A physiologically motivated gammachirp auditory filterbank Toshio Irino (NTT Communication Sciences. Lab. Japan) Masashi Unoki (CNBH, Univ. Cambridge/JAIST)

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

Analytic gammachirp

Gammachirp is a gammatone times an asymmetric function

Decompose asymmetric function

a fixed lowpass AF and a variable highpass AF

Passive BM

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

Physiological gammachirpFitted to revcor data of Carney et al. (1999)

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

ポスターの構成A3X15(1.6mX1.6m)

Title (p.1)

History(p.2-5)

PhysiologicalGammachirp

(p.6-10)

Filterbank(p.11)

MathematicalPresentation

(p.15)(or p.15-17)

Future work(p.12-14)

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