1. A method for transforming a noisy audio signal to an enhanced audio signal, comprising steps: acquiring the noisy audio signal from an environment; inputting the noisy audio signal to a deep neural network having network parameters to produce a magnitude mask and a phase estimate, wherein the deep neural network is a deep recurrent neural network (DRNN), a bidirectional long short-term memory (BLSTM) deep recurrent neural network (DRNN) or a long short-term memory (LSTM) network, wherein the deep neural network uses a phase-sensitive objective function based on an error in a complex spectrum that includes an error in amplitude and a phase of the noisy audio signal; using the magnitude mask and the phase estimate to obtain the enhanced audio signal, wherein the steps are performed in a processor.