1. Applied Psychoacoustics Lecture 3: Masking
Jonas Braasch

2. From ATH to masked detection thresholds
from tonmeister.ca after Zwicker & Fastl 1999
So far we have measured the absolute threshold of hearing (ATH) throughout
the auditory frequency range for sinusoids.
Now we would like to investigate how we detect sounds if other sounds are present as well.

3. Preliminary thoughts
We have seen that a sine sound does not only excite the part of the basilar membrane that corresponds to its frequency but also other frequencies as well (traveling waves).
The traveling wave moves from the base (high freqs.) to the apex (low freqs.) and declines after passing the resonance frequency.
Therefore, we expect that a sound at a given frequency also affects the detection of a sound at another frequency.
We will utilize this effect to the determine the shape of auditory filters.

4. Method
We now re-measure the threshold of hearing, but in this case we present to sinusoids to the listeners.
One, the masker, is fixed in frequency (1 kHz) and level (60 dB SPL).
The second one, the target, is varied in level as before.
We measure at various frequencies the minimum sound pressure level at which the second tone is detected.

5. Absolute Threshold of Hearing
from tonmeister.ca after Zwicker & Fastl 1999
Our absolute threshold of hearing (ATH) for a single tone now changes to …

6. Masked Detection Threshold
steep curve for low freqs
shallow slope for high freqs
from tonmeister.ca after Zwicker & Fastl 1999
… to this one.
We now speak of the masked detection threshold, with the sinusoids at 1 kHz, 60 dB SPL being the masker. Note that we find a steep slope just below 1 kHz, because in this range the basilar membrane is not much affected by the sound, while the slope is shallow for frequencies just above 1 kHz.

7. Masked Detection Threshold
from tonmeister.ca after Zwicker & Fastl 1999
Of course the masked detection threshold depends on the characteristics of the masker. In this graph, several thresholds curves are shown for various masker levels ( dB SPL). 100 dB SPL is a very high value. I recommend NOT to go above 85 dB SPL if you want to repeat this measurement at home.

8. Auditory Filters
Fletcher (1940) postulated that the auditory system behaves like a bank of pass-band filters with overlapping passband.
Helmholtz (1865) already had similar ideas.
Auditory filters can be measured in amplitude and phase as functions of frequency.

9. Measurement of auditory filters
We will firstly restrict ourselves to the amplitude of auditory filters.
We can use a similar paradigm to measure auditory filters as in our previous experiment:
present two sinusoids with same level and same frequency to the listener. The level was adjusted just above sensation level.
Next, we vary the frequency of the sinusoids in opposite direction.
The two sinusoids become inaudible at the point where they do not fall into one auditory filter anymore. In this case, the energy within each of the two auditory filters becomes to small to be detected.

10. Critical Bands: Zwicker (1961)
(Fig.:Terhardt 1998)
Zwicker (1961) measured the critical bandwidth using two narrow-band maskers which masked a sine target at the center of the critical band.
Zwicker recorded the detection threshold of the sine tone (varied in level) as a function of the frequency gap between both maskers.
Unfortunately, the interference between the lower frequency noise masker and an the sine target lead to interference effects, and combination tones at different frequencies become audible, while the signal remains undetected.
This leads to the abrupt decrease in the detection threshold at 0.3 kHz.

11. Zwicker’s critical bands
Linear range contradicts new findings

12. Zwicker’s critical band rate
Errors between measured and predicted values (from equations below)
Previous slide
The graph shows the Critical band rate in Bark as a function of
Frequency f. The equations were established to fit the data.

13. Zwicker’s critical bandwidth
Errors between measured and predicted values (from equations below)
The graph shows the Critical band width in Bark as a function of
Frequency f. The equation was established to fit the data.
Previous slide

14. Patterson ‘74: Measurement method
from Patterson (1974)
Hypothetical
MASKING
Shaded area: part of noise that is effectively masking the test tone
Patterson (1974) used a broadband noise masker to avoid harmonicity to influence the results.

