1. Gammachirp Auditory Filter
Alex Park
May 7th, 2003

2. Project Overview Goal: Background: Comparison: Extension:
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

3. 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
Cochlea
Auditory Nerve
Low freq (200 Hz)
Cortex
High freq (20 kHz)
Basilar Membrane

4. 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?

5. Non-stationary Nature of Speech
Why is speech a good candidate for local frequency analysis?
Waveform of the word “tapestry”
/t/
transient
/ae/
tone
/s/
noise

6. Time-Frequency Representation
The most common way of representing changing spectral content is the Short Time Fourier Transform (STFT)
Power
FFT

7. Spectrogram from STFT
“tapestry”

8. 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
Freq (Hz)

9. 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
Gamma Envelope
Tone carrier

10. Gammatone Characteristics
Unlike the STFT, the Gammatone filterbank uses the following basis
The corresponding frequency responses are
Freq (Hz)

11. 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

12. Gammachirp Characteristics
The Gammachirp filter developed by Irino & Patterson uses a modified version of the Gammatone kernel
Gamma Envelope
Tone carrier
Chirp term
Frequency response is asymmetric, can fit passive filter
Level-dependent parameters can fit changes due to stimulus

13. 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

14. Comparison: Tone vs. Passive Chirp outputs
Gammatone output seems to have better frequency res.
Passive Gammachirp output seems to have better time res.

15. Comparison: Tone vs. Active Chirp Outputs

16. 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
Get stimulus
level/channel
Filter w/ level
specific filter S1 S2 :
SN-1 SN
For each time frame
Reconstruct
Frames

17. Sample outputs
Clean
30dB SNR
40dB SNR
20dB SNR

18. References
Bleeck, S., Patterson, R.D., and Ives, T. (2003) Auditory Image Model for Matlab. Centre for the Neural Basis of Hearing
Irino, T. and Patterson, R.D. (2001). “A compressive gammachirp auditory filter for both physiological and psychophysical data,” J. Acoust. Soc. Am. 109,
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 #

19. Sidenote
Clean
40 dB
SNR
30 dB
SNR