  This paper presents a new approach in understanding how deep neural networks
(DNNs) work by applying homomorphic signal processing techniques. Focusing on
the task of multi-pitch estimation (MPE), this paper demonstrates the
equivalence relation between a generalized cepstrum and a DNN in terms of their
structures and functionality. Such an equivalence relation, together with pitch
perception theories and the recently established
rectified-correlations-on-a-sphere (RECOS) filter analysis, provide an
alternative way in explaining the role of the nonlinear activation function and
the multi-layer structure, both of which exist in a cepstrum and a DNN. To
validate the efficacy of this new approach, a new feature designed in the same
fashion is proposed for pitch salience function. The new feature outperforms
the one-layer spectrum in the MPE task and, as predicted, it addresses the
issue of the missing fundamental effect and also achieves better robustness to
noise.
