Post on 07-May-2020
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Hearing and Deafness
2. Ear as a frequency analyzer
Chris Darwin
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Demo Class
• Tuesday 24th Oct 2006 at 12:00 in CHI LT
• Demonstration of Excel spreadsheet toillustrate: auditory filtering & excitationpatterns.
• Spreadsheet available at:
http://www.lifesci.sussex.ac.uk/home/Chris_Darwin/Perception/Lectures/
Amadeus
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Frequency: 100-Hz Sine Wave
Time (s)0 0.05
-1.0
1.0
0
Waveform
Amplitude against time
Spectrum
Amplitude against frequency
1
100 Hz
amp
frequency
Sound is a change in the pressure of the air.
The waveform of any sound shows how the
pressure changes over time. The eardrum
moves in response to changes in pressure.
Any waveform shape can be produced by
adding together sine waves of appropriate
frequencies, amplitudes and phases. The
amplitudes of the sine waves give the
amplitude spectrum of the sound.
Theamplitude spectrum of a sine wave is a
single point at the frequency of the sine wave.
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Frequency: 500-Hz Sine Wave
Waveform
Amplitude against time
Spectrum
Amplitude against frequency
1
500
amp
frequency
1
100
amp
frequency500
Time (s)0 0.05
-1.0
1.0
0
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Amplitude: 500-Hz Sine Wave
Spectrum
Amplitude against frequency
1
500
amp
frequency
1
100
amp
frequency500
Time (s)0 0.05
0
Time (s)0 0.05
0
Amplitude is a measure of the pressure change
of a sound and is related to how loud the sound
is.
Amplitude squared is proportional to the
energy or intensity (I) of a sound.
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Phase: 500-Hz Sine Wave
The amplitude spectrum does
not show phase
1
500
amp
frequency
1
100
amp
frequency500
Time (s)
0 0.01–0.99
0.9899
0
Time (s)
0 0.01–0.99
0.99
0
sine
cosine
Phase - measured in degrees or radians,
indicates the relative time of a wave. The two
waveforms in the panel have identical;
frequencies and amplitudes, but differ in phase
by 90 degrees or !/2 radians.
A shift in phase for a sine-wave is equivalent to
shifting it in time.
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adding sine waves
ミ1
0
1Sine wave Sum
ミ1
0
1
ミ1
0
1
ミ1
0
1
0 0.025 0.05Time (s)
0 0.025 0.05Time (s)
1
amp
frequency
1
amp
frequency
1
amp
frequency
1
amp
frequency
Spectrum of Sum
A sound which has more than one (sine-wave)frequency component is a complex sound. A periodicsound is one which repeats itself at regular intervals.A sine wave is a simple periodic sound. Musicalinstruments or the voice produce complex periodicsounds. They have a spectrum consisting of a seriesof harmonics. The lowest frequency (of which all theothers a re multiples) is called the fundamentalfrequency.
Each harmonic is a sine wave that has a frequencythat is an integer multiple of the fundamentalfrequency.
The left column shows individual harmonics; theright shows their sum; the yellow panels show theamplitude spectrum of the sound.
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100-Hz fundamental Complex Wave
Waveform
Amplitude against time
Spectrum
Amplitude against frequency
Time (s)0 0.05
-1.7
5.0
0
1
500
amp
frequency
1
100
amp
frequency500
Here is 1/20th of a second of the waveform and alsothe spectrum of a complex periodic sound consistingof the first four harmonics of a fundamental of 100Hz. All the frequency components are integermultiples of 100 Hz.
A periodic sound consists of a section of waveformthat repeats itself. The period of the complex wave isthe duration of this section. In this case it is 1/100s or0.01s, or 10 ms. The period is the reciprocal of thefundamental frequency (in this case 100 Hz).
If you change the period of a complex sound, youchange its pitch. Shorter periods - higherfundamental frequency - higher pitch.
