ESE250:
Digital Audio Basics
Week 6
February 19, 2013
Human
Psychoacoustics
ESE 250 S’13 DeHon Kadric Kod Wilson-Shah
Week 6 – Psychoacoustics
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Course Map
ESE 250 S’13 DeHon Kadric Kod Wilson-Shah
Week 6 – Psychoacoustics
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•
Week 2

•

•
Received signal is sampled &
quantized
q = PCM[ r ]
Over
Sample
r(t)
q+n
Week 4

•
Where are we?

Sampled signal first
transformed into frequency
domain
Q = DFT[ q ]
Week 3


Quantized Signal is Coded
c =code[ q ]
p(t)
Produce
Week 4
Decode
Week 5
DFT
Store /
Transmit
Q+N
C
LPF
Q
Perceptual
Coding
Week 3
Week 5

•
signal oversampled & low
pass filtered
 Q = LPF[ DFT(q+n) ]
Week 6


•
Transformed signal analyzed
Using human psychoacoustic
models
[Painter & Spanias. Proc.IEEE, 88(4):451–512, 2000]
Week 6
Week 7


Acoustically Interesting signal
is “perceptually coded”
C = MP3[ Q]
ESE 250 S’13 DeHon Kadric Kod Wilson-Shah
Week 6 – Psychoacoustics
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The Physical Ear
[R. Munkong and B.-H. Juang. IEEE Sig. Proc. Mag., 25(3):98–117, 2008]
•
•
External Sound Waves
 Guided by outer ear
 into auditory canal
Excite Inner Ear
 Through mechanical
linkage
 connecting ear drum
 to cochlea
ESE 250 S’13 DeHon Kadric Kod Wilson-Shah
Week 6 – Psychoacoustics
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The Physical Ear
[R. Munkong and B.-H. Juang. IEEE Sig. Proc. Mag., 25(3):98–117, 2008]
•
•
Initiates signal
processing
 frequency domain
analysis
 Via analog
computation
 Video: Cochlea
What part of the
Cochlea vibrates
for an 800 Hz
square wave?
ESE 250 S’13 DeHon Kadric Kod Wilson-Shah
Week 6 – Psychoacoustics
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The Cognitive Ear
•
Modern Psychoacoustics
 Benefits greatly from
o
o
decades of neural recording
contemporary brain imaging technology
[R. Munkong and B.-H. Juang. IEEE Sig. Proc. Mag., 25(3):98–117, 2008]
ESE 250 S’13 DeHon Kadric Kod Wilson-Shah
Week 6 – Psychoacoustics
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Power Spectrum Model of Hearing
B.C.J. Moore. Int.Rev.Neurobiol., 70:49–86, 2005.
• Rough Picture (main content of today’s lecture):
 Critical Bands: Auditory system contains finite array
of adaptively tunable, overlapping bandpass filters
 Frequency Bins: humans process a signal’s
component (against noisy background) in the one
filter with closest center frequency
 Masking: certain signal components in a given band
are “favored” and others are filtered out
• Established through decades of psychoacoustic
experiments
ESE 250 S’13 DeHon Kadric Kod Wilson-Shah
Week 6 – Psychoacoustics
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Auditory Thresholds
•
•
In the lab, you varied the frequency, amplitude and
phase of signals
What was the effect of each, if any, on the sound you
heard?
 Frequency
s (t )  A sin( 2ft   )
 Amplitude
 Phase
ESE 250 S’13 DeHon Kadric Kod Wilson-Shah
Week 6 – Psychoacoustics
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Auditory Thresholds
•
Harvey Fletcher (1940)
 Played pure tones varying
o frequency, f [ Hz]
o Intensity,
I
o
[Dyn ¢ cm-2]
= 10-5 [N ¢ cm-2]
= 0.1 Pa
phase changes tend to be inaudible
 Large listener population
o Young
o Acute
• Recorded extreme thresholds
 faintest audible
 greatest tolerable
ESE 250 S’13 DeHon Kadric Kod Wilson-Shah
(http://www.et.byu.edu/)
Week 6 – Psychoacoustics
Auditory Thresholds
[H. Fletcher. Rev. Mod. Phys., 12(1):47–65, 1940].
• Results:
 pain-free hearing range extends at most over 20 Hz – 20 KHz
 with sensitivity » 2 ¢ 10-4 ¢ 0.1 Pa = 20  Pa
ESE 250 S’13 DeHon Kadric Kod Wilson-Shah
Week 6 – Psychoacoustics
0.1 Pa
10
The decibel unit
• Define standard pressure: p0 = 0.0002 ¢ 0.1 Pa = 20  Pa
• Threshold of human hearing
• Compute Sound Pressure Level as: LSPL = 20 log10(p/p0) dB
• LSPL for p1 = 20 Pa , for p2 = 200 Pa , for p3 = 20 mPa
0.1 Pa
Compare to
Ambient sea-level pressure:
1 Atmosphere
= 105 Pascal
• Q: why use log-log
scale?
• A1: dynamic range
• A2: “loudness” is a
power function
ESE 250 S’13 DeHon Kadric Kod Wilson-Shah
Week 6 – Psychoacoustics
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The decibel unit – Hearing intensity
(http://www.dspguide.com/ch22/1.htm)
Week 6 – Psychoacoustics
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Let’s try to reproduce these results!
• We will listen to single sine tones starting at a frequency of 10KHz, all the
•
way up to 20KHz, so each student can figure out their cut-off frequency
Suggestions to improve this experiment?
(http://www.dspguide.com/ch22/1.htm)
Week 6 – Psychoacoustics
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Animal hearing ranges
•
Dogs:
 Greater hearing range: 40Hz to 60KHz
 Ultrasonic dog whistles
•
Mice:





