Voice conversion is an important problem in audio signal processing. The goal of voice conversion is to transform the speech signal of a source speaker such that it sounds as if it had been uttered by a target speaker. Our contribution in this paper includes a new methodology for designing the relationship between two sets of spectral envelopes. Our systems perform by: (1) cascading deep neural networks and Gaussian mixture model to construct DNN–GMM and GMM–DNN–GMM models in order to find a global mapping relationship between the cepstral vectors of the two speakers; (2) using a new spectral synthesis process with cascaded cepstrum predictors and excitation and phase extracted from the target training space encoded as a KD-tree. Experimental results of the proposed methods exhibit a great improvement of the intelligibility, the quality and naturalness of the converted speech signals when compared with stimuli obtained by baseline conversion methods. The extraction of excitation and phase from the target training space, permits the preservation of target speaker’s identity.