An exact solution to the well-known integral transform that relates the spectral density of the instantaneous fractional frequency deviation, Sy(f), to the Allan variance, sigma2y(tau), is presented for the case of a power-law representation of Sy(f). The approximate solution to this integral transform, which is found throughout the literature, also is derived. A graphical convergence analysis is presented, showing the range of applicability of the approximate solution. The results reinforce the use of the approximate solution, which converges quickly to the exact solution under virtually all reasonable measurement conditions.