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Staggered sine-waves adding
simultaneous
staggered
time ->
freq
uen
cy -
>
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Bandpass filtering (narrow)
Time (s)0 0.05
-1.7
5.0
0
1
500
amp
frequency
1
100
amp
frequency500
Time(s)
0 0.05
0
1
50
0
amp
frequency
1
100
amp
frequency500
A filter lets through some frequencies but not others.A treble control acts as a low-pass filter, letting less ofthe high frequencies through as you turn the trebledown. A bass control acts as a high-pass filter, lettingless of the low frequencies through as you turn thebass down.
A band-pass filter only lets through frequencies thatfall within some range.
A slider on a graphic equalizer controls the outputlevel of a band-pass filter.
In the panel, the red band-pass filter's width isnarrow so that it only lets through one of the complexsound's harmonics. So the output waveform is a sinewave.
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Bandpass filtering (wide)
Time (s)0 0.05
-1.7
5.0
0
1
500
amp
frequency
1
100
amp
frequency500
1
amp
frequency
1
100
amp
frequency500Time (s)
0 0.05–0.9751
0.9751
0
In the panel, the red band-pass filter's width is widerso that it now lets through two of the complexsound's harmonics. The output waveform is now thesum of two sine waves, which beat.
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Beats
1
amp
frequency
1
100
amp
frequency500Time (s)
0 0.05–0.9751
0.9751
0
Repetition rate is the difference in frequency
between the two sine-wave components
1/100th second 500 - 400 = 100 Hz
400
When two sine waves are added together the
resulting complex wave has a beat rate which
corresponds to the difference in frequency
between the two sine waves.
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Excitation patterns(envelope of excitation)
distance along basilar membrane
amp
litu
de
of
vib
rati
on
base apex
high frequencies low frequencies
0
Basilar membrane excitation pattern is like a spectrum
If we draw an envelope around the vibration,
we get what is called an excitation pattern.
The panel shows the the excitation patterns for
three tones of different frequencies. If they
were all played together, the excitation pattern
would be (roughly) the sum of all three
individual patterns.
These three sounds are sufficiently wide apart
in frequency that the ear separates them well
on the basilar membrane. They are thus
resolved by the ear.
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Excitation pattern of complex tone on bm
-5.0
0.0
5.0
10.0
15.0
20.0
25.0
b m
vib
rati
on
base apexlog (ish) frequency
2004001600
resolvedunresolved
600800
Output of 1600 Hz filter Output of 200 Hz filter
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
0 0.2 0.4 0.6 0.8 1
1/200s = 5ms
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0 0.2 0.4 0.6 0.8 1
1/200s = 5ms
This is an important diagram !!!
It shows the excitation pattern of the basilar
membrane to a complex tone consisting of many,
equal-amplitude harmonics of a 200-Hz
fundamental.
Each of the low-numbered harmonics (upto about
the eighth) is resolved by the membrane, giving a
separate peak. At each of these peaks the membrane
vibrates sinusoidally at the frequency of the
harmonic that is being resolved there.
Above the eighth, the harmonics are NOT resolved
and the response of the membrane is a complex
wave that shows beats.
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Measurement of auditory bandwidth
with band-limited noise
Broadband Noise
1000 Hz
2000 Hz
frequency
250 Hz
Amadeus
The curves in the previous slide were generated
using data from human psychophysical
experiments measuring the bandwidth of the
auditory filters. A crude way of estimating
these bandwidths that makes an effective demo
is illustrated here. Only noise that is close in
frequency to a tone masks it.
We can estimate how wide the human auditory
filters are by seeing how narrow a noise band
must be before it becomes less effective at
masking a tone.
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A gardening analogy
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A gardening analogy
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A gardening analogy
Auditory bandwidth
Noise bandwidth
Detection mechanism
Tone
Noise
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Wider auditory filter
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Psychophysical tuning curves
Masker center frequency
Bandwidth
A more accurate way of measuring the human
auditory bandwidths is to use Forward
Masking. A target tone near threshold is
masked by a slightly earlier masking tone at
different frequencies.
