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EE599-020
Audio Signals and Systems
Kevin D. Donohue
Electrical and Computer Engineering
University of Kentucky
Question!
If a tree falls in the forest and nobody
is there to hear it, will it make a sound?
Sound provided by
http://www.therecordist.com/downloads.html
Ambiguity!
• Merriam-Webster Dictionary:
• Sound a : a particular auditory impression
b : the sensation perceived by the sense of
hearing c : mechanical radiant energy that is
transmitted by longitudinal pressure waves
in a material medium (as air) and is the
objective cause of hearing.
Electronic Audio Systems
Sound Sources –
Vibrations at
20Hz-20kHz
Transmission
Media
Playback
Information
Extraction /
Measurement
Storage
Electoacoustic
Transducer
Amplification,
Signal
Conditioning
Processing for
Intended
Application
Ultimate Target for Playback
Diagram from:
http://hyperphysics.phy-astr.gsu.edu/hbase/sound/hearcon.html
http://www1.omi.tulane.edu/departments/pathology/fermin/Hearing.html
http://www.ear-hearing.com/
http://ear.berkeley.edu/
http://www.chdr.org/advancedearfunction.html
Outer Ear
 Pinna – Provides
amplification and sound
source localization cues.
 Auditory (Ear) Canal –
Provides pressure gain at
the middle ear. A 10 dB
pressure gain occurs over 2
to 5kHz from the opening
of the canal to the middle
ear.
Resonance of Auditory Canal
Recall that frequency = speed/wavelength
f 
c

Assume the speed of sound in air is 331 m/s and the
auditory canal is about 3 cm long. Resonance in a
pipe will occur at odd multiples of the quarter
wavelength. Find the 2 lowest resonant frequencies
of the auditory canal modeled as a simple pipe
(closed on one end and open on the other).
Resonance of Auditory Canal
How does the
the result
derived in the
last example
help explain
the shape of
of the equalloudness
curves of the
human
auditory
system:
Middle Ear
 Tympanic Membrane
(Eardrum) – Transfers
vibrations in air to the Ossicles.
 Ossicles – 3 bones, the malleus
(hammer), incus (anvil), and
stapes (stirrup) that work as
levers to transfer pressure to the
oval window of the inner ear
(fluid filled cochlea). Can also
tighten system to improve
dynamic range and protect from
loud sounds.
Middle Ear
 The middle ear provides an acoustic impedance match to
improve the transfer of vibrations in air to vibrations in the
cochlear fluid.
 Power or intensity (I) of a sound wave in a material is
related to its pressure (p) by:
p2
I
Zo
where Zo is the acoustic impedance of the material related
to the density () and acoustic velocity (v) of the material:
Z o  v
Middle Ear
Compute the impedance mismatch between
air and cochlear fluid (water) given that
Water: velocity = 1500m/s, density = 1.0 Mg/m3
Air:
velocity = 330m/s, density = 1.293kg/m3
Compute the pressure gain required to
compensate for the intensity loss due to the
impedance mismatch.
Middle Ear
Given the area of the tympanic membrane
at 80 mm2, oval window of the cochlea is
3mm2, and the mechanical advantage of the
lever system of the ossicles vary between
1.3 and 3.1, compute the minimum and
maximum pressure gain provided by the
middle ear.
Inner Ear
Cochlea mechanically filters
the sound into
subbands and
converts mechanical
energy into
electrical energy for
transmission to the
brain over the
auditory nerves.
Cochlea
 Oval window – layer on Cochlea
exterior for transducing
vibrations into the cochlear fluid.
 Basilar Membrane - layer
suspended between cochlea fluid
with local frequency sensitivity.
 Organ of Corti – hair cells on
the basilar membrane that
Diagram from:
depolarize nerve cells when
http://hyperphysics.phydisplaced by the basilar
astr.gsu.edu/hbase/sound/hea
membrane vibrations.
rcon.html
Critical Bands of Hearing
 Hearing exhibits dynamic sensitivities. If various sound
stimuli are close in frequency, the dominant sound can
completely or partially mask the others.
 The bandwidths over the hearing spectrum in which
masking occurs are referred to as critical bands.
 Experimentally measured bandwidths are approximated
in terms of the equivalent rectangular bandwidth ERB in
Hz as function of the center frequency (f) in kHz by:
ERB  6.23 f 2  93.39 f  28 .52
Problem
 Write a program to compute a set of center
frequencies so that the hearing spectrum (20Hz
to 20kHz) is completely and efficiently covered
by a set of critical bands. Use a second order
BPF as a model for the frequency bands.
ERBi  hi  bi
A
A
f i  hi bi
2
fi
bi
hi
f
Hearing Properties and Auditory
Nerve Responses
 Adaptation – Neural firing rate decreases
exponentially in response to a steady state sound
(designed to detect changes in sound field).
 Tuning – Sensitivity of firing nerve fibers along the
basilar membrane have band-pass-like responses to
changes in frequency.
 Synchrony – Low frequency (< 5kHz) neural firing
is in phase with tonal stimulation (phase locking).
 Non linearity – Saturation, two tone suppression,
masking by noise, and combination tones.
Hearing Properties – Non linearity
 Saturation – High spontaneous rate fibers reach a maximum
firing rate for lower level stimulation and results in a loss of
spectral definition, while low spontaneous rate fibers do not
significantly increase with increasing stimulation level.
 Two Tone Suppression – The firing rate of a stimulated nerve
by a tone can be suppressed by the presence of another tone.
 Masking by Noise – The presence of broad band stimulation
(noise) reduces the nerve firing rate in response to a tone.
 Combination Tones – Tones played simultaneous may cause
other nerve fibers to fire in addition to those stimulated by the
actual tones.
Matlab Exercise
 Use the sine/cosine function in Matlab along with vector and
matrix manipulation to write a function that generates a major
scale (do not start with tones above 440 Hz and use a sampling
rate of 8 kHz). Let the Matlab function input arguments be the
starting frequency and the time interval in seconds for each
note in the scale. Let the output be a vector of samples that can
be played with Matlab command “soundsc(v,8000)” (where v
is the vector output of your function).
 A scale covers a one octave frequency range, which implies the
end frequency is twice the beginning. There are 10 semi-tones
or half steps between octave frequencies. A major scale
consists of a series of tones increasing in frequency by a whole,
whole, half, whole, whole, whole, and half step (8 notes
altogether – don’t forget the starting note).
Matlab Exercise - Scales
Just
Pythagorean
Equal Temperament
Interval - 0 (1)
1/1 = 1
1=1
2^(0)=1
Interval - 1
16/15
256/243
2^(1/12)
Interval - 2 (2)
10/9 (or 9/8)
9/8
2^(2/12)
Interval - 3
6/5
32/27
2^(3/12)
Interval - 4 (3)
5/4
81/64
2^(4/12)
Interval - 5 (4)
4/3
4/3
2^(5/12)
Interval - 6
45/32 (or 64/45)
1024/729 (or 729/512)
2^(6/12)
Interval - 7 (5)
3/2
3/2
2^(7/12)
Interval - 8
8/5
128/81
2^(8/12)
Interval - 9 (6)
5/3
27/16
2^(9/12)
Interval - 10
7/4 (or 16/19 or 9/5)
16/9
2^(10/12)
Interval - 11 (7)
15/8
243/128
2^(11/12)
Interval - 12 (8)
2/1 = 2
2/1 = 2
2^(12/12) = 2
Matlab Exercise – Famous Notes
Middle C = 261.626 Hz (standard tuning)
Concert A (A above middle C) = 440 Hz
Middle C = 256 Hz (Scientific tuning)