Lectures 5-6_fall_2010

Lectures 5-6_fall_2010 - Digital Digital Speech Processing...

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Digital Speech Processing Digital Speech Processing— Lectures 5 Lectures 5-6 Sound Propagation in the Vocal Tract 1
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Basics can use basic physics to formulate air flow equations for vocal tract need to make simplifying assumptions about vocal tract shape and energy losses to solve air flow equations some complicating factors: time variation of the vocal tract shape (we will look mainly at fixed shapes) sses flow at vocal tract walls (we will first assume no loss then a losses in flow at vocal tract walls (we will first assume no loss, then a simple model of loss) softness of vocal tract walls (leads to sound absorption issues) radiation of sound at lips (need to model how radiation occurs) nasal coupling (complicates the tube models as it leads to multi-tube solutions) excitation of sound in the vocal tract (need to worry about vocal source coupling to vocal tract as well as source-system interactions) Bottom Line : simplify as much as possible and see 2 what we can learn about the mechanics of sound propagation in the human vocal tract
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Sound in the Vocal Tract • Issues in creating a detailed physical model me varying acoustic system time varying acoustic system – losses due to heat conduction and friction in the walls. – radiation of sound at the lips and nostrils – softness of the walls 3 – nasal coupling – excitation of sound in the vocal tract
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Schematic Vocal Tract PDEs must be solved in this region • simplified vocal tract area => non-uniform tube with time varying cross section lane wave propagation long the axis of the tube (this assumption 4 plane wave propagation along the axis of the tube (this assumption valid for frequencies below about 4000 Hz) no losses at walls
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Sound Wave Propagation using the laws of conservation of mass, momentum and energy, it can be shown that sound wave propagation in a lossless tube satisfies the equations: (/) () pu A xt p A A ρ −= ∂∂ 2 1() where up xc t t + ( , ) sound pressure in the tube at position and time ( , ) volume velocity flow at position and p pxt x t uu x t x == time the density of air in the tube t ρ= the velocity of sound ( , ) the 'area function' of the tube, the cross sectional area normal to he axis of the tube c AA x t = 5 i.e., the cross-sectional area normal to the axis of the tube, as a function of the distance along the tube and as a function of time
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olutions to Wave Equation Solutions to Wave Equation no closed form solutions exist for the ropagation equations propagation equations – need boundary conditions , namely u(0,t) (the volume velocity flow at the glottis), and p(l,t), (the ound pressure at the lips) to solve the equations sound pressure at the lips) to solve the equations numerically (by a process of iteration) – need complete specification of A(x,t), the vocal act area function; for simplification purposes we will tract area function; for simplification purposes we will assume that there is no time variability in A(x,t) => the
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Lectures 5-6_fall_2010 - Digital Digital Speech Processing...

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