Ch5-Analysis_&_Synthesis_of_Pole-Zero_Models

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Speech Processing Analysis and Synthesis of Pole-Zero  Models
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February 11, 2012 Veton Këpuska 2 Introduction Deterministic: Speech, Music, … Sounds with periodic or impulse sources Stochastic: Speech, Music, … Sounds with noise sources Goal is to derive vocal tract model of each class of sound source.  It will be shown that solution equations for the two classes are  similar in structure. Solution approach is referred to as  linear predication  analysis . Linear prediction analysis leads to a method of speech synthesis  based on the all-pole model.
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February 11, 2012 Veton Këpuska 3 All-Pole Modeling of Deterministic  Signals 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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February 11, 2012 Veton Këpuska 4 All-Pole Modeling of Deterministic  Signals What about the fact that R(z) is a zero model? A single zero function can be expressed as a infinite set of poles.  Note: 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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February 11, 2012 Veton Këpuska 5 All-Pole Modeling of Deterministic  Signals In practice infinite number of poles are  approximated with a finite site of poles  since a k 0 as k . H(z) can be considered all-pole  representation: representing a zero with large number of poles  inefficient Estimating zeros directly a more efficient  approach (covered later in this chapter).  
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February 11, 2012 Veton Këpuska 6 Model Estimation Goal - Estimate :  filter coefficients {a 1 , a 2 , …,a p }; for a particular order p,  and A, Over a short time span of speech signal (typically 20 ms)  for which the signal is considered quasi-stationary. Use  linear prediction  method: Each speech sample is approximated as a  linear  combination  of past speech samples  Set of analysis techniques for estimating parameters of the all-pole model.
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February 11, 2012 Veton Këpuska 7 Model Estimation Consider z-transform of the vocal tract model: Which can be transformed into: In time domain it can be written as: 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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February 11, 2012 Veton Këpuska 8 Model Estimation
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