Large ears in comparison to their bodies
Hearing range: 1KHz to 70KHz
Can’t hear low frequency noises
Communicate with high frequency
Distress call (40KHz), alert of predator
ESE 250 S’13 DeHon Kadric Kod Wilson-Shah
Week 6 – Psychoacoustics
[Pictures from Wikipedia]
14
Why Sinusoids?
•
Why not some other harmonic series?
…. all sound
is produced
by vibrating
masses ….
 Fourier’s analysis shows
 harmonic analysis could be based on
 arbitrary smooth periodic fundamental
•
•
Why does the animal receiver use
sinusoids?
Hamiltonian Mechanics
b
m
x
k
 Simplest physical model of vibrating
masses
 Coupled spring-mass-damper mechanics
 Produce sinusoidal harmonics
•
Video: Cochlea
ESE 250 S’13 DeHon Kadric Kod Wilson-Shah
Week 6 – Psychoacoustics
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Masking - Spatial
•
Masking Paradigms
 “Masker” masking “maskee”
 Tone Masking Noise
o
pure tone


o
of 80 SPL
at 1 kHz
just masks “critical band” noise


of 56 SPL
centered at 1 kHz
 Masker-to-Maskee ratio
o
o
Constant for fixed relative frequency and varying amplitude
Changes with varying relative frequency
1 “Bark”
frequency
interval
[T. Painter and A. Spanias. Proc. IEEE, 88(4):451–512, 2000.]
ESE 250 S’13 DeHon Kadric Kod Wilson-Shah
Week 6 – Psychoacoustics
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Masking
The first graph shows the masking pattern for a 200Hz tone
 Mostly masks tones around 200Hz, but also at harmonics
The second graph shows the same plot for different frequencies,
but only the fundamental part
 Notice that the band gets wider for increasing frequencies
[H. Fletcher. Rev. Mod. Phys., 12(1):47–65, 1940].
…masker at fundamental
can somewhat mask maskees
at the harmonics …
… but the “spreading
curve” is traditionally
depicted over the
fundamental only
17
ESE 250 S’13 DeHon Kadric Kod Wilson-Shah
Week 6 – Psychoacoustics
Tone Masking Noise
• Are the following signals masked?
 200 Hz tone at 80dB
 200 Hz tone at 40dB
 300 Hz tone at 40dB
 400 Hz tone at 40dB
 700 Hz tone at 30dB
ESE 250 S’13 DeHon Kadric Kod Wilson-Shah
Week 6 – Psychoacoustics
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Masking
•
[H. Fletcher. Rev. Mod. Phys., 12(1):47–65, 1940].
Tone Masking Noise (Fig 12)
 value above quiet threshold
 such that a signal at the
•
abscissa frequency
 can be heard in presence of
top: 200 Hz tone
bottom: various frequencies
Noise Masking Tone (Fig 13)
 dots show pure tone magnitude
(in dB)
 required to be audible above
noise
o
o
o
Of the magnitude on the middle
curve
centered at that frequency
with bandwidth


