A Short History of Telephone Psychophysics

Transcription

1 LRR-REVIEW, April 20, History of Tel PP A Short History of Telephone Psychophysics J. B. Allen 1 AT&T Labs Research Florham Park, NJ /doc/personal/lrr.1997/aes97 talk.tex April 19, 1998

2 LRR-REVIEW, April 20, History of Tel PP CHRONOLOGICAL DEVELOPMENT ROAD MAP YEAR CONCEPT REFERENCE 1846 JND Weber 1860 Counting JNDs Fechner 1923 Hearing Threshold Fletcher and Wegel Masking wrt intensity Fletcher Tone JND Knudsen 1924 Masking Pattern Wegel and Lane Cochlear model Wegel and Lane 1928 Near-miss to Weber s law Riesz 1933 Masking and loudness Fletcher and Munson N JND (L 6I 6f) Riesz 1935 Masking as internal noise Montgomery 1938 The critical ratio and critical band Fletcher 1940 Hearing loss and loudness Steinberg and Gardner 1949 Wide band JND (J = 0:1) Miller 1950 Forward masking patterns Munson and Gardner Tones vs. NB noise maskers Egan and Hake The critical band, revisited: -4dB Stevens and Hawkins 1966 Signal detection theory Green and Swets

3 LRR-REVIEW, April 20, History of Tel PP SETTING THE STAGE: Weber The JND as internal noise 1846 Weber proposes that the just-noticeable discrimination (i.e., the JND) is proportional to the magnitude of a stimulus Examples: weight / weight B / B (B is the light intensity) I / I (I is the sound intensity) His idea: weight, B, I / perceptual noise Perceptual noise is analogous to floating point (actually -law) i.e.: I / RMS-error / mean I=I = I =I is a NOISE/SIGNAL RATIO J I=I = constant is called Weber s law PROBLEM: Weber formulated his problem in the physical domain, while the noise is internal

4 LRR-REVIEW, April 20, History of Tel PP The intensity JND reflects loudness uncertainty Perception is stochastic: Each time you hear (see) the same short tone (light) pulse, you hear (see) it with a different loudness (brightness) The intensity JND I (I) is a physical measure of this internal perceptual fluctuation The SIGNAL DETECTION MODEL of masking introduced into psychophysics by David Green in 1965: 100% % Correct 75% 50% s(t) = m(t) + α p(t) 0% α * α GAIN L Prob(L) α = 0 α = α σ L L L + L INTENSITY α = α when L= σ L

5 LRR-REVIEW, April 20, History of Tel PP SETTING THE STAGE: Fechner Fechner is called the father of psychophysics. PHYSICAL PSYCHOPHYSICAL Φ Ψ (e.g.: I, σ ) (e.g.: L, σ ) I OBSERVER L 1860 Fechner s idea was that the loudness L is proportional to the number of JND steps N JND given by: N JND Z dl Z L(L) = di I(I) He assumed that the internal noise L is constant He assumed that I=I = constant These assumptions give Fechner s Law: L(I) / log(i) Counting JNDs is a great conceptual start :) Both assumptions are wrong :(

6 LRR-REVIEW, April 20, History of Tel PP BASIC MODEL OF OBSERVER By transforming all the physical measurements to the loudness domain, Allen and Neely 1997 determined L(L) PHYSICAL Φ PSYCHOPHYSICAL Ψ (e.g.: I, σ ) (e.g.: L, σ ) I OBSERVER L log(loudness) Fechner s Hypothesis: L=const. PIN model: L3 L2 L1 L0 L L L ν = d log(l) d log(i) L= L I I I I0 I1 I2 WEBER S LAW: I / I = const. I3 log(intensity) Transform from I(I) to L(L) Since the loudness is Power-Law where L(I) / I : I L I(I) = (I) L(L) which is the same as SNR I = SNR L :

7 LRR-REVIEW, April 20, History of Tel PP SETTING THE STAGE: Bell Invention of the magnetic earphone (A.G. Bell) 1915 Invention and deployment of the vacuum tube (Arnold) 1917 Calibration of the thermophone (Arnold and Crandall): the first precise source of wideband sound

