Transcript Gammachirp Auditory Filter SPOKEN LANGUAGE SYSTEMS Alex Park May 7

SPOKEN LANGUAGE SYSTEMS
Gammachirp Auditory Filter
Alex Park
May 7th, 2003
MIT Laboratory for Computer Science
Project Overview
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• 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
Middle ear
Auditory Nerve
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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transient
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/ae/
tone
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noise
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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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FFT
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Power
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Time
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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
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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
at n 1 exp( 2b1 ERB ( f c )t )  exp( j 2f c t )
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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Freq
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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
at n 1 exp( 2b1 ERB ( f c )t )  exp( j 2f c t  jc ln t )
Gamma Envelope
Chirp term
Tone carrier
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Impulse response
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Freq (Hz)
• 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
Level dependent
chirps
Gammachirp
Filter Gain(dB)
Filter Gain (dB)
Level dependent
asymmetries
Asymmetric
Compensation Filter
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Frequency (Hz)
Gammatone
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Passive
Gammachirp
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Frequency (Hz)
Comparison: Tone vs. Passive Chirp outputs
Gammatone Spectrogram
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Time (s)
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Passive Gammachirp Spectrogram
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• 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
Gammatone
Active Gammachirp
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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
Compute
Passive GC
Spectrogram
Segment into
frames
For each time frame
Reconstruct
Frames
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Filter w/ level
specific filter
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Get stimulus
level/channel
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Sample outputs
Clean
30dB SNR
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/Introduction/
• 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 PattersonHoldsworth 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/interval/1998-010/
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Sidenote
Clean
40 dB
SNR
30 dB
SNR
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