CS 551651:

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CS 551/651 Structure of Spoken Language Lecture
11 Overview of Sound Perception, Part
II John-Paul Hosom Fall 2008
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Equal-Loudness Contours

• The subjective loudness of a sine wave may be
  determined as a function of frequency, creating
  an equal-loudness contour
• Instead of measuring loudness directly, what is
  measured is how intense a 1000-Hz tone must be to
  sound equally loud as the test frequency.
• Or, how intense a test frequency must be in order
  to sound as loud as a 1000-Hz tone
• The perceived equal loudness at each frequency
  can be plotted
• Results are easily influenced by test conditions
  exact shapes should not be taken too
  seriously (Moore, p. 54)
• These contours are only for steady sounds at a
  single frequency such sounds are almost never of
  practical interest.

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Equal-Loudness Contours
minimum audible field
Equal-loudness contours, from Moore p.55
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Critical Bands

• Fletcher (1940) conducted an experiment in which
  there was bandpass noise and a single sine wave.
  The frequency of the sine wave was always at the
  center frequency of the noise, and the power
  density of the noise was fixed. The bandwidth of
  the noise was varied, and for each bandwidth the
  minimum intensity at which the sine wave could be
  perceived was determined. (With increasing
  bandwidth, the total energy of the noise
  increased).

noise
noise
sine wave
sine wave
power (dB)
0 Hz
Nyquist
0 Hz
Nyquist
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Critical Bands
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Critical Bands

• The result was that the threshold for minimum
  detectability increased with bandwidth up to a
  limit after that limit, the noise could increase
  in bandwidth and power without affecting the
  perception of the sine wave
• This implies a band-pass filter structure to
  sound perception sound is filtered by a bank of
  overlapping band-pass filters called auditory
  filters. This filter structure is based on the
  structure of the BM.
• The bandwidth of the filter is related to the
  bandwidth of the noise at which the sine-wave
  threshold no longer increases. This bandwidth is
  called the critical bandwidth (CB)
• Within one band, if the signal-to-noise ratio
  exceeds some fixed threshold, the signal (sine
  wave) will be heard, independent of whats
  happening in other bands. This threshold may
  vary from person to person, typically 0.4

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Critical Bands

• The auditory filters can be approximated by
  rectangular filters, but better determination of
  the filter shape is possible.
• The critical bandwidth at a particular frequency
  can be estimated using the formulawhere P is
  the intensity of the signal, N0 is the intensity
  of the noise over a 1-Hz range, K is the
  threshold of detectability (usually 0.4), and W
  is the CB.
• For example, the CB at 1000 Hz is 160 Hz
  however, in reality rectangular filters are not
  accurate the shape changes with frequency and
  amplitude
• Better approximations of the auditory filters
  look like this

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Critical Bands
The shape of auditory filters, as a function of
frequency (as determined from masking
experiments) and amplitude (as determined from
notched-noise experiments) (From Moore, p.
105, 110)
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Critical Bands

• In general, CBs are nearly symmetric below levels
  of 45 dB at higher energies, bandwidth increases
  and cutoff skirt sharper above the center
  frequency.
• Cutoff skirt of 65 dB/oct. at 500 Hz to 100
  dB/oct. at 8 kHz.
• For frequencies lt 500 Hz, CB is about 100 Hz for
  frequencies gt 500 Hz, CB increases with
  frequency, bandwidth of 700 Hz near 4 kHz
• For frequencies above 1000 Hz, ratio of frequency
  to bandwidth roughly constant, Q5 or 6.
• If two sounds occur within one critical band, the
  sound with much higher energy dominates
  perception masks the other sound.
• From critical bands, models of perceptual
  non-linear warpings of the frequency scale have
  been developed, namely the Bark and Mel scales

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Mel Scale and Bark Scale
Mel scale Bark scale
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Masking

• Masking is a phenomenon in which perception of
  one sound is obscured by the presence of another
  sound
• Masking can occur in both the time and frequency
  domains, and prevents us from computing perceived
  loudness of a complex tone as the sum of its
  components.
• Frequency masking can be shown by fixing one
  sound (sine wave at a given frequency and
  intensity) and varying a second sine waves
  intensity to determine at what intensity it can
  be perceived.
• For example, given one tone at 1200 Hz and 80 dB,
  how loud does a second tone at X Hz have to be in
  order to be heard? This threshold can be
  plotted, as well as what the perceived sound is
  like when above the threshold

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Masking
(1929)
From OShaugnessy, p. 126
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Masking

