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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.