Cecilia R. Aragon
IEOR 170
UC Berkeley
Spring 2006

• “How the Ear Functions,” http://www.archive.org/details/HowtheEa1940
• Brian Bailey, http://wwwfaculty.cs.uiuc.edu/~bpbailey/teaching/2006-Spring/cs414/index.html
• Dan Russell, http://www.kettering.edu/~drussell/demos.html
• James Hillenbrand, http://homepages.wmich.edu/~hillenbr/AuditoryPerception.ppt
• Lawrence Rosenblum, http://www.faculty.ucr.edu/~rosenblu/labindex.html (McGurk effect)
• Andrew Green, http://www.uwm.edu/~ag/teach_pdf/lecturenotes/perception/
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• How the Ear Functions
• Physical Dimensions of Sound
• Perceptual Dimensions of Sound
• Sound Intensity and the Decibel Scale
• Pitch Perception
• Loudness Perception
• Timbre Perception
• Digitization of Sound
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http://www.archive.org/details/HowtheEa1940
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• Periodic disturbances that travel through a medium (e.g. air or water)
• Transport energy
• “What is a Wave?” Dan Russell, http://www.kettering.edu/~drussell/Demos/waves-intro/waves-intro.html
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• A longitudinal, mechanical wave
– caused by a vibrating source
• Pack molecules at different densities
– cause small changes in pressure
• Model pressure differences as sine waves
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• Pure Tones - simple waves
• Harmonics - complex waves consisting of combinations of pure tones (Fourier analysis) the quality of tone or its timbre (i.e. the difference between a given note on a trumpet and the same note on a violin) is given by the harmonics
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• Periodic stimulation of membrane matches frequency of sound
– one electrical impulse at every peak
– maps time differences of pulses to pitch
• Firing rate of neurons far below frequencies that a person can hear
– Volley theory : groups of neurons fire in wellcoordinated sequence
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• Waves move down basilar membrane
– stimulation increases, peaks, and quickly tapers
– location of peak depends on frequency of the sound, lower frequencies being further away
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• Amplitude
– height of a cycle
– relates to loudness
• Wavelength ( w )
– distance between peaks
• Frequency ( λ )
– cycles per second
– relates to pitch
– λ w = velocity
• Most sounds mix many frequencies & amplitudes Sound is repetitive changes in air pressure over time
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Auditory perception is a branch of psychophysics.
Psychophysics studies relationships between perception and physical properties of stimuli.
Physical dimensions : Aspects of a physical stimulus that can be measured with an instrument (e.g., a light meter, a sound level meter, a spectrum analyzer, a fundamental frequency meter, etc.)
Perceptual dimensions : These are the mental experiences that occur inside the mind of the observer. These experiences are actively created by the sensory system and brain based on an analysis of the physical properties of the stimulus. Perceptual dimensions can be measured, but not with a meter. Measuring perceptual dimensions requires an observer (e.g., a listener).
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Visual Psychophysics:
Perceptual Dimensions
Hue
Brightness
Shape
Physical Properties of Light
Wavelength
Luminance
Contour/Contrast
Auditory Psychophysics:
Perceptual Dimensions
Physical Properties of Sound
Pitch Fundamental Frequency
Loudness Intensity
Timbre (sound quality) Spectrum Envelope/Amp Env
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• Pitch ( not fundamental frequency)
• Loudness ( not intensity)
•
Timbre ( not spectrum envelope or amplitude envelope)
The terms pitch , loudness , and timbre refer not to the physical characteristics of sound, but to the mental experiences that occur in the minds of listeners.
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• Pitch
– higher frequencies perceived as higher pitch
– humans hear sounds in 20 Hz to 20,000 Hz range
• Loudness
– higher amplitude results in louder sounds
– measured in decibels (db), 0 db represents hearing threshold
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• Timbre
– complex patterns added to the lowest, or fundamental , frequency of a sound, referred to as spectrum envelope
– spectrum envelopes enable us to distinguish musical instruments
• Multiples of fundamental frequency give music
• Multiples of unrelated frequencies give noise
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• Intensity (I) of a wave is the rate at which sound energy flows through a unit area (A) perpendicular to the direction of travel
I

1
A

E
 t

P
A
P measured in watts (W), A measured in m 2
• Threshold of hearing I
0 is at 10 -12 W/m 2
• Threshold of pain is at 1 W/m 2
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• Describes intensity relative to threshold of hearing based on multiples of 10 dB