8 LRR-REVIEW, April 20, History of Tel PP THE UNMASKED THRESHOLD 1922 Fletcher and Wegel are first to measure the Threshold of hearing R.M.S. Pressure (dyn/cm 2 ) * * Sensitivity of the ear Summary of results of all observers Toepler and Boltzmann (1870) Rayleigh (1877) Wead (1883) Wien (1903) Webster (1904) Abraham (1905) * Kranz (1921) Fletcher and Wegel (1922) (db SPL) Frequency (Hz) They improved the accuracy of the threshold measurement more than 3 orders of magnitude Because of their electronics revolution they could now measure the masked threshold

9 LRR-REVIEW, April 20, History of Tel PP THE MASKED THRESHOLD 1923 Fletcher asked: How does the threshold change in the presence of a masking signal? Slope of masking growth is a NL cochlear effect MASKING of by a 400 Hz 80 M(Im,fp) (db SL) Im (db) fp (khz) 3 4 M(Im,fp) (db SL) Hz TONE MASKER and a TONE PROBE Im (db SL) M = I Freq

10 LRR-REVIEW, April 20, History of Tel PP DEMO: ASYMMETRY OF MASKING Intensity A: Upward spread of masking (Fp > Fm) masker probe 1200 (Hz) x PLACE EAR EQUIPMENT Intensity B: Downward spread of masking (Fp < Fm) masker 2000 (Hz) probe x PLACE

11 LRR-REVIEW, April 20, History of Tel PP MASKING PATTERNS The masking pattern, first quantified by Wegel and Lane in 1924, is the masking expressed in terms of a basilar membrane place coordinates

12 LRR-REVIEW, April 20, History of Tel PP COCHLEAR MODEL Wegel and Lane s 1924 paper also introduced a theoretical cochlear model, as an electrical circuit

13 LRR-REVIEW, April 20, History of Tel PP ROAD MAP YEAR CONCEPT REFERENCE 1846 JND Weber 1860 Counting JNDs Fechner 1923 Hearing Threshold Fletcher and Wegel Masking wrt intensity Fletcher Tone JND Knudsen 1924 Masking Pattern Wegel and Lane Cochlear model Wegel and Lane 1928 Near-miss to Weber s law Riesz 1933 Masking and loudness Fletcher and Munson N JND (L 6I 6f) Riesz 1935 Masking as internal noise Montgomery L = L 1938 The critical ratio and critical band Fletcher 1940 Hearing loss and loudness Steinberg and Gardner 1949 Wide band JND (J = 0:1) Miller 1950 Forward masking patterns Munson and Gardner Tones vs. NB noise maskers Egan and Hake The critical band, revisited: -4dB Stevens and Hawkins 1966 Signal detection theory Green and Swets

14 LRR-REVIEW, April 20, History of Tel PP PURE-TONE INTENSITY DISCRIMINATION Weber s law says that I / I 1928 Riesz establishes the near-miss to Weber s law for tones Riesz used two beating tones 3 Hz apart for this measurement (i.e., 1000 Hz masker and a low-level 1003 Hz probe) Riesz s pure tone JND RELATIVE PROBE INTENSITY (DI/I) INTENSITY of 1000 Hz tone (db SL) The near-miss to Weber s Law results from the fact that the internal noise L / L(L) is not independent of L Allen and Neely 1997

15 LRR-REVIEW, April 20, History of Tel PP LOUDNESS LEVEL AND LOUDNESS 1933 Fletcher and Munson s Iso-loudness curves " " Loudness level table I; "o" Values from figure Loudness level (db SL) FREQUENCY (Hz) Below about 500 Hz the dynamic range decreases from 100 db to 50 db 1933 Fletcher and Munson s loudness growth data based on loudness additivity is now called Stevens Law L(I) = I 0: Fletcher Munson 1933 L(I) at 1 khz L(I), 2L(I), 10L(I) L(I) = L( 1000 I) 2 L(I) = L( 8 I) L(I) Loudness vs. intensity for 1, 2, and 10 equally loud components INTENSITY (db SL)

16 LRR-REVIEW, April 20, History of Tel PP RIESZ S COUNTING RATIO HYPOTHESIS By 1933, Riesz was honing Fechner s 1860 (incorrect) proposal that L = const. and N JND / L Using his I=I JND data, and Fletcher and Munson s L(I) data, Riesz showed: The number of tone JNDs is solely a function of loudness Z di = F (L 6I 6f) N JND I(I) where F () is some function of L, butnot a function of intensity or frequency Therefore Fechner s linear hypothesis L = N JND was wrong Riesz s relationship suggests that the JND is an internal noise