15. Patterson ‘74: Measurement method

16. Measuring the ATH one more time
100%
Hearing threshold/masked threshold
Number of correct responses [%] 0%
Sound pressure level
… would be nice, but in reality

17. … it looks like this 75 % threshold 50 % threshold
Probability for correct response
50 % threshold
Log-normalized stimulus intensity
(e.g, sound pressure level)
In signal detection theory, we explain this variation with internal noise
in the central nervous system

18. Patterson 74: Results

19. Patterson 74: Results

20. Off-Frequency Listening
on-frequency
listening
masker
Auditory filter
tone
off-frequency
listening
masker
Auditory filter
tone
By placing the center frequency of of the Auditory Filter above the test-tone frequency, the signal-to-noise ratio between the tone and the masker can be increased. This way the test tone is easier targeted.

21. Avoiding off-Frequency Listening
Auditory filter
on-frequency
listening
masker
2. masker
tone Df Df
Auditory filter
2. masker
off-frequency
listening
masker
tone
In this two masker case off-frequency listening does not pay off anymore. By shifting the auditory filter, the influence of one masker is reduced, while the influence of the 2. masker is increased. Overall the signal-to-noise ratio balance decreases. In this experiment, it is assumed that the auditory filter is symmetrical, which is a good-enough approximation.

22. Noise Gap Masking (Fig.: Moore 2004)
To avoid off-frequency listening, Patterson (1976) measured the threshold of the sinusoidal signal as a function of the width of the spectral notch in the noise masker. The shaded areas shows the amount of noise passing through the auditory filter.

23. Auditory filter shape (Fig.: Moore 2004)
Typical shape of an auditory filter as measured by Patterson (1976). The center frequency is 1 kHz.

24. Auditory Filter non-linearity
80 dB
30 dB
This graph shows the non-linearity of the auditory filter. In the left graph the filter curves
Are normalized to 0 dB. The filters were measured for several 2-kHz sine tones from 30 to 80 dBs. Note how the filter broadens toward low frequencies with increasing level. In the right graph the filters were not normalized.
(Fig.: Moore 2004)

25. Auditory Filter Bandwidths
(Fig.: Moore 2004)
Width of auditory filters measured with different techniques. The dashed curve shows
the values of Zwicker (1961), the solid line the ERBN values which was measured
using Patterson’s (1976) notched-noise method.
Note the large deviations of Zwicker’s results at low frequencies, which are based on indirect measures.

26. ERB calculations ERBN in Hz, f=frequency in kHz
Glasberg and Moore (1990)

27. Psychophysical Tuning Curves
Fig.: Moore 2004
The psychophysical tuning curves (PTC) were determined by measuring the masked detection thresholds for 6 sine tones which were presented 10 dB above sensation level (black circles). The masker was a sine tone as well which was varied in level (Data from Vogten, 1974).

28. Tuning curves of the auditory nerve
Neurons tuned toward higher frequencies
CFs
Each curve shows the tuning curve for a specific auditory nerve neuron of an anesthetized cat. The curves show the minimal sound pressure of a sinusoidal sound pressure to excite the neuron above a given threshold (also called frequency-threshold curves). The minimum of each curves show the CF of the neuron.
from Palmer (1987)

29. Isointensity contours
Curve near threshold
level. CF
Possible firing rate
threshold to
determine the tuning curve
Isointensity curves are another way of describing the response patterns of neurons. Here, the firing rate in spikes per seconds are depicted for sinusoids at different sound pressure levels (in this case for one auditory nerve neuron of a squirrel monkeys). Note how the increase in sound pressure level increases the firing rate, and broadens the frequency range. Note also the shift of the CF with increase in SPL.
from Rose et al. (1971)

30. Tuning curves vs. Isointensity contours
Tuning curves show the Sound pressure level that is needed at a particular frequency to exceed a threshold firing rate. Often describes behavior at low sound pressure levels.
Isointensity contours show the firing rate for a sinusoid with a given sound pressure level as a function of frequency. Often describes behavior at higher sound pressure levels.

31. Phase Sensitivity
Human responses to phase variation can be measured through stimuli that just differ in their phase, but not amplitude.

