Ch5-Analysis_&_Synthesis_of_Pole-Zero_Models

Ch5-Analysis_&_Synthesis_of_Pole-Zero_Models -...

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Unformatted text preview: Speech Processing Analysis and Synthesis of Pole-Zero Models 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. 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 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 1 1 ( 29 a z z-b z a az k k k k k = =-∏ ∑ ∞ =-∞ =--1 1 1 1 poles of number infinite 1 zero simple 1 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). 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. 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....
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This note was uploaded on 02/10/2012 for the course ECE 3552 taught by Professor Staff during the Fall '10 term at FIT.

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Ch5-Analysis_&amp;_Synthesis_of_Pole-Zero_Models -...

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