A new application of the simulated annealing Monte Carlo procedure is presented and applied to the extraction of the relaxation time distribution from dielectric spectroscopy either in time or frequency domain. This decomposition method named simulated annealing direct signal analysis (SADSA), is applied to computer generated curves, epsilon(t), epsilon'(omega), and epsilon'(omega), by using the most widely accepted empirical distributions. The discretized distribution fits exactly the analytical expression which can be evaluated in these cases for the set of parameters used in the simulation. Also, both distribution functions are found to be identical which proves that the method is certainly converging to the right solution in both cases. Experimental results on amorphous poly(aryl ether ether ketone) for epsilon(t), epsilon'(omega), and epsilon'(omega) are analyzed with SADSA and the obtained relaxation time distribution is used to go from time to frequency domain and reciprocally. The results are compared to those obtained by assuming a Havriliak-Negami profile for the distribution function.