A physiologically motivated gammachirp auditory filterbank
Toshio Irino (NTT Communication Sciences. Lab. Japan)
Masashi Unoki (CNBH, Univ. Cambridge/JAIST)
Roy D. Patterson (CNBH, Univ. Cambridge)
Sept. 2000 – August 2001
Early HistoryHuman Masking Data
Roex filter Gammachirp filter
Schofield and Cooke, 1985
Irino and Patterson, 1997Mag. Spectrum Gammatone AF
Well-defined impulse response
Recent Developments (1)Physiological Data
de Boer and de Jongh (1978)
de Boer and Nuttall (1997)
.
20
150 1.0
Time (ms)
0.5 1.5
Gamma-distribution envelope
Inst
. F
req.
(H
z)
Ear phone
Stimulusgenerator
Amplifier
Analog signalInput
'Event'input
Computer
Estimation ofauditory filter
response:revcor function
Physiol. prep. animal
(a) Experimental setup
(b) Filter Response (guinea pig)
Trigger
'Gliding'instantaneous
frequency
BF=18kHz
Gammachirp
Gamma tone
chirp
Recent Developments (2)
Chirp in Carney’s Revcor data (1999) » level-independent
Chirp in BMM observed post-mortem at high SPL (Recio et al. 1998). » chirp is a property of passive BM response
Compressive gain in membrane motion
» also in human masking data» on frequency but not off frequency
Input
Disp.
Input Level
Compressive
Chirp in Revcor data (Carney et al., 1999)
Zero crossings
chirpNot level dependent
Noise LevelWaveform
Instant.Freq.
Where is level dependency?
Analytic gammachirp (Irino and Patterson, 1997)
Decomposition type (Irino and Unoki, 1999)
Physiological gammachirp (Irino and Patterson, 2000)
GT Asymmetric func.
GT LP-AC HP-AC
Level dependent shape
Level independent shapeLevel dependent cf
GT LP-AC HP-AC
Physiological Gammachirp Fitted to human masking data of Rosen and Baker (1994), at 2 kHz
Vary centre frequency of highpass, asymmetric function with level
tails must converge
tails converge
Passive BM Gain change
Filterbank structure
(A)Linear
Gammatone Filterbank
(D) Parameter Controller
(c) Linear Gammachirp
Filterbank Output
(d) Gammachirp Filterbank Output
(C) Asymmetric
Compensation Filterbank
(B)Linear
Asymmetric Compensation
Filterbank
(b) Linear Gammatone
Filterbank Output
IIR gammatone( Slaney, 1993 )
IIR Asymmetric Compensation Filter (Irino & Unoki, 1999)
(a) Signal Input
Current work (1) Cross frequency parameter constraints in the gammachirp filterbank
500, 2k, 4k
Fitted to human masking data of Rosen, Baker and Darling (1998)
Left tails are a little high.
It is possible to reduce the rms error.
Note: 250, 1k, 3k, and 6kHz data omitted for clarity
Current work (2)Constructing a parameter controller
(A)Linear
Gammatone Filterbank
(D) Parameter Controller
(B), (C)Asymmetric
Compensation Filterbank
(C) Asymmetric
Compensation Filterbank
(A)Linear
Gammatone Filterbank
(D) Parameter Controller
(B) LinearAsymmetric
Compensation Filterbank
• Analytical type (Irino & Unoki, 1999)
• Physiological type
LILI
LI
LI
LI Wei
ghti
ng Σ
Convert Activity
to Para-
meter
K-th Parameter Control Unit
Varying Param. c
Varying center freq.
from adjacentchannels
k-th k-th
Summary
Physiological gammachirp filter» Consistent with physiological data
– Level-independent chirp» Excellent fit to human masking data
– Level-dependent gain and filter shape A physiological gammachirp filterbank
» Enable us to simulate an active BM
Mathematical presentationPhysiological Gammachirp
Gammachirp
n , b1 , c1
fp1
AsymmetricFunction
fr2
b2 , c2
Peak Frequency
Gct ( f ) a exp(c
1
1)
2[{b1ERB(fr 1)}2 ( f fr1 )2 ]
n exp(c2 2 )
Passive gammachirp Asymmetric function
1arctan ( f f
r1) / b
1ERB( f
r1)
2 arctan ( f fr 2 ) / b2 ERB(fr 2 )
Level-independent
Level-dependent
Center Frequency
fr2 (d 0 d 1 PS ) fp1
2fr / fs
IIR Asymmetric Compensation Filter
4 cascaded 2nd order IIR filter:
Symmetrically placed poles and zeros, smaller than 1
HC (z) HCk (z)k
HCk (z) (1 rke
j k z 1)(1 rke j k z 1)
(1 rkejk z 1)(1 rke
j k z 1)
rk exp{ k p1 2 bERB( fr ) / fs}
k 2{ fr 2k 1p2 cbERB( fr )}/ fs
k 2{fr 2k 1p2 cbERB( fr )}/ fs
Good Approximation
ー Original Gammachirp
-- IIR Gammachirp rms error: 0.68 dB
(90 data pairs)
ー Asymmetric function-- IIR Asymmetric Compensation filter
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