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Unformatted text preview: Speech Processing Analysis and Synthesis of Pole Zero Speech Models 2/13/12 Veton Kpuska 2 Introduction u Deterministic: n Speech Sounds with periodic or impulse sources u Stochastic: n Speech Sounds with noise sources u Goal is to derive vocal tract model of each class of sound source. u It will be shown that solution equations for the two classes are similar in structure. u Solution approach is referred to as linear prediction analysis . n Linear prediction analysis leads to a method of speech synthesis based on the allpole model. u Note that allpole model is intimately associated with the concatenated lossless tube model of previous chapter (i.e., Chapter 4). 2/13/12 Veton Kpuska 3 AllPole Modeling of Deterministic Signals u Consider a vocal tract transfer function during voiced source: T=pitch U g[n] A Glottal Model G( z ) Vocal Track Model V( z ) Radiation Model R( z ) s [n] Speech ( 29 ( 29 ( 29 ( 29 ( 29 = = = P k k k z a A z H z R z V z AG z H 1 1 2/13/12 Veton Kpuska 4 AllPole Modeling of Deterministic Signals u What about the fact that R(z) is a zero model? u A single zero function can be expressed as a infinite set of poles. Note: u From the above expression one can derive: ( 29 z a az az z a az k k k k k < < = = = = 1 , 1 1 1 1 1 ( 29 a z zb z a az k k k k k = = = = 1 1 1 1 poles of number infinite 1 zero simple 1 2/13/12 Veton Kpuska 5 AllPole Modeling of Deterministic Signals u In practice infinite number of poles are approximated with a finite site of poles since akfi 0 as kfi . u H(z) can be considered allpole representation: n representing a zero with large number of poles inefficient n Estimating zeros directly a more efficient approach (covered later in this chapter). 2/13/12 Veton Kpuska 6 Model Estimation u Goal  Estimate : n filter coefficients {a1, a2, ,ap}; for a particular order p, and n A, Over a short time span of speech signal (typically 20 ms) for which the signal is considered quasistationary. u Use linear prediction method: n Each speech sample is approximated as a linear combination of past speech samples n Set of analysis techniques for estimating parameters of the allpole model. 2/13/12 Veton Kpuska 7 Model Estimation u Consider ztransform of the vocal tract model: u Which can be transformed into: u In time domain it can be written as: u Referred to us as a autoregressive (AR) model....
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 Fall '10
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