[kzrvwmdz] random oscillating field

model a real scalar field oscillating in space and time as a sum of cosines:

f(t,x,y,z) = sum over i of a[i]*cos(b[i] + c[i]*t + d[i]*x + e[i]*y + f[i]*z)

note that constant offset DC can be represented by b[0] = c[0] = d[0] = e[0] = 0.

does this capture all typical shapes?  I think it still works even if you do a rotation or translation of axes.

can it model spherical waves f(t,r)?

can it model dipole radiation?  dipole radiation is a time-varying vector not scalar field, so model it is 3 scalar fields, one for each coordinate.  or, model just its magnitude.

3D or 4D Fourier transform might be better.  3D Fourier is sum of spherical harmonics (I think): how can they be made to vary over time?

oscillating vector fields?  tensor fields (in flat space)?  complex scalar fields?  Fourier series with complex exponentials probably gets you complex scalar fields.