17 LRR-REVIEW, April 20, History of Tel PP BASIC MODEL OF OBSERVER 1935 The JND I(I) and the masking M (I m f p ) are loudness noise (Montgomery)

18 LRR-REVIEW, April 20, History of Tel PP Loudness and the JND 1938 Stevens and Davis found that for tones the number of JNDs is proportional to the root-loudness: N JND Z dl L = L0:4545 Working backwards, with L(L) = counting formula, p L in the JND N JND = Z dl pl = 2L 0:5 This shows that the loudness noise is close to Poisson 10 5 DL vs. Loudness 10 4 DL Loudness

19 LRR-REVIEW, April 20, History of Tel PP TONES VERSUS NOISE The internal noise is estimated for the cases of tones and WB noise, and they are the same Allen and Neely1997 Assuming we know SNR L (L), given the loudness L, we may calculate the internal noise L = L since L (L) = L SNR L (L) :

20 LRR-REVIEW, April 20, History of Tel PP Effect of correlations between a masker and probe 1950 Egan and Hake show a large asymmetry of masking PROBE THRESHOLD INTENSITY (db SL) MASKER: 65 db SL, 400 Hz PURE TONE 90 Hz BAND OF NOISE PROBE FREQUENCY (Hz) Masking of equally-loud tone and narrow-band noise α MASKER m(t) SIGNAL s(t) = m(t) + p(t) α PROBE p(t) s(t) = m(t) + p(t) e = SNR L (L)

21 LRR-REVIEW, April 20, History of Tel PP Topics DATE Concept/Law Name -correlate -source 1860 Weber s Law Internal noise Loudness SNR Neural noise 1924 Upward spread masking growth NL-ity at noise site 1924 Critical band 1 spread of masking cochlear filter 1933 Critical band 2 Loudness additivity cochlear filter 1940 Critical band 3 WB masking Critical ratio cochlear filter 1933 Stevens Law Loudness growth recruitment loss OHC compression 1940 recruitment Loudness growth recruitment loss OHC damage

22 LRR-REVIEW, April 20, History of Tel PP Mathematical Development Name (abbreviation) Symbol Definition Intensity I Eq.6orE[ e I] Decibel level 10 log 10 (I=I ref ) Energy/Intensity detector e I Model decision variable Single trial loudness e L loudness decision variable Loudness L E[ e L] Loudness s.d. e L E[( L(I) ;L(I)) 2 ] 1=2 dl Intensity s.d. I L = Probe masker pressure ratio di Eq. 8 Intensity increment I() I() ; I(0) Loudness increment L() L() ; L(0) d-prime d 0 () I()= I = L()= L Threshold probe scale factor d 0 ( ) 1 Intensity JND (JND I ) I I( ) Loudness JND (JND L ) L L( ) Weber Fraction J I=I Intensity SNR (SNR I ) SNR I I= I Intensity detector SNR (SNR I ) SNR I I= I Loudness SNR (SNR L ) SNR L L= L Decilog loudness L log 10 log 10 (L) Loudness exponent dl log =d

23 IHC LRR-REVIEW, April 20, History of Tel PP V B V c INPUT SIGNAL MIDDLE EAR COCHLEAR FLUID BM IMPEDANCE K bm (V ) ohc TECTORIAL MEMBRANE OUTER HAIR CELLS SLOW ACTING ACTIVE FEEDBACK R C INNER HAIR CELLS AUDITORY NERVE NOISE MODEL OF INNER HAIR CELL MAGNITUDE GAIN: CILIA/Pin (db) GAIN: BM/Pin (db) BM RESP 60 db 80 db 60 db 80 db 20 db 20 db 0 db 0 db BM-TM FILTER Z 0 db LOG-MAGNITUDE BM IMPEDANCE FREQUENCY (Hz) 80 db PLACE X Neural Tuning for 5 khz tonal stimulus ( db SPL) 14 db TM OHC TENSION 124 db BM Distance from Stapes (cm)