Irino, T

Matsui, T

Patterson, RD

Yokota, K

English

Apollo (Cambridge)

ACTA ACUSTICA UNITED WITH ACUSTICAVol. 104 (2018) 887 – 890DOI 10.3813/AAA.919247Auditory Filter Derivation at Low Levels whereMasked Threshold Interacts with AbsoluteThresholdToshio Irino1), Kenji Yokota1), Toshie Matsui1,2), Roy D. Patterson3)1)Faculty of Systems Engineering, Wakayama University, Japan. irino@sys.wakayama-u.ac.jp2)Department of Computer Science and Engineering, Toyohashi University of Technology, Japan.tmatsui@cs.tut.ac.jp3)Department of Physiology, Development and Neuroscience, University of Cambridge, UK.rdp1@cam.ac.ukSummaryThis paper reports a notched noise (NN) experiment with a large proportion of low-level, wide-notch conditionswhere masked threshold asymptotes to a low level that is near, but distinctly above, absolute threshold. Theeffects of this low level limit on the derivation of auditory filter shape are traditionally mitigated by the inclusionof an arbitrary constant, P0, in the model of NN masking. We show that the threshold limit can be explainedby assuming that there is a noise floor in the cochlea. This more physiological model of masking improves thereliability of filter shape fitting and, if the noise floor is stimulus-level dependent, the fit of the gammachirp (GC)auditory filter model is remarkably good.© 2018 The Author(s). Published by S. Hirzel Verlag · EAA. This is an open access article under the terms of theCreative Commons Attribution (CCBY4.0) license (https://creativecommons.org/licenses/by/4.0/).PACS no. 43.66.-x1. IntroductionIn an early NN filter-shape experiment that included verywide notches, threshold asymptoted to a low level some-what above absolute threshold [1]. In subsequent papers,to prevent these asymptotic thresholds from distorting thederived filter shape, some researchers simply avoided widenotch conditions when the noise spectrum level was be-low 40 dB SPL [2], and some included a threshold floorparameter, P0, in the power spectrum model (PSM) ofmasking[3].This paper reports a NN experiment with a large pro-portion of low-level, wide-notch conditions to test the as-sumption that the threshold limit is produced by a cochlearnoise floor in the region of the signal. This modificationmakes it possible to include absolute threshold explicitlyin the PSM of NN masking.2. The experimentA standard two-alternative, forced-choice, NN experimentwas performed with noise spectrum levels ranging froma moderate 38 dB down to a very low −12 dB in 10-dBReceived 28 February 2018,accepted 3 August 2018.steps. The signal frequency fswas 2.0 kHz. The width ofthe noise bands was 0.4fs.2.1. Notched-noise conditionsThe normalized frequency distances from the signal tothe nearer edges of the lower and upper noise bands{Δfl/fs,Δfu/fs} were {0, 0; 0.1, 0.1; 0.2, 0.2; 0.4, 0.4;0.3, 0.5; 0.5, 0.3}. The same notches were used at eachspectrum level. Initially, threshold was measured for fivenoise spectrum levels between 38 and −2 dB in random or-der (for all notch widths and levels). Subsequently, thresh-old was also measured for −12 dB to ensure that the dataset included a substantial number of thresholds in the re-gion of absolute threshold.2.2. Equipment and listenersEight normal-hearing (NH) listeners participated in the ex-periment after giving informed consent. They all had hear-ing levels (HLs) less than 20 dB between 125 and 8000Hz.The experiment was approved by the local ethics commit-tee of Wakayama University.The stimuli were presented over headphones (PM-1,OPPO) via a USB interface (HA-1, OPPO) at a 48-kHzsampling rate and 24-bit resolution. The listeners wereseated in a sound attenuated room.© 2018 The Author(s). Published by S. Hirzel Verlag · EAA.This is an open access article under the terms of the CC BY 4.0 license. 887ACTA ACUSTICA UNITED WITH ACUSTICA Irino et al.: Auditory filter derivationVol. 