10 log
I
I
0
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Spring 2006
Sound
Rustling leaves
Whisper
Ambient office noise
Conversation
Auto traffic
Concert
Jet motor
Spacecraft launch
Decibels
10
30
45
60
80
120
140
180
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• 0 dB = threshold of hearing (TOH)
• 10 dB = 10 times more intense than TOH
• 20 dB = 100 times more intense than TOH
• 30 dB = 1000 times more intense than TOH
• An increase in 10 dB means that the intensity of the sound increases by a factor of 10
• If a sound is 10 x times more intense than another, then it has a sound level that is 10*x more decibels than the less intense sound
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• Use energy combination equation
L
L
1

10 log( 10 10
L
2

10 10

...

10
L
N
10 ) where L
1
, L
2
, …, L n are in dB
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• Show that the threshold of hearing is at 0 dB
• Show that the threshold of pain is at 120 dB
• Suppose an electric fan produces an intensity of 40 dB. How many times more intense is the sound of a conversation if it produces an intensity of 60 dB?
• One guitar produces 45 dB while another produces 50 dB. What is the dB reading when both are played?
• If you double the physical intensity of a sound, how many more decibels is the resulting sound?
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Pitch and Fundamental Frequency
All else being equal, the higher the F
0
, the higher the perceived pitch.
Lower F
0, lower pitch
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Higher F
0, higher pitch
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The ear is more sensitive to F
0 differences in the low frequencies than the higher frequencies. This means that:
300 vs. 350

3000 vs. 3050
That is, the difference in perceived pitch (not F
0
) between
300 and 350 Hz is NOT the same as the difference in pitch between 3000 and 3050 Hz, even though the physical differences in F
0 are the same.
300-350: 3000-3050:
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Spring 2006
•Tone height: A sound quality whereby a sound is heard to be of higher or lower pitch; monotonically related to frequency
•Tone chroma: A sound quality shared by tones that have the same octave interval
•Musical helix: Can help visualize musical pitch
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1 f
2 f
1 octave
3 f
4 f
2 octaves
8 f
3 octaves
Spring 2006
Length of string or pipe
IEOR 170
• Strings or pipes (trombone, flute organ) all have resonant frequencies.
• They may vibrate at that frequency or some multiple of it
• All instruments and voices carry some harmonics and dampen others
31

