I've solved this problem. In case anyone ever finds my post via search and needs the answer, I'll go ahead and detail my solution.

y(t) = sum from k = -inf to inf of c_y[k]exp(j2 pi k t /T0)

c_y[k] = H(k/T0)c_x[k]

c_x[k] = X(k/T0)

where c_y[k] is the harmonic function of y(t), c_x[k] is the harmonic function of x(t), X(k/T0) is the CTFT of x(t) evaluated at K/T0, and H(k/T0) is the frequency response evaluated at k/T0.