104 (2018)0 0.1 0.2 0.3 0.4Δ f / fs-10010203040506070Threshold(dBSPL)3828188-2-12Figure 1. Average NN threshold (solid lines) for eight listeners,and their average absolute threshold (dashed line). The signalfrequency was 2.0 kHz. The abscissa is normalized notch width(Δf/fs). The circles (◦) show symmetric notch conditions; theright-pointing triangles () show conditions with additional shift-ing of the upper noise band by 0.2; the left-pointing triangles ()show conditions with additional shifting of the lower noise bandby 0.2. The parameter beneath each threshold curve is noise spec-trum level which was the same for the lower and upper bands.The noise levels for the triangles are the same as the levels of thethreshold curves just above.2.3. ResultsFigure 1 shows average NN threshold for the eight listen-ers at the six masker levels (solid lines), along with theaverage absolute threshold (dashed line). The thresholdsassociated with the two highest noise levels, 28 and 38 dB,remain well above absolute threshold out to the widestnotches. At lower noise levels (18, 8 and −2), however,threshold is limited by the proximity of absolute thresh-old, and threshold for the −12 dB noise level convergesonto absolote threshold at the wider notch widths. The setof curves suggests that NN threshold should converge ontoabsolute threshold in the masking model. In earlier stud-ies, absolute threshold was not directly represented in themodel used to derive the shape and gain of the auditoryfilter.3. Auditory filter derivationThe power spectrum model of masking produces an es-timate of signal threshold,ˆPs(on a dB scale), using thefollowing pair of equations,ˆPs= K +ˆPext, (1)ˆPext= N0+ 10 log10	flmaxflminW (f ) df +	fumaxfuminW (f ) df,(2)whereK is the signal-to-noise ratio at the output of the au-ditory filter andˆPextis an estimate of the external noise thatpasses through the auditory filter.N0is the spectrum levelof the noise in the bands that produce the notch, andW (f )is the power weighting function of the auditory filter.When the auditory filter is modeled with the gammachirp,Gc(f ) [4], the filter weighting function, W (f ) becomes|T (f )Gc(f )|2where T (f ) is the transfer of sound fromthe free field or headphone to the input of the cochlea.3.1. The P0threshold limitGlasberg andMoore [3] introduced a term, P0, to representthe lower limit of NN threshold and prevent it from distort-ing the representation of the tails of the auditory filter. Inthis case,ˆP(P0)s= 10 log1010ˆPs/10+ 10P0/10. (3)The coefficients of the auditory filter were estimated usingthe least-squared method to minimize the error betweenthe measured thresholds, Ps, and the thresholds predictedby the model,ˆPs; that isc(P0)gc= argmincgc1NNi=1(Psi−ˆP(P0)si)2, (4)where c(P0)gcis a vector of the GC coefficients, {b1, c1, f(0)rat,f(1)rat, b2, c2}, plus the constants {K&P0}. Glasberg andMoore showed that P0is effective in reducing rms error.They suggested that P0is related to absolute threshold butthey did not explain the relationship in detail. This stan-dard model of auditory filter derivation will be referred toas the “P0model” in what follows.3.2. A cochlear-noise threshold limitOne method of incorporating absolute threshold into thepower spectrum model of masking is to assume that thereis some form of noise floor in the cochlea, Nc(f ). Inthat case, the power spectrum model has two components(Equation 5), as in the P0model (Equation 3), and the firstcomponent,ˆPext, is produced by the external noise (Equa-tion 2). The second component,ˆPint, is produced by aninternal, cochlear noise, as in Equation (6).ˆPs= K + 10 log1010ˆPext/10+ 10ˆPint/10, (5)ˆPint= 10 log10	famaxfaminNc(f )Gc(f )2df. (6)Gc(f ) is the filter function used in the iterative fitting pro-cess. Nc(f ) is the spectral distribution of the cochlearnoise and the integral is performed over the human au-dible range. We assumed Nc(f ) is similar to the 0-dB HLfunction [5] which is close to that of the internal “self-generated noise” recently reported by Buss et al. [6]. Butthe selection of function would not affect the resulting fitbecause, in this study, the data were all gathered at onesignal frequency (2 kHz). Any variation associated withdifferent parameter values will be absorbed by a constantNc(fref) associated with the reference frequency, fref.888Irino et al.: Auditory filter derivation ACTA ACUSTICA UNITED WITH ACUSTICAVol. 