Non-linear speech representation based on local predictability exponents

Abstract

Looking for new perspectives to analyze non-linear dynamics of speech, this paper presents a novel approach based on a microcanonical multiscale formulation which allows the geometric and statistical description of multiscale properties of the complex dynamics. Speech is a complex system whose dynamics can be, to some extent, geometrically and statistically accessed by the computation of Local Predictability Exponents (LPEs) unlocking the determination of the most informative subset (Most Singular Manifold or MSM), leading to associated compact representation and reconstruction. But the complex intertwining of different dynamics in speech (added to purely turbulent descriptions) suggests the definition of appropriate multiscale functionals that might influence the evaluation of LPEs, hence leading to more compact MSM. Consequently, by using the classical and generic Sauer/Allebach algorithm for signal reconstruction from irregularly spaced samples, we show that speech reconstruction of good quality can be achieved using MSM of low cardinality. Moreover, in order to further show the potential of the new methodology, we develop a simple and efficient waveform coder which achieves almost the same level of perceptual quality as a standard coder, while having a lower bit-rate.

Detection of Glottal Closure Instants Based on the Microcanonical Multiscale Formalism

“…However, For the case of speech signals, the direct 1-D adaptation of the same procedure reduces the resulting Γ r (•) to simple directional finite differences. In [38], we followed a similar path and searched for a Γ r (•) that results in a relatively more compact MSM from which the whole speech signal can be reconstructed; we used a classical method for reconstruction of a given signal from a subset of its irregularly spaced samples (MSM in our case) and compared various definition of Γ r (•) to find the one that results in a more compact MSM from which the signal can be reconstructed with good perceptual quality (evaluated using the PESQ measure of signal quality). As such, the multi-scale integral of the following scaledependent functional was defined:…”

“…We discussed in [38] that such definition reduces the effect of inter-sample correlations of the speech signal in estimation of SEs and we showed that it effectively results in a compact representation of the speech signal. On the other hand, the GCI detection application that we are considering in this paper allows us to provide an intuitive justification for this multiscale measure.…”