• Masking occurs in both time and frequency
  domains two successive signals within the same
  CB may show masking effects
• For example, noise will mask a following tone if
  the noise is sufficiently loud and the delay
  between noise and tone is short (forward masking)
• Energy needed to mask the tone increases with
  delay and duration of tone beyond 100 - 200 msec
  no masking occurs
• Backward masking occurs (a tone may be masked by
  a subsequent noise), but only within a 20 msec
  window.
• Backward masking may not be purely involuntary
  trained subjects may show no backward masking
  (Moore, p. 129)

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Masking Complex Stimuli

• These CB and masking experiments typically use
  simple stimuli sine waves, clicks, and/or
  band-pass white noise
• Processing of complex sounds not as simple as
  extrapolating effects of simple sounds
• For example, phase-locking is suppressed in
  regions between speech formants, enhancing the
  effect of formants.
• Complex sounds are louder if they occur over more
  than one critical band
• Two tones, both individually below the threshold
  of hearing, may be perceived when played
  simultaneously roughly speaking, the total
  energy of all tones within a CB determines the
  threshold.
• In general, most phenomena can be understood in
  terms of bands of overlapping band-pass filters

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Temporal Integration

• Absolute thresholds and loudness depend on
  duration of the stimulus
• For durations lt 200 msec, intensity necessary for
  detection increases with shorter duration
• For detecting short-duration tones, the threshold
  for detection is the product of the tone
  intensity relative to an intensity-detection
  threshold for longer sounds, and a
  time-integration constant (I - IL) ? ?
  detection threshold (energy)where I is the
  intensity of the short stimulus, IL is the
  intensity at which the stimulus is detected with
  duration gt 200 msec, and ? is the integration
  time of the auditory system.
• Some experiments show that ? varies with
  frequency other experiments show that it
  doesnt at any rate, ? has a value between 150
  and 375 msec.

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Temporal Integration

• Detecting change in intensity is slightly
  different
• Usually a two-alternative forced-choice (2AFC)
  test is used(a) two successive stimuli are
  presented, which differ in one target
  aspect,(b) the subject indicates which of the
  two stimuli have more of the target aspect
  (e.g. loudness, amplitude modulation) The point
  at which 75 of responses are correct is the
  threshold for detecting the change.
• The threshold for detecting intensity has the
  following model
• For band-pass filtered noise, the ratio of ?I/I
  is constantthis is an example of Webers law,
  which states that the smallest detectable change
  is proportional to the magnitude of the stimulus.
  Usually, ?L is 0.5 to 1 dB

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Temporal Integration

• For pure tones, Webers law doesnt quite hold a
  plot of ?I to I yields a line with slope 0.9
  instead of 1.0 (discrimination improves slightly
  at higher intensity levels)
• The time-domain window sizes for computing I and
  ?I are not specified by the model within one
  frequency band, a large window for computing I
  and smaller window for computing ?I can show
  relatives energy changes within the band

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Pitch Perception

• Pitch is the perceived main frequency of a sound
  closely related to objective measure of F0.
• Timing Theory of PitchLower frequencies have
  pitch estimated based on phase-locking
  (time-synchronous firing of neurons)
• Place Theory of PitchAll frequencies have pitch
  estimated based on location on BM at which
  neurons fire most frequently
• Pitch can be perceived even when the fundamental
  frequency is not present pitch determination
  based on higher harmonics (e.g. telephone-band
  speech which has energy only gt 300 Hz)
• Harmonics in F1 region especially important for
  pitch
• Both timing and place are important timing
  allows fine resolution, place allows pitch
  perception in higher frequencies

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Pitch Perception

• Frequency discrimination of pure tones the
  smallest detectable change in frequency increases
  with frequency
• Tests done using two-alternative forced choice
  (2AFC) which has higher pitch?

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Pitch Perception

• Zwickers place model detection of pitch of pure
  tones is equivalent to detecting change in
  excitation level on low-frequency side of
  excitation pattern
• However, this model doesnt account for all
  observed phenomena, lending support to the
  phase-lock time theory in which pitch is measured
  directly by the inverse of the time between
  neural firings (at least for frequencies lt 4 kHz)

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Pitch Perception

• Pitch perception of complex tones depends on
  harmonics of the fundamental if clicks occur
  with harmonics every 200 Hz, and if all harmonics
  other than those at 1800, 2000, and 2200 Hz are
  filtered out (removed), the perceived pitch is
  still 200 Hz.
• Pattern recognition modelsBasic Idea find a
  fundamental frequency which has harmonics that
  match the existing harmonics. Details can become
  very complex (Moore, 189-192)
• Temporal modelsBasic Idea the pitch value is
  determined by the periodicity of the total
  waveform containing harmonics in other words,
  determined by constructive interference of
  several harmonics in time domain.
• No model alone accounts for all phenomena of
  perceived pitch