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This paper presents a new approach in understanding how deep neural networks(DNNs) work by applying homomorphic signal processing techniques. Focusing onthe task of multi-pitch estimation (MPE), this paper demonstrates theequivalence relation between a generalized cepstrum and a DNN in terms of theirstructures and functionality. Such an equivalence relation, together with pitchperception theories and the recently establishedrectified-correlations-on-a-sphere (RECOS) filter analysis, provide analternative way in explaining the role of the nonlinear activation function andthe multi-layer structure, both of which exist in a cepstrum and a DNN. Tovalidate the efficacy of this new approach, a new feature designed in the samefashion is proposed for pitch salience function. The new feature outperformsthe one-layer spectrum in the MPE task and, as predicted, it addresses theissue of the missing fundamental effect and also achieves better robustness tonoise.

Between Homomorphic Signal Processing and Deep Neural Networks: Constructing Deep Algorithms for Polyphonic Music Transcription