A random force F(t) has average value given by
〈F(t)〉 = 0 (33.85)
and its autocorrelation function is given by
〈F(t)F(t^{\prime })〉 = Aδ(t−t^{\prime }), (33.86)
where δ(t−t^{\prime }) is a Dirac delta function.{}^{9} Find the power spectrum.
{}^{9}See Appendix C.10.
By the Wiener–Khinchin theorem, the power spectrum is simply the Fourier transform of the autocorrelation function, and hence
〈|F(ω)|²〉 = A (33.87)
is a flat power spectrum.