INTRODUCTIONINTRODUCTIONI. EXPERIMENT 1. FORWARD MASKING WITH A 6-kHzII. EXPERIMENT 2. MEASURING COMPRESSION ATIII. CONCLUDING REMARKSIV. SUMMARYACKNOWLEDGMENTSAPPENDIX: EFFECTS OF BACKGROUND NOISEA behavioral measure of basilar-membrane nonlinearityin listeners with normal and impaired hearingAndrew J. OxenhamInstitute for Perception Research (IPO), P.O. Box 513, 5600 MB Eindhoven, The NetherlandsChristopher J. PlackLaboratory of Experimental Psychology, University of Sussex, Brighton, E. Sussex BN1 9QG, England~Received 16 July 1996; revised 5 February 1997; accepted 14 February 1997!This paper examines the possibility of estimating basilar-membrane ~BM! nonlinearity using apsychophysical technique. The level of a forward masker required to mask a brief signal wasmeasured for conditions where the masker was either at, or one octave below, the signal frequency.The level of the forward masker at masked threshold provided an indirect measure of the BMresponse to the signal, as follows. Consistent with physiological studies, it was assumed that the BMresponds linearly to frequencies well below the characteristic frequency ~CF!. Thus the ratio of theslopes of the masking functions between a masker at the signal frequency and a masker well belowthe signal frequency should provide an estimate of BM compression at CF. Results obtained fromnormally hearing listeners were in quantitative agreement with physiological estimates of BMcompression. Furthermore, differences between normally hearing listeners and listeners withcochlear hearing impairment were consistent with the physiological effects of damage to thecochlea. The results support the hypothesis that BM nonlinearity governs the nonlinear growth ofthe upward spread of masking, and suggest that this technique provides a straightforward method forestimating BM nonlinearity in humans. © 1997 Acoustical Society of America.@S0001-4966~97!01706-2#PACS numbers: 43.66.Dc, 43.66.Ba, 43.66.Sr, 43.66.Mk @WJ#INTRODUCTIONPhysiological studies of cochlear mechanics have estab-lished that the response of the basilar membrane ~BM! totones at characteristic frequency ~CF! is generally nonlinearand compressive ~Rhode, 1971; Sellick et al., 1982; Robleset al., 1986; Ruggero, 1992!. Damage to the cochlea, and inparticular the outer hair cells ~OHCs!, results in a reductionin sensitivity and a loss of compression at CF ~Ruggero andRich, 1991; Ruggero et al., 1993, 1995!. Many of the diffi-culties experienced by people with sensorineural hearing lossmay be explained in terms of the physiological changes as-sociated with damage to the cochlea. For instance, the effectof abnormal growth of loudness, or ‘‘loudness recruitment’’~Fowler, 1936!, may be due to a loss of compression in thecochlea ~Yates, 1990; Glasberg and Moore, 1992!. Similarly,the deterioration of performance in some measures of tem-poral resolution, such as gap detection in narrow-band noise~Glasberg and Moore, 1992! and the decay of forward mask-ing ~Oxenham and Moore, 1997!, can also be explained interms of loss of BM compression. Finally, a reduction in BMsensitivity to stimuli at CF results in reduced frequency se-lectivity, which is also a common symptom of cochlear hear-ing loss ~e.g., Glasberg and Moore, 1986!.Given its likely influence on perception, a measure ofcochlear compression in human hearing would be of consid-erable value. The aim of the research reported in this paper istherefore to provide a behavioral measure of BM nonlinear-ity in humans. The method applied here relates to the non-linear growth of masking ~GOM! observed when a masker iswell below the signal in frequency ~e.g., Wegel and Lane,1924; Egan and Hake, 1950!.One explanation for the nonlinear GOM when themasker is well below the signal in frequency is as follows.The BM responds linearly to tones with a frequency wellbelow CF ~e.g., Sellick et al., 1982!. A given increase inmasker level will therefore be reflected by a proportionalincrease in BM motion at the place with a CF correspondingto the signal frequency. In contrast, the BM response to thesignal at CF is compressive, and so the signal level must beincreased by more than the masker level in order to producethe same change in response at the relevant place along theBM ~Oxenham and Moore, 1995!. Essentially the same ar-gument has also been applied to differences in the rate-intensity functions of auditory-nerve fibers between stimuliat CF and those well below CF ~Stelmachowicz et al., 1987!.Accordingly, a loss of compression due to cochlear hearingloss should produce a more linear GOM function. Psycho-acoustic measurements using hearing-impaired listeners sup-port this prediction ~Stelmachowicz et al., 1987; Murnaneand Turner, 1991; Dubno and Ahlstrom, 1995; Nelson andSchroder, 1996, 1997!.While the above theory can qualitatively account for thenonlinear growth of the upward spread of masking, there is adiscrepancy between the slope of the predicted GOM func-tion, based on physiological measurements of BM nonlinear-ity, and that actually observed. For instance, most recentstudies of BM motion have observed growth in the responseto a tone at CF of around 0.2 dB/dB or less for levels aboveabout 40 dB SPL ~Sellick et al., 1982; Yates et al., 1990;Ruggero, 1992; Murugasu and Russell, 1995!. This leads to3666 3666J. Acoust. Soc. Am. 101 (6), June 1997 0001-4966/97/101(6)/3666/10/$10.00 © 1997 Acoustical Society of Americathe prediction that the slope of a GOM function for a maskerwell below the signal frequency should be five or more timessteeper than the GOM slope for an on-frequency masker. Forsimultaneous masking, a 1-dB increase in masker levelshould therefore produce a 5-dB increase in signal level. In-stead, a survey of previous studies by Stelmachowicz et al.~1987! showed that, even when the masker was an octave ormore below the signal frequency, the slope of the GOMfunction rarely exceeded 2. The slope appears to be steepestfor tone-on-tone masking ~van der Heijden and Kohlrausch,1995!, but even here maximum estimates range from be-tween 2 ~Scho¨ne, 1979! and 2.5 ~van der Heijden and Kohl-rausch, 1995!.The discrepancy between the physiological predictionsand the psychophysical results may be related to differencesin the method of stimulus presentation. In the physiologicalstudies, the response to a single tone is measured over arange of levels. In most psychophysical masking experi-ments, the masker and signal are presented