Erwin is right: the Fourier TRANSFORM does not assume periodicity,
because it calculates the fourier 'coefficients' for every frequency
on the real axis (i.e. a transform of a function f(t) is another
function F(omega): for instance the fourier transform of a
sin(omega_zero*t) is a delta function with peak at 'omega_zero'; in a
complementary way a transform of an impulse has constant power density
for all frequencies). Now Fourier SERIES do assume a period (i.e. a
fundamental frequency).

Having said that, even Fourier transform 'likes' the periodic functions,
in the sense that the transforms of them have nicer properties than
transforms of arbitrary f(t).