Gammachirp Auditory Filter

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Gammachirp Auditory Filter

• Alex Park
• May 7th, 2003

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Project Overview

• Goal
• Investigate use of (non-linear) auditory filters
  for speech analysis
• Background
• Sound analysis in auditory periphery similar to
  wavelet transform
• Comparison
• Traditional Short-Time Fourier analysis
• Gammatone wavelet based analysis (auditory
  filter)
• Extension
• Gammachirp filter has level-dependent parameters
  which can model non-linear characteristics of
  auditory periphery
• Implementation
• Specifics of Gammachirp implementation
• How to incorporate level dependency

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Auditory Physiology

• Sound pressure variation in the air is transduced
  through the outer and middle ears onto end of
  cochlea
• Basilar membrane which runs throughout the
  cochlea maps place of maximal displacement to
  frequency

Outer ear
Auditory Nerve
Middle ear
Cochlea
Low freq (200 Hz)
Cortex
High freq (20 kHz)
Basilar Membrane
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Motivation Why better auditory models?

• Automatic Speech Recognition (ASR)
• ASR systems perform adequately in clean
  conditions
• Robustness is a major problem degradation in low
  SNR conditions is much worse than humans
• Hearing research
• Build better hearing aids and cochlear implants
• Hearing impaired subjects with damaged cochlea
  have trouble understanding speech in noisy
  environments
• Current hearing aids perform linear
  amplification, amplify noise as well as the
  signal
• Is the lack of compressive non-linearity in the
  front-end a common link?

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Non-stationary Nature of Speech

• Why is speech a good candidate for local
  frequency analysis?

Waveform of the word tapestry
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Time-Frequency Representation

• The most common way of representing changing
  spectral content is the Short Time Fourier
  Transform (STFT)

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Spectrogram from STFT
tapestry
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STFT Characteristics

• We can think of the STFT as filtering using the
  following basis

• In the frequency domain, we are using a
  filterbank consisting of linearly spaced,
  constant bandwidth filters

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Auditory Filterbanks

• Unlike the STFT, physiological data indicates
  that auditory filters
• are spaced more closely at lower freq than at
  high freq
• have narrower bandwidths at lower frequencies
  (constant-Q)
• The Gammatone filter bank proposed by Patterson,
  models these characteristics using a wavelet
  transform.
• The mother wavelet, or kernel function, is

Tone carrier
Gamma Envelope
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Gammatone Characteristics

• Unlike the STFT, the Gammatone filterbank uses
  the following basis

• The corresponding frequency responses are

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What are we missing?

• The Gammatone filterbank has constant-Q
  bandwidths and logarithmic spacing of center
  frequencies
• Also, Gamma envelope guarantees compact support
• But, the filters are 1) symmetric and 2) linear
• Psychophysical experiments indicate that auditory
  filter shapes are
• 1) Asymmetric
• Sharper drop-off on high frequency side
• 2) Non-linear
• Filter shape and gain change depending on input
  level
• Compressive non-linearity of the cochlea
• Important for hearing in noise and for dynamic
  range

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Gammachirp Characteristics

• The Gammachirp filter developed by Irino
  Patterson uses a modified version of the
  Gammatone kernel

Chirp term
Gamma Envelope
Tone carrier

• Frequency response is asymmetric, can fit passive
  filter
• Level-dependent parameters can fit changes due to
  stimulus

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Implementation

• Looking in the frequency domain, the Gammachirp
  can be obtained by cascading a fixed Gammatone
  filter with an asymmetric filter
• To fit psychophysical data, a fixed Gammachirp is
  cascaded with level-dependent asymmetric IIR
  filters

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Comparison Tone vs. Passive Chirp outputs

• Gammatone output seems to have better frequency
  res.
• Passive Gammachirp output seems to have better
  time res.

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Comparison Tone vs. Active Chirp Outputs
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Incorporating level dependency

• As illustrated in previous slide, passive
  Gammachirp output offers little advantage on
  clean speech using fixed stimulus levels
• We can incorporate parameter control via feedback

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Sample outputs
30dB SNR
Clean
40dB SNR
20dB SNR
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References

• Bleeck, S., Patterson, R.D., and Ives, T. (2003)
  Auditory Image Model for Matlab. Centre for the
  Neural Basis of Hearing.
  http//www.mrc-cbu.cam.ac.uk/cnbh/aimmanual/Introd
  uction/
• Irino, T. and Patterson, R.D. (2001). A
  compressive gammachirp auditory filter for both
  physiological and psychophysical data, J.
  Acoust. Soc. Am. 109, 2008-2022.
• Pickles, J.O. (1988). An Introduction to the
  Physiology of Hearing (Academic, London).
• Slaney, M. (1993). An efficient implementation
  of the Patterson-Holdsworth auditory filterbank,
  Apple Computer Technical Report 35.
• Slaney, M. (1998). Auditory Toolbox for
  Matlab, Interval Research Technical Report
  1998-010. http//rvl4.ecn.purdue.edu/malcolm/int
  erval/1998-010/

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Sidenote
Clean
40 dB SNR
30 dB SNR