104 (2018)500 1000 1500 2000 2500 3000 4000Frequency (Hz)-60-50-40-30-20-100102030(a)Gain(dB)500 1000 1500 2000 2500 3000 4000Frequency (Hz)-60-50-40-30-20-100102030(b)Gain(dB)500 1000 1500 2000 2500 3000 4000Frequency (Hz)-60-50-40-30-20-100102030(c)Gain(dB)20 40 60 80 100CP input (dB)00.511.522.533.5(d)RelativeERBwidthERBN(241 Hz)P0NcNc(LD)0 20 40 60 80 100CP input (dB)20406080100(e)CPoutput(dB)Min SlopeP0: 0.21 (dB/dB)P0Nc: 0.20 (dB/dB)NcNc(LD): 0.19 (dB/dB)Nc(LD)Figure 2. Upper row: GammaChirp auditory filter sets derived with (a) theNcmodel, (b) the P0model, and (c) theN(LD)cmodel fromthe 36 NN thresholds shown in Figure 1. The abscissa is warped to the ERBNnumber scale but it is still labeled in frequency units (Hz).Filters are plotted for cochlear input levels between 30 and 70 dB in 10-dB steps. The thick solid lines show the GC filters; the thindashed lines show the corresponding pGC and HP-AF components of the GC filter as detailed in [4]. Lower row: Relative bandwidths(d) and input-output functions (e) for the Nc, P0, and N(LD)cfilter sets. CP (Cochlear Partition) input is the dB value at the input tothe cochlea which is calculated from the dB SPL value at the ear drum and the middle ear transfer function. CP output is the internalexcitation level when the input and output dB values are equalized at the CP input value of 100 dB.In the absence of external noise, the masking expression(Equation 5) reduces naturally to an estimate of absolutethreshold based on the PSM of masking; namely,ˆPabs= K +ˆPint. (7)This effectively incorporates the observed absolute thresh-olds into the auditory filter fit. The fitting criterion isc(Nc)gc= argmincgc1NNi=1(Psi−ˆPsi)2+(Pabs−ˆPabs)2, (8)where c(Nc)gcis a vector of gammachirp coefficients,{b1, c1, f(0)rat, f(1)rat, b2, c2}, plus the constants {K&Nc(fref)}.The process jointly minimizes the error associated withNN threshold and the error associated with absolutethreshold, which allows this “Nc” model of masking topredict the continuous change from low-level NN thresh-old to observed absolute threshold. The Ncinterpretationof the transition to absolute threshold provides a betterfoundation for the masking model than the ambiguousconstant, P0.3.3. Comparison of Ncand P0fitsThe Ncand P0models were initially compared in termsof the fits they provided to the full set of 36 NN thresh-olds shown in Figure 1. Each model was fitted to the 36thresholds 10 times, using different initial values for theGC coefficients, chosen randomly within a range ±20% ofthe summary coefficient values reported in [4]. The best ofthe 10 filters was the one that minimized the rms error.Figure 2a shows the best GC filter set for theNcmodel.The rms error for the NN thresholds was 2.6 dB; the errorfor absolute threshold was 0.42 dB. Thus the Ncmodel ofNNmasking provides a good fit to both aspects of the data.Figure 2a shows that the gain and the selectivity of the GCfilter increase as signal level decreases. The filter shape ismore symmetric than that reported in [4].Figure 2b shows the best GC filter set for the P0model.The rms error for the NN thresholds is 2.2 dB which isslightly less than that for theNcmodel. The filter shape issimilar to that reported in [4] where the P0model was usedin the fitting process. The P0value is 3.9 dB above absolutethreshold, indicating that the P0value cannot serve as anestimate of absolute threshold.Figure 2d shows the bandwidths of the estimated GC fil-ters. The bandwidth for theNcmodel is about 2 ×ERBNor more. The bandwidth for the P0model is narrower. Fig-ure 2e shows the input-output functions. They have a broadcompressive region between 30 and 70 dB where the min-imum slopes are 0.20 dB/dB (Nc) and 0.21 dB/dB (P0).889ACTA ACUSTICA UNITED WITH ACUSTICA Irino et al.: Auditory filter derivationVol. 104 (2018)We also compared the Ncand P0models by testingwhether they can predict the “unknown thresholds” whenthe fits were performed separately with the upper or lowerhalves of the full set of 36 NN thresholds in Figure 1 (seesupplement for details). The results showed the Ncmodelprovides more stable predictions than the P0model.In summary, the Ncmodel can explain absolute thresh-old and provide stable estimation but the resultant filtershapes seem overly symmetric.4. A level-dependent, cochlear-noise modelFinally, we constructed a model in which the cochlearnoise level depends on the level of the external noise at fre-quencies distant from the signal. In this N(LD)cmodel, thelevel of the internal noise spectrum, on a dB scale, varieslinearly with the external NN level,N0, asN(LD)c(dB)(f ) := Nc(dB)(f ) + nLD·N0−N(abs)0. (9)Nc(dB)(f ) is the cochlear-noise spectrum on a dB scale.nLDis the slope of the level dependence. N(abs)0is the N0level just below that which would affect absolute thresh-old; it is less than −12 dB and may be as low as −20 dBin the current experiment. The N(LD)cmodel was fitted tothe full set of thresholds shown in Figure 1. Figure 2cshows the auditory filters for the best N(LD)cmodel, inwhich