32. Amplitude Modulation Amplitude Modulation (AM) fc fc−g fc+g f
m=modulation index (m=0 no modulation, m=1 100% modulation),
fc=frequency in Hz fc
fc−g
fc+g
Sidebands f

33. Frequency Modulation (FM)
b=modulation index (b=0 no modulation, b=1 100% modulation),
fc=carrier frequency in Hz, g=modulation frequency in Hz.
For low modulation indexes, we can simulate the FM signal using quasi-frequency modulation (QFM), which consists of three sinusoids with appropriate amplitudes and phases:
Quasi-Frequency Modulation (QFM)
with fc1= fc2−g, fc1= fc3+g
AM and QFM differ only in phase, but not in amplitude. This feature makes the stimuli interesting for psychoacoustic experiments. If the listeners do not respond differently to both stimuli, the underlying processes are most likely not dependent on phase.

34. Amplitude vs. Frequency Modulation
(Fig.: Moore 2004)
Amplitude Modulation (AM)
Frequency Modulation (FM)

35. Perception of Modulation
For low modulation frequencies (e.g., g=5 Hz):
Amplitude modulation is perceived as loudness fluctuation
Frequency modulation is perceived as frequency fluctuation

36. Critical Modulation Frequency (CMF)
AM and QFM modulation thresholds for a 1-kHz sinusoidal tone as a function of the modulation frequency g. In both cases the threshold decreases with modulation frequency.
The lower graph shows the ratio b/m. At 90 Hz, the so-called critical modulation frequency (CMF) the ratio becomes one. Above this frequency, which highly correlates with the width of the auditory filter, the auditory system becomes insensitive towards the phase of the components:
->The phase of different frequency components plays only a role if they are processed by the same frequency band!
(Fig.: Moore 2004)
1000-Hz carrier

37. Audibility of single partials of a complex tone
(Fig.: Moore 2004, after data of Plomp, 1964a; Plomp and Mimpen, 1968).
The x’s and open circles show the minimal separation frequency as a function of partial frequency above which the partial can be heard out with 75% accuracy. The long-dashed curve shows the ERBN function ×1.25. Basically, partials cannot be heard out, if its share the same auditory band with other partials.

38. Masking Patterns (Fig.: Moore 2004, data from Egan and Hake, 1950)
Masking patterns (audiograms) for a narrow band of noise centered 410 Hz. The curves show the increase in threshold for a sinusoidal signal as a function of frequency. The number above each curve gives the SPL of the noise masker.

39. Excitation Patterns (Fig.: Moore 2004)
Estimation of the excitation pattern from auditory filterbank data for a 1-kHz sinusoid. For each filter band the filter amplitude at the frequency of the test tone is determined (points a-e). Afterwards, these points are plotted at the center frequency of the corresponding filter, which represents the excitation pattern.

40. Excitation Patterns
The figure shows the excitation patterns for the 1-kHz sinusoid for various sound pressure levels from 20 to 90 dB in steps of 10 dB.
(Fig.: Moore 2004)

41. Co-Modulation Masking Release1. 1.
target
1. The masker increases the detection threshold of the target
masker f
2. The threshold is not affected if a second masker is presented far enough in frequency 2. f
3. However, if we co-modulate both maskers, the detection threshold is lowered (co-modulation masking release) 3.
co-modulated
masker f

42. Co-Modulation Masking Release
Is a phenomenon that tells us how the auditory system integrates information over several frequency bands.
It is important to understand how the auditory system groups information to form one or several auditory events (See upcoming lecture on Auditory Scene Analysis).

43. Co-Modulation Masking Release
(Fig.: Hall et al. 1984)
Masker components
NOT co-modulated
Masker components
co-modulated
Test tone:
1-kHz sinusoid
Masker:
Band-pass filtered
noise

44. Temporal masking
Temporal masking occurs because of the sluggishness of the basilar membrane, and time-dependent processing of the hair-cells and other neurons (refractory time).
Simultaneous masking: masking induced by a simultaneous masker
Forward masking: masking induced by a masker that precedes the test tone in time.
Backward Masking: Masking that occurs for a target that precedes a masker
Overshoot: Initial masked threshold increase during the onset phase of the masker.

45. Noise vs. tonal masker 410 Hz, 90 Hz bandwidth 400 Hz
Egan and Hake (1950)