ELSEVIER Wzarlng Research 73 (lYY4) 73 I-243 Characterising auditory filter nonlinearity Stuart Rosen *, Richard J. Baker Depurtmc’nt of’Phorwtic.s ud Linguistics, Unirrrsitv College London. 4 Steplwrwn W’uv, Londot~ NW’1 ?Hk, LJii (Received 8 October 1992; Revision received 24 October lYY3: Accepted 30 October lYY3) zyxwvutsrqponmlkjihgfedcbaZ Abstract An important aspect of auditory nonlinearity is that psychoacoustically mcasurcd auditory filters broaden as the level at which they arc measured increases. However, it is not yet clear whether the change in filter shape is controlled primarily by the level of the probe or that of the masker. We have therefore developed a new m&hod for fitting filter shapes to notched-noise data in which filter parameters depend explicitly on signal level (tither probe or masker). By applying this technique to a set 01 notched-noise data in which both fixed-probe and fixed-masker paradigms have been used at a range of Icvels. wc have been able to show that models in which filter parameters depend on probe level are considerably more successful than models in which filter parameters depend upon masker level. The results from this new procedure have cnablcd us to dcscribc the nonlinear changes in auditory filter shape at 2 kHz with only five parameters. Also discussed are the implications of thcsc findings for the generation of excitation patterns and for the computational implementation of simple, yet reasonably realistic nonlinear auditory filters whose shape depends on their output. zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA Kq words: Frequency selectivity; Notched-noise masking; Excitation patterns; Auditory filters: Auditory nonlinearity 1. Introduction Perhaps the most fundamental property of the pe- ripheral auditory system is that it operates as a fre- quency analysrr. One popular way to conceptualise the frequency-analytic properties of the ear is as a bank of bandpass filters, typically known as auditory filters in psychoacoustical studies. Although often assumed to be linear (especially for computational purposes), it has long been known that auditory filters are inherently nonlinear. In particular, a number of notched-noise masking studies have shown that auditory filter band- widths typically increase with level (e.g., Rosen and Stock, 1997; Weber, 1977) in a way which is at least qualitatively similar to changes in basilar membrane tuning with level (Rhode, 1971; Ruggero et al., 1992). Because of this nonlinearity, there is an important controversy as to whether the masker should be fixed in level across a set of notches (and the probe level varied to determine a masked threshold) or whether * Corresponding author. (Present address) Northwestern University, Audiology and Hearing Sciences Program, Frances Searle Building, 2299 North Campus Drive, Evanston IL 6020X-3550. LISA. Fax: (70X) 491-2523: e-mail: polyfit@ mcrle.acns.nwu.edu. 037X-S955/Y4/$1~7.00 ,C’m 1994 Elsevier Science B.V. All rights reserved SSDI ~)37X-5~)5gtYi)EoIX4-D the probe level should be fixed (and the masker level varied). In a linear system. of course. both methods would lead to the same filter shape. This dispute, about whether the probe or the masker should be fixed in notched-noise expcrimcnts, indicates a fundamental uncertainty about what aspects of the input signal control filter shape and bandwidth. It is not merely a matter of semantics, or alternative param- eterisations. For one thing, any realistic tcchniquc for calculating excitation patterns (the amount of cxcita- tion caused by a particular sound across the auditov filter array) must make an assumption about how filter nonlinearity is controlled. But there arc also important implications in this issue cvcn t’or aimplc determina- tions of auditory filter shape. Suppose filter shapes arc in fact determined primarily by the level of the probe. In that case, masked thresholds obtained using a fixed-masker paradigm would bc obtained from filters which r’up in shape as the level of the probe changes with notch width. The filter shape inferred from such measurements would not be genuinely representative of auditory filtering at any particular sound pressure level. Although there have been a number of studies cx- plicitly aimed at deciding whether it is the probe or the