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Ch5-Analysis_&_Synthesis_of_Pole-Zero_Speech_Models

Ch5-Analysis_&_Synthesis_of_Pole-Zero_Speech_Models...

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Speech Processing Analysis and Synthesis of Pole- Zero Speech Models
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2/13/12 Veton K ë puska 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 all-pole model. u Note that all-pole model is intimately associated with the  concatenated lossless tube model of previous chapter (i.e.,  Chapter 4).  
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2/13/12 Veton K ë puska 3 All-Pole 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
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2/13/12 Veton K ë puska 4 All-Pole 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 0 1 0 1 ( 29 a z z -b z a az k k k k k = = - = - = - - 1 1 1 1 poles of number infinite 0 1 0 zero simple 1
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2/13/12 Veton K ë puska 5 All-Pole 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 all-pole  representation: n representing a zero with large number of poles  inefficient n Estimating zeros directly a more efficient  approach (covered later in this chapter).  
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2/13/12 Veton K ë puska 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 quasi-stationary. 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 all-pole model.
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2/13/12 Veton K ë puska 7 Model Estimation u Consider z-transform 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. ( 29 ( 29 ( 29 = - - = = p k k k g z a A z U z S z H 1 1 ( 29 ( 29 ( 29 ( 29 z AU z z S a z S z a z S g p k k k p k k k = - = - = - = - 1 1 1 [ ] [ ] [ ] = + - = p k g k n Au k n s a n s 1 Current Sample Past Samples Scaling Factor – Linear Prediction Coefficients Input
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2/13/12 Veton K ë puska 8 Model Estimation u
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