Harmonic/noise models

Laroche et al., 1993a] Laroche, J., Moulines, E., and Stylianou, Y. (1993a). HNS Speech modification based on a harmonic + noise model. Proc. IEEE ICASSP-93, Minneapolis, pages 550-553. 

We will now explore the Harmonic/Noise model (HNM) of Stylianou [421] in detail, as this model was developed specifically for TTS. As the name suggests the model is composed of a harmonic component (as above) and a noise component. This noise component is more sophisticated that some models in that it explicitly models the fact that noise in real speech can have very specific temporal patterns. In stops for example, the noise component is rapidly evolving over time, such that a model which enforces uniformity across the frame will lack important detail. The noise part is therefor given by... 

Harmonic Noise models are similar to sinusoidal models, except that they have an additional noise component which allows accurate modelling of noisy high frequency portions of voiced speech and all parts of unvoiced speech. 

The notion of sines plus noise modeling was posed and implemented by Xavier Serra and Julius Smith in the Spectral Modeling Synthesis (SMS) system. They called the sinusoidal components the deterministic component of the signal, and the leftover noise part the residual or stochastic component. Figure 6.12 shows the decomposition of a sung ahh sound into deterministic (harmonic sinusoidal) and stochastic (noise residue) components. 

Stylianou, Y. Concatenative speech synthesis using a harmonic plus noise model. In Proceedings of the third ESC A Speech Synthesis Workshop (1998). 

Hereafter we put /ig = 1. Below we express our results in terms of the statistical properties (correlators) of the environment s noise, X(t). Depending on the physical situation at hand, one can choose to model the environment via a bath of harmonic oscillators [6, 3]. In this case the generalized coordinate of the reservoir is defined as X = ]T)Awhere xi are the coordinate operators of the oscillators and Aj are the respective couplings. Eq. 2 is then referred to as the spin-boson Hamiltonian [8]. Another example of a reservoir could be a spin bath [11] 5. However, in our analysis below we do not specify the type of the environment. We will only assume that the reservoir gives rise to markovian evolution on the time scales of interest. More specifically, the evolution is markovian at time scales longer than a certain characteristic time rc, determined by the environment 6. We assume that rc is shorter than the dissipative time scales introduced by the environment, such as the dephasing or relaxation times and the inverse Lamb shift (the scale of the shortest of which we denote as Tdiss, tc [Pg.14]

In this procedure it is assumed that musical signals are made up as additive combinations of tones (sinusoids) which represent the fundamental and harmonics of all the musical notes which are playing. Since this is certainly not the case for most non-musical signals, we might expect the method to fail for, say, speech extracts or acoustical noises. Fortunately, it is for musical extracts that pitch variation defects are most critical. The pitch variation process is modelled as a smoothly varying waveform with no sharp discontinuities, which is reasonable for most wow generation mechanisms. 

FIGURE 12.4 Distance dependence of the heat current in non-Markovian systems for harmonic (full), and anharmonic (dotted) models, (a) Gaussian white noise (h) O-U noise with Xc = 8 X 10" ps (c) O-U noise with = 0.01 ps (d) O-U noise with X =0.04ps. Tr = 300 K,... 

The calculated overall sound power levels include a factor of 2 to allow for analytical modeling uncertainties. The sound power is distributed as broadband noise over a large frequency range and as pure tone at the circulator blade passing frequency (BPF) and harmonics. The main circulator and SCS circulator BPF are 4237 Hz and 5833 Hz, respectively, based on rotational speeds at 100 percent operation. 

This technique successfully reverses the MFCC coding operation. The main weakness is that because we threw away the harmonic information in the filter bank step, we have to resort to a classical LP style technique of using an impulse to drive the LP filter. A number of improvements have been made to this, with the motivation of generating a more natural source, while still keeping a model systems where the parameters are largely statistically independent. For example in the technique of Yoshimura et al [510] a munber of excitation parameters are used that allow mixing of noise and impulse, and allow a degree of aperiodicity in the positions of the impulses. 

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