Show explicitly by use of the Poisson sum formula or other means that, if the motion of a radiating particle repeats itself with periodicity T, the continuous frequency spectrum becomes a discrete spectrum containing frequencies that are integral multiples of the fundamental. Show that a general expression for the time-averaged power radiated per unit solid angle in each multiple m of the fundamental frequency ω0=2π/T is:
dΩdPm=(2πc)3e2ω04m2∫02π/ω0v(t)×nexp[imω0(t−cn⋅x(t))]dt2