We measure how loud the masking tone has to
be to just mask the target tone. That value is
plotted on the graph as a function of the
masking tone's frequency.
The next slide shows the bandwidth of this
curve plotted as a function of frequency.
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Human auditory bandwidth
0
200
400
600
800
1000
0 2000 4000 6000 8000
At 1kHz the bandwidth is about 130 Hz;
at 5kHz the bandwidth is about 650 Hz.
BW = freq / 8
roughly
Normal
SNHL
The black curve in the slide shows how the
human auditory bandwidth varies with center
frequency.
The bandwidth increases roughly proportional
to frequency - it is about freq/8. This increase
explains why only low numbered harmonics
are resolved.
The bandwidth is much larger for people with
OHC damage in sensori-neural hearing loss.
The red curve shows possible bandwidths for
someone with a severe hearing loss of this
type.
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Normal auditory non-linearities
• Normal loudness growth (follows Weber’s Law,
which is logarithmic, not linear)
• Combination tones
• Two-tone suppression
• Oto-acoustic emissions
The normal auditory system is non -linear, so
that you cannot strictly predict how it will
behave to a sum of two sine waves by simply
adding up its responses to the sine waves
presented on their own.
The non-linearity is a consequence of OHC
activity and helps to give the system its large
dynamic range.
As a consequence of OHC activity, we can
detect various non-linear aspects of the ear's
response.
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Combinations Tones
(Tartini tones)
1
amp
frequency
1
1000
amp
frequency1200800
The Italian composer Tartini noticed that he could
hear a third tone when two tones were played close
together in frequency.
The third tone is heard best when the frequency of
one primary tone (f1) is about 20% lower than the
other (f2). It is then about 20 dB lower in level than
the primaries.The combination tone's frequency is
given by 2f2 - f1.
For complex periodic sounds, the combination tones
created by closely-spaced harmonics are created at
harmonic frequencies and so are difficult to hear.
Combination tones are created where the excitation
patterns of the two tones overlap. Hence they get
weaker as the two primary tones are separated in
frequency.
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Two-tone suppression
log frequency
log
am
pli
tud
e (d
B S
PL
)
100
80
60
40
20
Test tone at Characteristic Frequency
Regions for two-tone suppression
If the auditory system were linear, we should
be able to predict the response to a sum of two
sounds by simply adding the response to the
two sounds presented separately.
Two-tone suppresssion is a spectacular
example of this linear additivity NOT being
true.
A tone presented at the frequency and
amplitude of the triangle, makes the auditory
fiber fire.
When we add a tone from the shaded area of
the graph the auditory nerve will stop firing,
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Conductive vs Sensori-neural deafness
Conductive Sensori-neural Sensori-neural
Origin Middle-ear Cochlea (IHCs) Cochlea (OHCs)
Thresholds Increased Increased Increased
Filter bandwidths Normal Normal Increased
Loudness growth Normal Normal Increased (Recruitment
BM response becomes linear, so
• No combination tones
• No two-tone suppression
SNHL usually a combination
of OHC and IHC damage
The table summarises the differences between
conductive and two sorts of sensori-neural
deafness.
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Symptoms of SNHL
• Raised thresholds:
helped by amplification
• Wider bandwidths:
no help possible
• Recruitment (restricted dynamic range):
partly helped by automatic gain controls in
modern digital aids
• Other non-linearities also reduced:
combination tones, two-tone suppression
•Often accompanied by tinnitus
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Normal vs Impaired Dynamic Range
Illustration of the impaired dynamic range
found with OHC damage in sensori-neural
hearing loss. Notice that sounds are
uncomfortably loud at the same level for both
the normal ears and the impaired ears. But the
impaired ears have a much higher threshold,
so loudness grows much faster for them.
This "loudness recruitment" rises because the
OHCs are not amplifying the quieter sounds.