Processing multi-channel audio waveforms

Methods, including computer programs encoded on a computer storage medium, for enhancing the processing of audio waveforms for speech recognition using various neural network processing techniques. In one aspect, a method includes: receiving multiple channels of audio data corresponding to an utterance; convolving each of multiple filters, in a time domain, with each of the multiple channels of audio waveform data to generate convolution outputs, wherein the multiple filters have parameters that have been learned during a training process that jointly trains the multiple filters and trains a deep neural network as an acoustic model; combining, for each of the multiple filters, the convolution outputs for the filter for the multiple channels of audio waveform data; inputting the combined convolution outputs to the deep neural network trained jointly with the multiple filters; and providing a transcription for the utterance that is determined.