theta = PHA*(pi/180) (Initial phase in radians)

This is useful when performing tests of Fourier Spectral Analysis, for example.

The program comes with the example on the screenshot.