Formant estimation of speech signals using subspace-based spectral analysis

The objective of this paper is to propose a signal processing scheme that employs subspace-based spectral analysis for the purpose of formant estimation of speech signals. Specifically, the scheme is based on decimative spectral estimation that uses Eigenanalysis and SVD (Singular Value Decomposition). The underlying model assumes a decomposition of the processed signal into complex damped sinusoids. In the case of formant tracking, the algorithm is applied on a small amount of the autocorrelation coefficients of a speech frame. The proposed scheme is evaluated on both artificial and real speech utterances from the TIMIT database. For the first case, comparative results to standard methods are provided which indicate that the proposed methodology successfully estimates formant trajectories.

Sensitivity analysis of a time-delayed thermo-acoustic system via an adjoint-based approach

We apply adjoint-based sensitivity analysis to a time-delayed thermo-acoustic system: a Rijke tube containing a hot wire. We calculate how the growth rate and frequency of small oscillations about a base state are affected either by a generic passive control element in the system (the structural sensitivity analysis) or by a generic change to its base state (the base-state sensitivity analysis). We illustrate the structural sensitivity by calculating the effect of a second hot wire with a small heat-release parameter. In a single calculation, this shows how the second hot wire changes the growth rate and frequency of the small oscillations, as a function of its position in the tube. We then examine the components of the structural sensitivity in order to determine the passive control mechanism that has the strongest influence on the growth rate. We find that a force applied to the acoustic momentum equation in the opposite direction to the instantaneous velocity is the most stabilizing feedback mechanism. We also find that its effect is maximized when it is placed at the downstream end of the tube. This feedback mechanism could be supplied, for example, by an adiabatic mesh. We illustrate the base-state sensitivity by calculating the effects of small variations in the damping factor, the heat-release time-delay coefficient, the heat-release parameter, and the hot-wire location. The successful application of sensitivity analysis to thermo-acoustics opens up new possibilities for the passive control of thermo-acoustic oscillations by providing gradient information that can be combined with constrained optimization algorithms in order to reduce linear growth rates. © Cambridge University Press 2013.