nLDwas employed as an optimization parameterand nLD· N(abs)0was a constant fixed manually. The re-sultant GC filter has strong asymmetry with a steep high-frequency skirt. Most notably, the rms error for the fit tothe 36 NN thresholds was 1.0 dB – much smaller thanthe rms error for either the Ncmodel (2.6 dB) or theP0model (2.2 dB). The error for absolute threshold was1.3 dB, which is slightly greater than that of theNcmodel(0.42 dB) and is less than that of the P0model (3.9 dB).The dashed-dotted line, labeledN(LD)cin Figure 2d showsthat the bandwidth values are less than those of the Ncmodel. The dashed-dotted line in Figure 2e shows thatthe input-output function has the expected broad compres-sive region between 30 and 60 dB; the minimum slope is0.19 dB/dB. Interestingly, the estimated value of the slopenLDin Equation (9) was 0.39 dB/dB, which is highly com-pressive.These results indicate that the N(LD)cmodel of NNmasking provides an excellent fit which justifies the extracoefficient used to make the cochlear noise level depen-dent. The accuracy of the fit suggests that the hypothesisthat the cochlear noise floor depends on the external noiselevel at distant frequencies warrants further investigation.The source of the level dependence is not at all clear,however. One candidate could be distortion products em-anating from the upper noise band [7]. Another candidatecould be suppression [8]. It seems, however, unlikely be-cause the internal representations of both signal and noisewould be suppressed to the same degree and there wouldbe no effect on the level dependence. Finally, it could bea nonlinearity involved with subsequent neural transduc-tion, but that is beyond the scope of this paper. It is notclear, however, whether any of these factors could explainthe form of the level dependence observed, that is, an nLDvalue of 0.39 dB/dB.5. ConclusionsThis paper provides a detailed set of NN threshold values,including low-level noises, to show how threshold con-verges onto absolute threshold as notch width increases atlow noise levels. To explain the data, the power spectrummodel of masking was extended with the assumption thatabsolute threshold represents the effect of a noise floor inthe cochlea which limits threshold at wide notch widths.This Ncmodel of masking was shown to provide betterprediction of absolute threshold than the conventional P0model. However, the Nc-model filter shapes seem overlysymmetric. When the cochlear noise floor was made leveldependent, the resultant N(LD)cmodel provided an excel-lent fit that appears to combine the merits of both the P0andNcmodels, as well as a major reduction in the rms er-ror of the filter-shape estimation. It is not clear, however,why the level of the cochlear noise should depend on thespectrum level of the external masking noise.AcknowledgementThis work was partially supported by JSPS KAKENHIGrant Number JP16H01734.References[1] R. D. Patterson, I. Nimmo-Smith: Off-frequency listeningand auditory-filter asymmetry. J Acoust Soc Am 67 (1980)229–245.[2] B. R. Glasberg, B. C. J. Moore: Derivation of auditory filtershapes from notched-noise data. Hear Res (1990) 103–138.[3] B. R. Glasberg, B. C. J. Moore: Frequency selectivity as afunction of level and frequency measured with uniformlyexciting noise. J Acoust Soc Am 108 (2000) 2318–2328.[4] R. D. Patterson, M. Unoki, T. Irino: Extending the domainof center frequencies for the compressive gammachirp au-ditory filter. J Acoust Soc Am (2003) 1529–1542.[5] ANSI: ANSI S3.6-2010 Specification for audiometers,American National Standards Institute, New York, 2010.[6] E. Buss, H. L. Porter, L. J. Leibold, J. H. Grose, J. W. HallIII: Effects of self-generated noise on estimates of detectionthreshold in quiet for school-age children and adults. Ear &Hearing 37 (2016) 650–659.[7] B. C. J. Moore, B. R. Glasberg, M. van der Heijden, A.J. M. Houtsma, A. Kohlrausch: Comparison of auditoryfilter shapes obtained with notched-noise and noise-tonemaskers. J Acoust Soc Am 97 (1995) 1175-1182.[8] T. Houtgast: Psychophysical Evidence for Lateral Inhibi-tion in Hearing. J Acoust Soc Am 51 (1972) 1885–1984.890

Auditory filter derivation at low levels where masked threshold interacts with absolute threshold

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Auditory filter derivation at low levels where masked threshold interacts with absolute threshold

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