On the role of the partial trigonometric moment problem in AR speech modelling
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چکیده
ON THE ROLE OF THE PARTIAL TRIGONOMETRIC MOMENT PROBLEM IN AR SPEECH MODELLING P. Delsarte, V. Genin, Y. Kamp, P. Van Dooren Philips Research Laboratory Brussels Ày. Van Becelaere 2, Box 8, B1170 Brussels, Belgium PARTIAL TRIGONOMETRIC MOMENT PROBLEM ICASSP 83, BOSTON CH1841-6l83/0000-0789 $1.00 © 1983 IEEE 789 The partial trigonometric moment problem is shown to provide a unifying framework for several speech modelling techniques, such as the classical LPC autoregressive model, the line spectral pairs and composite sinusoidal waves models, and the Toeplitz eigenvector model for formant extraction. From a mathematical viewpoint, this moment problem can be identified to an extension problem in the class of impedance functions or equivalently in the class of nonnegative definite Toeplitz matrices.
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