# The Deterministic plus Stochastic Model of the Residual Signal and its Applications

arXiv: https://arxiv.org/abs/2001.01000 · HTML: https://mlsanity.com/paper/2001.01000/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Dec 2019.

## Built on by (most cited first, 1 of 1)

- [NeuralDPS: Neural Deterministic Plus Stochastic Model with Multiband Excitation for Noise-Controllable Waveform Generation](https://mlsanity.com/paper/2203.02678/) (2022)

## Abstract (arXiv)

The modeling of speech production often relies on a source-filter approach. Although methods parameterizing the filter have nowadays reached a certain maturity, there is still a lot to be gained for several speech processing applications in finding an appropriate excitation model. This manuscript presents a Deterministic plus Stochastic Model (DSM) of the residual signal. The DSM consists of two contributions acting in two distinct spectral bands delimited by a maximum voiced frequency. Both components are extracted from an analysis performed on a speaker-dependent dataset of pitch-synchronous residual frames. The deterministic part models the low-frequency contents and arises from an orthonormal decomposition of these frames. As for the stochastic component, it is a high-frequency noise modulated both in time and frequency. Some interesting phonetic and computational properties of the DSM are also highlighted. The applicability of the DSM in two fields of speech processing is then studied. First, it is shown that incorporating the DSM vocoder in HMM-based speech synthesis enhances the delivered quality. The proposed approach turns out to significantly outperform the traditional pulse excitation and provides a quality equivalent to STRAIGHT. In a second application, the potential of glottal signatures derived from the proposed DSM is investigated for speaker identification purpose. Interestingly, these signatures are shown to lead to better recognition rates than other glottal-based methods.