Removing noise and interference from a signal by calculating a joint time-frequency domain of the signal, estimating instantaneous frequencies of the joint time-frequency domain, modifying each estimated instantaneous frequency, if necessary, to correspond to a frequency of the joint time-frequency domain to which it most closely compares, redistributing elements within the joint time-frequency domain according to the modified instantaneous frequencies, computing a magnitude for each element in the redistributed joint time-frequency domain, plotting the results, identifying peak values, eliminating from the redistributed joint time-frequency domain elements that do not correspond to the peak values, identifying noise and interference in the peak values, eliminating the noise and the interference from the redistributed joint time-frequency domain elements, and recovering a signal devoid of noise and interference from the modified redistributed joint time-frequency domain.