  Convolutional deep neural networks (DNN) are state of the art in many
engineering problems but have not yet addressed the issue of how to deal with
complex spectrograms. Here, we use circular statistics to provide a convenient
probabilistic estimate of spectrogram phase in a complex convolutional DNN. In
a typical cocktail party source separation scenario, we trained a convolutional
DNN to re-synthesize the complex spectrograms of two source speech signals
given a complex spectrogram of the monaural mixture - a discriminative deep
transform (DT). We then used this complex convolutional DT to obtain
probabilistic estimates of the magnitude and phase components of the source
spectrograms. Our separation results are on a par with equivalent binary-mask
based non-complex separation approaches.
