{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,19]],"date-time":"2026-09-19T19:23:34Z","timestamp":1789845814474,"version":"4.0.1"},"reference-count":48,"publisher":"Acoustical Society of America (ASA)","issue":"6","content-domain":{"domain":["pubs.aip.org"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[2011,12,1]]},"abstract":"<jats:p>A cascade of two-pole\u2013two-zero filter stages is a good model of the auditory periphery in two distinct ways. First, in the form of the pole\u2013zero filter cascade, it acts as an auditory filter model that provides an excellent fit to data on human detection of tones in masking noise, with fewer fitting parameters than previously reported filter models such as the roex and gammachirp models. Second, when extended to the form of the cascade of asymmetric resonators with fast-acting compression, it serves as an efficient front-end filterbank for machine-hearing applications, including dynamic nonlinear effects such as fast wide-dynamic-range compression. In their underlying linear approximations, these filters are described by their poles and zeros, that is, by rational transfer functions, which makes them simple to implement in analog or digital domains. Other advantages in these models derive from the close connection of the filter-cascade architecture to wave propagation in the cochlea. These models also reflect the automatic-gain-control function of the auditory system and can maintain approximately constant impulse-response zero-crossing times as the level-dependent parameters change.<\/jats:p>","DOI":"10.1121\/1.3658470","type":"journal-article","created":{"date-parts":[[2011,12,16]],"date-time":"2011-12-16T00:34:53Z","timestamp":1323995693000},"page":"3893-3904","update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":47,"title":["Cascades of two-pole\u2013two-zero asymmetric resonators are good models of peripheral auditory function"],"prefix":"10.1121","volume":"130","author":[{"given":"Richard F.","family":"Lyon","sequence":"first","affiliation":[{"name":"Google Inc., 1600 Amphitheatre Parkway, Mountain View, California 94043"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"231","published-online":{"date-parts":[[2011,12,15]]},"reference":[{"key":"2023073107264956700_c1","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/0-387-21530-1_1","article-title":"Overview of auditory compression","volume-title":"Compression: From Cochlea to Cochlear Implants","author":"Bacon","year":"2004"},{"key":"2023073107264956700_c2","first-page":"81","article-title":"An efficient characterisation of human auditory filtering across level and frequency that is also physiologically reasonable","volume-title":"Psychophysical and Physiological Advances in Hearing","author":"Palmer","year":"1998"},{"key":"2023073107264956700_c3","doi-asserted-by":"publisher","first-page":"401","DOI":"10.1121\/1.405620","article-title":"A model for the responses of low-frequency auditory-nerve fibers in cat","volume":"93","year":"1993","journal-title":"J. Acoust. Soc. Am."},{"key":"2023073107264956700_c4","doi-asserted-by":"publisher","first-page":"2384","DOI":"10.1121\/1.426843","article-title":"Frequency glides in the impulse responses of auditory-nerve fibers","volume":"105","year":"1999","journal-title":"J. Acoust. Soc. Am."},{"key":"2023073107264956700_c5","doi-asserted-by":"publisher","first-page":"1443","DOI":"10.1109\/PROC.1976.10348","article-title":"Cross-correlation function of a bandpass nonlinear network","volume":"64","year":"1976","journal-title":"Proc. IEEE"},{"key":"2023073107264956700_c6","doi-asserted-by":"publisher","first-page":"115","DOI":"10.1121\/1.381704","article-title":"On cochlear encoding: Potentialities and limitations of the reverse-correlation technique","volume":"63","year":"1978","journal-title":"J. Acoust. Soc. Am."},{"key":"2023073107264956700_c7","doi-asserted-by":"publisher","first-page":"1889","DOI":"10.1121\/1.1694999","article-title":"Comment on \u2018An approximate transfer function for the dual-resonance nonlinear filter model of auditory frequency selectivity\u2019 [J. Acoust. Soc. Am. 114, 2112\u20132117]","volume":"115","year":"2004","journal-title":"J. Acoust. Soc. Am."},{"key":"2023073107264956700_c8","doi-asserted-by":"crossref","first-page":"1163","DOI":"10.1002\/j.1538-7305.1960.tb03955.x","article-title":"Models for approximating basilar membrane displacement","volume":"39","year":"1960","journal-title":"Bell Sys. Tech. J."},{"key":"2023073107264956700_c9","doi-asserted-by":"crossref","first-page":"959","DOI":"10.1002\/j.1538-7305.1962.tb00485.x","article-title":"Models for approximating basilar membrane displacement\u2014Part II. Effects of middle-ear transmission and some relations between subjective and physiological behavior","volume":"41","year":"1962","journal-title":"Bell Sys. Tech. J."},{"key":"2023073107264956700_c10","doi-asserted-by":"publisher","first-page":"103","DOI":"10.1016\/0378-5955(90)90170-T","article-title":"Derivation of auditory filter shapes from notched noise data","volume":"47","year":"1990","journal-title":"Hearing Res."