1. A method for enhancing an input noisy signal, wherein the input noisy signal is a mixture of a clean speech signal and a noise signal, comprising: determining from the input noisy signal, using a model of the clean speech signal and a model of the noise signal, sequences of hidden variables including at least one sequence of hidden variables representing an excitation component of the clean speech signal, at least one sequence of hidden variables representing a filter component of the clean speech signal, and at least one sequence of hidden variables representing the noise signal, wherein the model of the clean speech signal includes a non-negative source-filter dynamical system (NSFDS) constraining the hidden variables representing the excitation component to be statistically dependent over time and constraining the hidden variables representing the filter component to be statistically dependent over time, and wherein the sequences of hidden variables include hidden variables determined as a non-negative linear combination of non-negative basis functions; and generating an output signal using a product of corresponding hidden variables representing the excitation and the filter components, wherein steps of the method are performed by a processor.