Dialogue systems Luděk Bártek Physical Acoustics Physiological Acoustics H Dialogue systems H Luděk Bártek Laboratory of Searching and Dialogue, Faculty of Informatics Masaryk University, Brno jaro 2023 Sound Dialogue systems Luděk Bártek Sound ■ oscillation of an environment molecules (air) ■ caused by transmission medium resistance. Oscillation of a mass point ■ move of a point from equilibrium position into a place with maximum deflection (an amplitude) and from there to the opposite point with maximum deflection, etc. Oscillations Dialogue systems Luděk Bártek Physical Acoustics Physiological Acoustics perioda Oscillations Physical Quantities Dialogue systems Luděk Bártek Amplitude - maximum deviation of the osculation. Period (T) ■ the time of a repetition of a periodic event. ■ Unit -Is (second). Frequency (f) ■ the number of periodic event repetition per time unit (usually per second). ■ applies f = y ■ the unit is 1 Hz (Hertz). Oscillations Physical Quantities Dialogue systems Luděk Bártek The force acting on the oscillating point: ■ F = — ks, k - spring stiffness, s - current spring deflection ■ F = ms =>* ms = —ks, m — body mass, a - acceleration ■ a + u2s = 0 [u2 = ^, u - angular velocity of oscillatory motion: uj = ^) phase of oscillatory motion: ij) = cut current deflection: y = ymsinujt = ymsimj) current speed: v = ujymsinujt = ymsintj) current acceleration: a = —ujymsinujt = ymsinij) Harmonic vs. Damped vs. Forced Oscillations Dialogue systems Luděk Bártek Harmonic oscillations ■ no external force acts on the body ■ we hardly ever meet him in practice (air resistance, ...). Damped oscillation ■ the resistance of the environment acts against the movement ■ the amplitude decreases with time (the distance from the source). Forced oscillation, resonance ■ there is an additional periodic force acting on a solid point G = sinat ■ F = ma = —ky + sinat a + oj y — sinat ■ particular solution: %nat2 Sound - mechanic osculation of a flexible environment (air, water, metal, ...) Acoustics - a science studding sound (from a Greek akustikos - related to hearing): ■ physical - sound as a physical oscillations ■ physiological acoustics - a creation and a perception of sound by human ■ musical - sound from the musical point of view ■ molecular - relation of acoustic properties and molecular structure. Classification of sounds: ■ infra sound - frequency < 16 Hz ■ audible sound - 16 Hz - 16kHz ■ ultrasound - > 16 kHz ■ hyper sound - up to 108 Hz - utilized by molecular acoustics for example. Simple vs. Composed Tone Dialogue systems Luděk Bártek ■ Basic (simple) tone - intensity course can be estimated using a simple sinusoidal function. Physical Acoustics Physiological Acoustics ( \ ; ■ Composed tone - linear combination of basic tones. 0.8 0.6 0.4 0.2 0 ■0.2 ■0.4 ■0.6 ■o.s 0.5*sin(x)+0.5*5in[2*x) - í 1 2 3 4 5 6 □ S Acoustic Spectrum of a Sound Dialogue systems Luděk Bártek Acoustic spectrum - set of a basic tones forming a particular sound. Obtaining spectrum - Fourier transformation: ■ F(x) must fulfil the Dirichlet's conditions ■ a periodic function with period T ■ partially continuous in the given interval (only finite count of a points of discontinuity of a 1st kind) ■ finite count of extremes on the interval ■ defined in endpoints of the interval: Acoustic Spectrum Calculation Dialogue systems Luděk Bártek Physical Acoustics Physiological Acoustics Exploits decomposition using the Fourier series: F(x) = ^ + a;cos(iu)x) + bisin(iujx oo ;=1 2tt T best F(x) approximation using coefficients a a b\ 3k = T cos(kx)dx 2 T J F(x)sin(kx)dx Spectral coefficients values Sk = 4 + bl □ S I -E ► < Sound Acoustic Spectrum cont. Dialogue systems Luděk Bártek Physical Acoustics Physiological ■ Problem - sound is periodic on a small intervals. Acoustics ■ analysis on a short interval where is assumed that the sound is periodic. ■ Physiological acoustics point of view - spectrum corresponds to resonation of the fibres of the Coorti organ or to the reaction of the corresponding neurons. Sound Pressure Dialogue systems Luděk Bártek Sound pressure ■ Corresponds to the force acting on an area element in the acoustic oscillation environment. ■ For a sine wave: p = p0sin(ujt) ■ po - maximum sound pressure during a period m uo - angular speed ■ t - time. Acoustic Intensity and Acoustic Pressure Dialogue systems Luděk Bártek Acoustic intensity ■ It expresses the amount of acoustic energy passing through a unit area per unit of a time. ■ Proportional to the square of acoustic pressure. ■ Sound intensity range - from minimal (/o) to maximum (/i) acoustic intensity where we can hear a tone with frequency 1 kHz. ■ Sensitivity threshold - po = 2 • 10~2Nm~2. ■ Threshold of pain - pi = 102Nm~2. ■ Range-2,5-1013A/A77-2. Sound Perception Dialogue systems Luděk Bártek Web-Fechner's psychophysical law: ■ The loudness subjectively perceived by a human increases with geometric increase of intensity approximately linearly ■ We calculate the level of a sound intensity using the formula: L = 10 • \ogl- '0 ■ unit - 1 bel (original bell) [B] ■ The derived unit decibel [dB] is commonly used. (10-1B). The Acoustic Intensity Approximate Values Dialogue systems Luděk Bártek Physical Acoustics Physiological Acoustics whisper - 10 - 20 dB muffled talk - 35 - 45 dB symphonic orchestra - 70 - 90 dB rock music - 110 - 130 dB. □ i5P Fundamentals of a Physiological Acoustics Dialogue systems Luděk Bártek Physical Acoustics Physiological Acoustics Physiological acoustics areas: ■ speech production ■ speech perception. Uses Helmholtz's resonance theory. Helmholtz resonator Dialogue systems Luděk Bártek Physical Acoustics Physiological Acoustics Operation principle: ■ By introducing air into the resonator, overpressure is created in it. ■ It pushes out excess air and creates negative pressure that causes intake of surrounding air. ■ This forms periodic plot: f = Speech Production Mechanism Dialogue systems Luděk Bártek ■ Speech is created by vocal system (placed in larynx). Physical Acoustics ■ Vocal cords forms narrow slit and are agitated by passing Physiological air. Acoustics ■ Frequency of their vibrations forms the basic vocal tone - Fo ■ The sound formed in larynx using the vocal cords (vowels, voiced consonants) is modified in resonance cavities: ■ laryngeal ■ oral ■ nasopharyngeal. ■ The resonance cavities principle is similar to the Helmholtz resonator. Vocal Cords and the Human Voice Organ Diagram Dialogue systems Luděk Bártek Physical Acoustics Physiological Acoustics ■ Vocal Cords JMÜM glotso-epiglottic fold '.refold cart Huge Corniculate cartilage Trachea ■ Vocal Cords location □ e Speech Perception Mechanism Dialogue systems Luděk Bártek Sound is perceived with the auditory organ. Auditory organ: ■ outer ear - captures, concentrates and brings sound waves to the middle ear ■ middle ear ■ transmits the sound energy using a mechanical way between outer and inner ear ■ contains mechanism to making up the difference between outer environment and auditory organ ■ inner ear - converts the sound energy into the excitations that are transmitted into a brain. Auditory Organ Diagram Dialogue systems Luděk Bártek Physical Acoustics Physiological Acoustics Obrázek: Auditory organ diagram □ s Outer Ear Dialogue systems Luděk Bártek Consist of: ■ Auricle - concentrates sound waves into the ear canal. ■ Ear canal - conducts the sound energy (waves) to the tympanic membrane. ■ Tympanic membrane: ■ thin membrane at the end of ear canal - thickness approx 0.1 mm. ■ It amplifies and transfers sound energy to the ossicles of middle ear. ■ Contains: ■ Ossicless of the middle ear: ■ malleus - adjoins the timpanic membrane ■ incus ■ stapes - adjoins the oval window of the inner ear, through which is energy transmitted to the inner ear. ■ Oval window - membrane through which is the movement of middle ear ossicles transferred to the inner ear. ■ Eustachian tube: ■ Tube between middle ear and nasopharynx. ■ Serves to balance the pressure between outer environment and the middle ear, to protect the the auditory organ. Inner Ear Dialogue systems Luděk Bártek Cochlea: ■ Is filled with aqueous solution. ■ An organ in the shape of a snail shell containing Coorti organ. ■ Coorti organ contains approx. 20000 fibres with length between 40 /im - 0,5 mm. ■ Fibres are connected to the nerve endings that conduct impulses to the hearing centre of the brain. Balance organ.