at least wider
than the bars of Fig 12
ESE 250 S’13 DeHon Kadric Kod Wilson-Shah
Week 6 – Psychoacoustics
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Noise Masking Tone
• Are the
following
signals masked
by the noise?
 200Hz at 60dB
 1KHz at 60dB
ESE 250 S’13 DeHon Kadric Kod Wilson-Shah
Week 6 – Psychoacoustics
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Noise Masking Tone
• Are the
following
signals masked
by the noise?
 200Hz at 60dB
o Yes!
noise
 1KHz at 60dB
ESE 250 S’13 DeHon Kadric Kod Wilson-Shah
Week 6 – Psychoacoustics
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Noise Masking Tone
• Are the
following
signals masked
by the noise?
 200Hz at 60dB
o No!
 1KHz at 60dB
ESE 250 S’13 DeHon Kadric Kod Wilson-Shah
Week 6 – Psychoacoustics
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Noise Masking Tone
• Are the
following
signals masked
by the noise?
 200Hz at 60dB
 1KHz at 60dB
o No!
ESE 250 S’13 DeHon Kadric Kod Wilson-Shah
Week 6 – Psychoacoustics
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Noise Masking Tone
• Are the
following
signals masked
by the noise?
 200Hz at 60dB
 1KHz at 60dB
o No!
ESE 250 S’13 DeHon Kadric Kod Wilson-Shah
Week 6 – Psychoacoustics
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Masking - Temporal
• Temporal Masking
 Masker effect persists for tenths of a second
 Masker effect is “acausal”
o on ~ 2/100 timescales
ESE 250 S’13 DeHon Kadric Kod Wilson-Shah
Week 6 – Psychoacoustics
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Pitch JND
[H. Fletcher. Rev. Mod. Phys., 12(1):47–65, 1940].
• JND = “just noticeable difference”
 change in stimulus that “just” elicits perceptual notice
 where “just” means that a smaller variations of stimulus cannot be discerned
•
What can you say
about the JND:

Below 1000 Hz?
o
o

roughly constant
~ 3 Hz
Above 1000 Hz?
roughly log-log
linear
Log[Jnd(f2)] - Log[ Jnd(f1)]
~ n (Log[f2] - Log[f1])
o
o
What is n?
e.g. f1 =2000 f2 =4000
6 = 10 – 4 ~ n( Log10[2] )
)
n ~ 20
•
Suggests that as
frequency increases


