Speech Recognition SPHINX Phone Set A Wideb in addition to Spectrogram A Wideb in addition to Spectrogram A Narrowb in addition to Spectrogram

Speech Recognition SPHINX Phone Set A Wideb in addition to Spectrogram A Wideb in addition to Spectrogram A Narrowb in addition to Spectrogram www.phwiki.com

Speech Recognition SPHINX Phone Set A Wideb in addition to Spectrogram A Wideb in addition to Spectrogram A Narrowb in addition to Spectrogram

Thym, Jolene, Food Editor has reference to this Academic Journal, PHwiki organized this Journal Speech Recognition Acoustic Theory of Speech Production Veton Këpuska Acoustic Theory of Speech Production Overview Sound sources Vocal tract transfer function Wave equations Sound propagation in a uni as long as m acoustic tube Representing the vocal tract with simple acoustic tubes Estimating natural frequencies from area functions Representing the vocal tract with multiple uni as long as m tubes Veton Këpuska Anatomical Structures as long as Speech Production

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Veton Këpuska Places of Articulation as long as Speech Sounds Veton Këpuska Phonemes in American English SPHINX Phone Set Veton Këpuska

Veton Këpuska Speech Wave as long as m: An Example Veton Këpuska A Wideb in addition to Spectrogram A Wideb in addition to Spectrogram Veton Këpuska

A Narrowb in addition to Spectrogram Veton Këpuska Veton Këpuska Physics of Sound Sound Generation: Vibration of particles in a medium (e.g., air, water). Speech Production: Perturbation of air particles near the lips. Speech Communication: Propagation of particle vibrations/perturbations as chain reaction through free space (e.g., a medium like air) from the source (i.e., lips of a speaker) to the destination (i.e., ear of a listener). Listener’s ear ear-drum caused vibrations trigger series of transductions initiated by this mechanical motion leading to neural firing ultimately perceived by the brain. Veton Këpuska Physics of Sound A sound wave is the propagation of a disturbance of particles through an air medium (or more generally any conducting medium) without the permanent displacement of the particles themselves. Alternating compression in addition to rarefaction phases create a traveling wave. Associated with disturbance are local changes in particle: Pressure Displacement Velocity

Veton Këpuska Physics of Sound Sound wave: Wavelength, : distance between two consecutive peak compressions (or rarefactions) in space (not in time). Wavelength, ,is also the distance the wave travels in one cycle of the vibration of air particles. Frequency, f: is the number of cycles of compression (or rarefaction) of air particle vibration per second. Wave travels a distance of f wavelengths in one second. Velocity of sound, c: is thus given by c = f. At sea level in addition to temperature of 70oF, c=344 m/s. Wavenumber, k: Radian frequency: =2f /c=2/=k Veton Këpuska Traveling Wave Veton Këpuska Physics of Sound Suppose the frequency of a sound wave is f = 50 Hz, 1000 Hz, in addition to 10000 Hz. Also assume that the velocity of sound at sea level is c = 344 m/s. The wavelength of sound wave is respectively: = 6.88 m, 0.344 m in addition to 0.0344 m. Speech sounds have wide range of wavelengths values: Audio range: fmin = 30 Hz =11.5 m fmax = 20 kHz =0.0172 m In audible range a propagation of sound wave is considered to be an adiabatic process, that is, heat generated by particle collision during pressure fluctuations, has not time to dissipate away in addition to there as long as e temperature changes occur locally in the medium.

Veton Këpuska Acoustic Theory of Speech Production The acoustic characteristics of speech are usually modeled as a sequence of source, vocal tract filter, in addition to radiation characteristics Pr (j) = S(j) T (j) R(j) For vowel production: S(j) = UG(j) T (j) = UL(j) /UG(j) R(j) = Pr (j) /UL(j) Veton Këpuska Sound Source: Vocal Fold Vibration Modeled as a volume velocity source at glottis, UG(j) Veton Këpuska Sound Source: Turbulence Noise Turbulence noise is produced at a constriction in the vocal tract Aspiration noise is produced at glottis Frication noise is produced above the glottis Modeled as series pressure source at constriction, PS(j)

Veton Këpuska Vocal Tract Wave Equations Define: u(x,t) particle velocity U(x,t) volume velocity (U = uA) p(x,t) sound pressure variation (P = PO + p) density of air c velocity of sound Assuming plane wave propagation ( as long as across dimension ), in addition to a one-dimensional wave motion, it can be shown that: Veton Këpuska The Plane Wave Equation First as long as m of Wave Equation: Second as long as m is obtained by differentiating equations above with respect to x in addition to t respectively: Veton Këpuska Solution of Wave Equations

Veton Këpuska Propagation of Sound in a Uni as long as m Tube The vocal tract transfer function of volume velocities is Veton Këpuska Analogy with Electrical Circuit Transmission Line Veton Këpuska Propagation of Sound in a Uni as long as m Tube Using the boundary conditions U (0,s)=UG(s) in addition to P(-l,s)=0 The poles of the transfer function T (j) are where cos(l/c)=0

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Veton Këpuska Propagation of Sound in a Uni as long as m Tube (con’t) For c =34,000 cm/sec, l =17 cm, the natural frequencies (also called the as long as mants) are at 500 Hz, 1500 Hz, 2500 Hz, The transfer function of a tube with no side branches, excited at one end in addition to response measured at another, only has poles The as long as mant frequencies will have finite b in addition to width when vocal tract losses are considered (e.g., radiation, walls, viscosity, heat) The length of the vocal tract, l, corresponds to 1/41, 3/42, 5/43, , where i is the wavelength of the ith natural frequency Veton Këpuska Uni as long as m Tube Model Example Consider a uni as long as m tube of length l=35 cm. If speed of sound is 350 m/s calculate its resonances in Hz. Compare its resonances with a tube of length l = 17.5 cm. f=/2 Veton Këpuska Uni as long as m Tube Model For 17.5 cm tube:

Veton Këpuska St in addition to ing Wave Patterns in a Uni as long as m Tube A uni as long as m tube closed at one end in addition to open at the other is often referred to as a quarter wavelength resonator Veton Këpuska Natural Frequencies of Simple Acoustic Tubes Veton Këpuska Approximating Vocal Tract Shapes

Veton Këpuska Digital Model of Multi-Tube Vocal Tract Updates at tube boundaries occur synchronously every 2 If excitation is b in addition to -limited, inputs can be sampled every T =2 Each tube section has a delay of z-1/2. The choice of N depends on the sampling rate T Veton Këpuska Acoustic Theory of Speech Production References Stevens, Acoustic Phonetics, MIT Press, 1998. Rabiner & Schafer, Digital Processing of Speech Signals, Prentice-Hall, 1978. Quatieri, Discrete-time Speech Signal Processing Principles in addition to Practice, Prentice-Hall, 2002

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