By Murat Kunt, Heinz Hugli (auth.), Renato De Mori, Ching Y. Suen (eds.)

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In this context, the prediction problem consists in finding the set coefficients a(i) from y(k) in order to represent this signal in the best possible way eq. (52). according to a criterion - Since in this equation Q(z) is a denominator polynomial, we have an all pole system for H(z). 3 COMPUTING THE PREDICTION COEFFICIENTS The prediction coefficients are obtained by minimizing the energy of the prediction error e(k). This energy is given by : by 28 x(k) y(k) H(z) O(z) oc(i) a(i) Hypothesis Reality Fig.

This is rather an uncomfortable situation in which it is not difficult to mix up time and frequency. To overcome this difficulty, the inverse Fourier transform of both sides of eq. (83) can be taken, leading to : x(k) = -1 1 In [X(n)] (84) which is now a time domain equation for linearly combined signals. filtering can be applied to this equation to recover Xl (k) or x2(k). Linear Then, to transform everything back to the original representation, a discrete Fourier transform should be computed first.

Signal has noise characteristics. The 49 The vocal tract acts as a resonator and modifies the excitation signal. For voiced sounds, the vocal tract usually shows 4 resonances which are called formants and which characterize the sound. Fig. 10 shows a typical spectrum of a voiced sound where both the periodic excitation spectrum and the formants are visible. When the nasal tract is also active then the overall transfer function also includes zeros call antiformants. 2 SPEECH MODEL All speech production models have in common the separation of excitation features, which are accounted for by two pulse train generators and resonator features, which are accounted for by a time-varying linear system.

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