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Loudness and Intensity
All else being equal, the higher the intensity, the greater the loudness.
Higher intensity, higher loudness Lower intensity, lower loudness
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The relationship between intensity and loudness
Doubling intensity does not double loudness. In order to double loudness, intensity must be increased by a factor of 10 , or by 10 dB [10 x log
= 10 x 1 = 10 dB]. This is called the 10 dB rule .
10
(10)
Two signals differing by 10 dB:
(500 Hz sinusoids)
Note that the more intense sound is NOT 10 times louder even though it is 10 times more intense.
The 10 dB rule means that a 70 dB signal is twice as loud as a 60 dB signal, four times as loud as a 50 dB signal, eight times as loud as a 40 dB signal, etc.
A 30 dB hearing loss is considered mild -- just outside the range of normal hearing. Based on the 10 dB rule, how much is loudness affected by a 30 dB hearing loss?
(Answer: 1/8th. But note that this does not mean that someone with a 30 dB loss will have 8 times more difficulty with speech understanding than someone with normal hearing.)
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Loudness is strongly affected by the frequency of the signal. If intensity is held constant, a midfrequency signal (in the range from ~1000-4000
Hz) will be louder than lower or higher frequency signals .
125 Hz, 3000 Hz, 8000 Hz
The 3000 Hz signal should appear louder than the
125 or the 8000 signal, despite the fact that their intensities are equal.
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• More sensitive to loudness at mid frequencies than at other frequencies
– intermediate frequencies at [500hz, 5000hz]
• Perceived loudness of a sound changes based on the frequency of that sound
– basilar membrane reacts more to intermediate frequencies than other frequencies
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Spring 2006
Each contour represents an equal perceived sound
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• < 20 Hz - infrasound
• > 20 KHz - ultrasound
• human auditory range decreases with age
• TV 17.7 KHz horizontal scanning frequency
• “ultrasonic” cleaning devices, burglar alarms (20-40 KHz)
• CD 20 KHz cutoff, LP
60-80 KHz
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Timbre , also known as sound quality or tone color , is oddly defined in terms of what it is not:
When two sounds are heard that match for pitch, loudness, and duration, and a difference can still be heard between the two sounds, that difference is called timbre.
For example: a clarinet, a saxophone, and a piano all play a middle C at the same loudness and same duration. Each of these instruments has a unique sound quality. This difference is called timbre , tone color , or simply sound quality .
There are also many examples of timbre difference in speech. For example, two vowels (e.g., /
å
/ and /i/) spoken at the same loudness and same pitch differ from one another in timbre.
There are two physical correlates of timbre: spectrum envelope amplitude envelope
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Timbre and Spectrum Envelope
Timbre differences between one musical instrument and another are partly related to differences in spectrum envelope -- differences in the relative amplitudes of the individual harmonics. In the examples above, we would expect all of these sounds to have the same pitch because the harmonic spacing is the same in all cases. The timbre differences that you would hear are controlled in part by the differences in the shape of the spectrum envelope.
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Six Synthesized Sounds Differing in Spectrum Envelope
Note the similarities in pitch (due to constant F
0
/harmonic spacing) and the differences in timbre or sound quality .
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Vowels Also Differ in Spectrum Envelope
Shown here are the smoothed envelopes only (i.e., the harmonic fine structure is not shown) of 10 American-English vowels.
* Note that each vowel has a unique shape to its spectrum envelope . Perceptually, these sounds differ from one another in timbre .
Purely as a matter of convention, the term timbre is seldom used by phoneticians, although it applies just as well here as it does in musical acoustics. In phonetics, timbre differences among vowels are typically referred to as differences in vowel quality or vowel color .
* From Hillenbrand, J.M, Houde, R.A., Clark, M.J., and Nearey, T.M. Vowel recognition from harmonic spectra. Acoustical Society of America , Berlin, March,
1999.
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Aperiodic sounds can also differ in spectrum envelope, and the perceptual differences are properly described as timbre differences.
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Amplitude Envelope
• Timbre also affected by amplitude envelope
• sometimes called the amplitude contour or energy contour of the sound wave
• the way sounds are turned on and turned off
Leading edge = attack Trailing edge = decay
The attack especially has a large effect on timbre .
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Music examples
(timbre differences related to amplitude envelope)
Plucked vs. bowed stringed instruments
The damping pedal on a piano
The difference in sound quality between a hammered string (e.g., a piano) and a string that is plucked by a quill (e.g., a harpsichord).
The timbre differences that distinguish one musical instrument from another appear to be more closely related to differences in amplitude envelope -- and especially the attack -- than to the shape of the spectrum envelope (although both play a role). For example, when the amplitude contour of an oboe tone is imposed on a violin tone, the resulting tone sounds more like an oboe than a violin.
*
* White, G.D. The Audio Dictionary, 1987, Seattle: University of Washington Press.
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Same melody, same spectrum envelope (if sustained), different amplitude envelopes (i.e., different attack and decay characteristics).
Note differences in timbre or sound quality as the amplitude envelope varies .
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Timbre differences related to amplitude envelope also play a role in speech. Note the differences in the shape of the attack for /b/ vs.
/w/ and /S/ vs. /tS/.
abrupt attack more gradual attack abrupt attack more gradual attack
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http://www.faculty.ucr.edu/~rosenblu/lab-index.html
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[Steinmetz and Nahrstedt]
52

Microphones, video cameras produce analog signals
(continuous-valued voltages)
To get audio or video into a computer, we must digitize it
(convert it into a stream of numbers)
So, we have to understand discrete sampling (both time and voltage)
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• Sampling -- divide the horizontal axis (the time dimension) into discrete pieces. Uniform sampling is ubiquitous.
• Quantization -- divide the vertical axis (signal strength) into pieces. Sometimes, a non-linear function is applied.

8 bit quantization divides the vertical axis into 256 levels. 16 bit gives you
65536 levels.
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• Measure amplitude at regular intervals
• How many times should we sample?
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• Suppose we are sampling a sine wave. How often do we need to sample it to figure out its frequency?

If we sample at 1 time per cycle, we can think it's a constant.
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
If we sample at 1.5 times per cycle, we can think it's a lower frequency sine wave.

Nyquist rate -- "For lossless digitization, the sampling rate should be at least twice the maximum frequency response."
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• Standard music CD:
– Sampling Rate: 44.1 kHz
– 16-bit samples
– 2-channel stereo
– Data transfer rate = 2 
16

44,100 = 1.4 Mbits/s
– 1 hour of music = 1.4

3,600 = 635 MB
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