broader frequency
bands
 “assigned” to same
length of cochlear
tissue
Remember cochlea model
ESE 250 S’13 DeHon Kadric Kod Wilson-Shah
Week 6 – Psychoacoustics
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JND experiment
• The following audio files contain a single
•
•
tone playing for 10 seconds. The sine
starts at 200Hz, then changes to a higher
frequency (201, 202, 203, 205, 210).
This change occurs after a number of
“noises”: 1, 2, 3, 4, 5, 6, 7, 8 or 9.
Can you notice when the change
happens?
ESE 250 S’13 DeHon Kadric Kod Wilson-Shah
Week 6 – Psychoacoustics
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Critical Bands
Decades of empirical study
• reveal that human audio frequency
•
•
•
perception
is quantized into < 30 “critical
bands”
of perceptually near-identical pitch
classes
corresponding to ~equal length
bands of cochlear tissue (neurons)
ESE 250 S’13 DeHon Kadric Kod Wilson-Shah
Week 6 – Psychoacoustics
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Critical Bands: Evidence
[T. Painter and A. Spanias. Proc. IEEE, 88(4):451–512, 2000.]
 Tone masking Noise (Fig. a & c)
o
o
o
o
o
noise audibility threshold
for small bandwidth noise
remains constant
until tone frequency locus
falls away from critical
bandwidth
 Noise masking Tone (Fig. b & d)
o
o
same effect
with masker and maskee
roles reversed
ESE 250 S’13 DeHon Kadric Kod Wilson-Shah
Week 6 – Psychoacoustics
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The Bark Scale
[E. Zwicker. J. Acoust. Soc.Am., 33(2):248, February 1961]
•
“Bark” units: Uniform JND scale for frequency
 Maps frequency intervals into their respective critical band number
ESE 250 S’13 DeHon Kadric Kod Wilson-Shah
Week 6 – Psychoacoustics
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The Bark Scale
[E. Zwicker. J. Acoust. Soc.Am., 33(2):248, February 1961]
•
Frequency-to-Bark function
 First Principles vs. Empirical Modeling
B( f )  13 tan 1 (0.00076 f )  3.5 tan 1 (( f / 7500) 2 )
ESE 250 S’13 DeHon Kadric Kod Wilson-Shah
Week 6 – Psychoacoustics
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Compression opportunities
Consider the following recording
Any ways to improve the compression?
ESE 250 S’13 DeHon Kadric Kod Wilson-Shah
Week 6 – Psychoacoustics
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Compression opportunities
Zooming in on a smaller portion
Any ways to improve the compression?
120
dB
100
80
60
40
20
Masked
0
193
194
195Hz
196
197
198
199
200Hz
ESE 250 S’13 DeHon Kadric Kod Wilson-Shah
201
202
203
204
205Hz
206
Week 6 – Psychoacoustics
207
208
Frequency
33
Compression opportunities
Zooming in on a smaller portion
Any ways to improve the compression?
120
JND:
Could only
represent integer
frequency values
dB
100
80
60
40
20
0
193
194
195Hz
196
197
198
199
200Hz
ESE 250 S’13 DeHon Kadric Kod Wilson-Shah
201
202
203
204
205Hz
206
Week 6 – Psychoacoustics
207
208
Frequency
34
Compression opportunities
Zooming in on a smaller portion
Any ways to improve the compression?
120
dB
100
80
60
40
20
0
193
194
195Hz
196
197
198
199
200Hz
ESE 250 S’13 DeHon Kadric Kod Wilson-Shah
201
202
203
204
205Hz
206
Week 6 – Psychoacoustics
207
208
Frequency
35
Next Week
• How can we use what we know about
human perception to compress music?
 Frequency hearing range
 Masking
o Temporal
o Spatial
o JND
o Barks
ESE 250 S’13 DeHon Kadric Kod Wilson-Shah
Week 6 – Psychoacoustics
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Big Ideas
•
•
•
Sound is a pressure wave that makes the Cochlea
vibrate
 with frequencies from ~20Hz (at the tip) to ~20KHz (at the base)
This vibration is sinusoidal (physics)
 This is why sound harmonics are best represented as sinusoidal signals
Masking
 Temporal – A masker tone can mask another tone that is present either
right before or a little after the masker
 Spatial – A single tone can mask an entire frequency band (that contains
the tone) if its intensity is high enough
 There are <30 such bands (Bark scale), and they are wider for higher
frequencies
ESE 250 S’13 DeHon Kadric Kod Wilson-Shah
Week 6 – Psychoacoustics
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Admin
• Lab 5 report due tomorrow
• On Thursday: Lab 6
 You will be designing your own experiments
o
o
To measure the range of frequencies you can hear
To perform spatial masking experiments
ESE 250 S’13 DeHon Kadric Kod Wilson-Shah
Week 6 – Psychoacoustics
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ESE250:
Digital Audio Basics
End Week 6 Lecture
Human
Psychoacoustics
ESE 250 S’13 DeHon Kadric Kod Wilson-Shah
Week 6 – Psychoacoustics
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