ECE 598: The Speech Chain

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ECE 598 The Speech Chain

• Lecture 10 Auditory Physiology

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Today

• Outer Ear Sound Localization
• Middle Ear Impedance Matching
• Basilar Membrane Frequency Analysis
• Mechanical Principles
• Frequency Response of Auditory Filters
• Nonlinearity of Basilar Membrane Response
• Mechano-Electric Transduction
• Inner and Outer Hair Cells
• Neuro-transmitter Uptake Models
• Neural Activation Thresholds

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Auditory Anatomy Overview
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Localization of Sound Inter-Aural Time Delay
(ITD)
Wavefronts (lines of constant pressure)
rcosq
q
r(p/2-q)
r
Diffusion of sound around the head
Wave traveling direction
ITD (r/c)(p/2-qcosq)
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Localization of Sound Inter-Aural Amplitude
Difference

• f lt c/4r 1kHz head ltlt lc/f sound diffuses
  around head
• f gt c/2r 2kHz head gt l, so sound is blocked by
  the head

High frequency, Short wavelength (shown wave
troughs, i.e., pressure minima)
Low frequency, Long wavelength (shown wave
troughs, i.e., pressure minima)
Sound diffuses around the head no shadow
Head shadow Sound unable to diffuse around large
obstacle
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Localization of Sound Echoes from the Pinna and
Shoulders
Direct Sound
Pinna Echo
Shoulder Echo
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Localization of Sound, Summary Head-Related
Transfer Function

• Source
• s(t) cos(wt)
• Received at near ear
• xR(t) AR(w) cos(wtfR(w))
• Received at far ear
• xL(t) AL(w) cos(wtfL(w)-wtITD)
• Near ear frequency response
• HR(w) AR(w)ejfR(w)
• Far ear frequency response
• HL(w) AL(w)ej(fL(w)-wtITD)

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Middle Ear Functions

• Impedance Matching
• Sound transmission in water (inner ear) requires
  much higher pressure than sound transmission in
  air (outer ear).
• Without middle ear, sound incident on oval window
  would bounce away (g1)
• Middle ear reduces g so that not all sound is
  reflected
• Reduce Exposure to Loud Environments
• Strap muscles loosen in loud environments,
  reducing the amplitude of sound transmitted to
  inner ear
• Effect is relatively slow (hundreds of
  milliseconds), so not useful for adaptation to
  rapid sounds (gunshots)

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Impedance Mis-Match Between Water and Air
Without a Middle Ear, What Would You Hear?
Scala Vestibuli, contents perilymph sodium
water
Auditory Canal, contents air
Oval Window
pw
pa
A
pw-
pa-

• Continuity of pressure at the boundary
• (papa-) (pwpw-)
• Continuity of volume velocity at the boundary
• (A/raca) (pa-pa-) (A/rwcw) (pw-pw-)
• Densities ra 0.001 g/cc, rw 1
  g/cc
• Speeds of Sound ca 354m/s, cw1000m/s
• Suppose pw-0, meaning that the only input sound
  is pa
• Then
• The reflected sound is pa- (rwcw-raca)/(rwcwra
  ca) pa 0.9994 pa
• The transmitted sound is pw
  2raca/(rwcwraca) pa 0.0006 pa

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Hammer-Anvil-Stirrup Lever-Based Impedance
Matching System
Eardrum Velocity (1/raca)(pa-pa-) Pressure
(papa-)
Oval Window Velocity (1/Lraca)(pa-pa-) Pressur
e L (papa-)
L units length
1 unit length

• Lever system reduces the effective input
  impedance (zp/v) of water by a factor of L2
• Resulting reflection coefficient
• g (rwcw-L2raca)/(rwcwL2raca) 0.98-0.99 lt 1

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Acoustic Impedance of Ear Canal Informative About
Middle Ear Function
Outer Ear, contents air
pa
Eardrum
pa-
x
0
-L

• Remember how to calculate impedance?
• Impose a Boundary Condition at Far End
• pa-gpa
• Calculate zp/v at Near End
• z p/v rc (pae-jkxpa-ejkx)/(pae-jkx-pa-ejkx)
  
• rc (e2jkL g)/(e-2jkL - g)
• So by measuring the acoustic input impedance of
  the auditory canal very precisely, its possible
  to deduce g at different frequencies, and thus to
  learn something about health of the middle ear
  (product Mimosa Acoustics)

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Inner Ear Anatomy(image courtesy Alec Salt,
Otolaryngology, Washington University)
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Inner Ear Anatomy Charged Fluids(image courtesy
of Alec Salt, Otolaryngology, Washington
University)
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Cross-Section of the Basilar Membrane(image
courtesy wikipedia)
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Frequency Selectivity of Places on the Basilar
Membrane
Basilar Membrane (separates scala media scala
tympani)
Unroll
Oval Window
Apex, x3cm Low Stiffness High Mass fc
(k/m)1/2/2p 40Hz
Base, x0mm High Stiffness Low Mass fc
(k/m)1/2/2p 16000Hz
In between Each position, x, is tuned to a
different mechanical resonance x(fc) 30mm
(11mm) ln(1 46fc/(fc14700))
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Frequency Selectivity of Places on the Basilar
Membrane
Scala Vestibuli
Oval Window
Wave pwe-jwx/c propagates forward at c1000m/s
until
Round Window
Scala Tympani
Wave energy is absorbed by oscillation of the
basilar membrane at x(fcw/2p)
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Frequency Selectivity of Places on the Basilar
Membrane

• Traveling waves in the cochlea.
• Concerning the pleasures of observing, and the
  mechanics of the inner ear,
• Nobel Lecture, 1961,
• Georg von Békésy
• (courtesy of Pacific Biosciences Research Center
  Hawaii)

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Bandwidth of the Auditory Filters 100Hz at
fclt500Hz, 0.2fc at fcgt500Hz(image courtesy
Julius Smith and Jonathan Abel, CCRMA, Stanford)

• Equivalent Rectangular Bandwidth (ERB)
• Bandwidth of an ideal BPF that passes the same
  total energy as the basilar membrane section at
  the same fc

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Velocity of Basilar Membrane Causes Inner Hair
Cell Follicles to Bend
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Velocity of Basilar Membrane Causes Inner Hair
Cell Follicles to Bend
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Bending of Follicles Causes Depolarization of IHC

• Scala Media (80mV)

Cations enter through follicle tips when
follicles bend
Organ of Corti (0mV)
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Depolarization of IHC Causes Release of
Neurotransmitter
Cations enter through follicle tips when
follicles bend
Neurotransmitter released
Synapse, afferent neuron
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Neurotransmitter Dynamics(Three-Store Model
Meddis, JASA 1986)
Neurotransmitter Re-uptake (several ms)
Neurotransmitter release (instant)
Neurotransmitter binding (several ms)
Result probability of neuron firing is a
smoothed (lowpass filtered) version of the IHC
voltage
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Signal Processing in the Inner Ear (Simulated)
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Neural Response to a Synthetic Vowel(Cariani,
2000)