},{"key":"2023073107264956700_c11","doi-asserted-by":"publisher","first-page":"2318","DOI":"10.1121\/1.1315291","article-title":"Frequency selectivity as a function of level and frequency measured with uniformly exciting notched noise","volume":"108","year":"2000","journal-title":"J. Acoust. Soc. Am."},{"key":"2023073107264956700_c12","doi-asserted-by":"publisher","first-page":"419","DOI":"10.1121\/1.391584","article-title":"Dynamic range and asymmetry of the auditory filter","volume":"76","year":"1984","journal-title":"J. Acoust. Soc. Am."},{"key":"2023073107264956700_c13","doi-asserted-by":"publisher","first-page":"412","DOI":"10.1121\/1.417975","article-title":"A time-domain, level-dependent auditory filter: The gammachirp","volume":"101","year":"1997","journal-title":"J. Acoust. Soc. Am."},{"key":"2023073107264956700_c14","doi-asserted-by":"publisher","first-page":"2008","DOI":"10.1121\/1.1367253","article-title":"A compressive gammachirp auditory filter for both physiological and psychophysical data","volume":"109","year":"2001","journal-title":"J. Acoust. Soc. Am."},{"key":"2023073107264956700_c15","doi-asserted-by":"publisher","first-page":"2222","DOI":"10.1109\/TASL.2006.874669","article-title":"A dynamic compressive gammachirp auditory filterbank","volume":"14","year":"2006","journal-title":"IEEE Trans. Audio Speech Language Process."},{"key":"2023073107264956700_c16","first-page":"58","article-title":"The pre-response stimulus ensemble of neurons in the cochlear nucleus","volume-title":"Proc. IPO Symposium on Hearing Theory","author":"Cardozo","year":"1972"},{"key":"2023073107264956700_c17","doi-asserted-by":"publisher","first-page":"63685","DOI":"10.1155\/2007\/63685","article-title":"Practical gammatone-like filters for auditory processing","volume":"2007","year":"2007","journal-title":"EURASIP J. Audio Speech Music Process."},{"key":"2023073107264956700_c18","doi-asserted-by":"publisher","first-page":"1517","DOI":"10.1121\/1.1914449","article-title":"A system of nonlinear differential equations modeling basilar-membrane motion","volume":"54","year":"1973","journal-title":"J. Acoust. Soc. Am."},{"key":"2023073107264956700_c19","doi-asserted-by":"publisher","first-page":"3107","DOI":"10.1121\/1.1416197","article-title":"A human nonlinear cochlear filterbank","volume":"110","year":"2001","journal-title":"J. Acoust. Soc. Am."},{"key":"2023073107264956700_c20","doi-asserted-by":"publisher","first-page":"739","DOI":"10.1121\/1.391260","article-title":"On the growth of masking asymmetry with stimulus intensity","volume":"76","year":"1984","journal-title":"J. Acoust. Soc. Am."},{"key":"2023073107264956700_c21","first-page":"1282","article-title":"A computational model of filtering, detection, and compression in the cochlea","year":"1982"},{"key":"2023073107264956700_c22","doi-asserted-by":"crossref","first-page":"395","DOI":"10.1007\/978-1-4757-4341-8","article-title":"Automatic gain control in cochlear mechanics","volume-title":"The Mechanics and Biophysics of Hearing","author":"Dallos","year":"1990"},{"key":"2023073107264956700_c23","doi-asserted-by":"crossref","first-page":"205","DOI":"10.1142\/3147","article-title":"All-pole models of auditory filtering","volume-title":"Diversity in Auditory Mechanics","author":"Lewis","year":"1997"},{"key":"2023073107264956700_c24","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1007\/b102308","article-title":"Filter cascades as analogs of the cochlea","volume-title":"Neuromorphic Systems Engineering: Neural Networks in Silicon","author":"Lande","year":"1998"},{"key":"2023073107264956700_c25","first-page":"3809","article-title":"History and future of auditory filter models","year":"2010"},{"key":"2023073107264956700_c26","doi-asserted-by":"publisher","first-page":"1119","DOI":"10.1109\/29.1639","article-title":"An analog electronic cochlea","volume":"36","year":"1988","journal-title":"IEEE Trans. Acoust. Speech Signal Process."},{"key":"2023073107264956700_c27","doi-asserted-by":"publisher","first-page":"2390","DOI":"10.1162\/NECO_a_00011","article-title":"Sound retrieval and ranking using sparse auditory representations","volume":"22","year":"2010","journal-title":"Neural Comp."},{"key":"2023073107264956700_c28","doi-asserted-by":"crossref","first-page":"161","DOI":"10.1016\/B978-012505626-7\/50007-8","article-title":"Frequency analysis and masking","volume-title":"Hearing","author":"Moore","year":"1995"},{"key":"2023073107264956700_c29","doi-asserted-by":"publisher","first-page":"209","DOI":"10.1016\/0378-5955(87)90050-5","article-title":"Formulae describing frequency selectivity as a function of frequency and level, and their use in calculating excitation patterns","volume":"28","year":"1987","journal-title":"Hearing Res."},{"key":"2023073107264956700_c30","doi-asserted-by":"publisher","first-page":"132","DOI":"10.1121\/1.399960","article-title":"Auditory filter shapes at low center frequencies","volume":"88","year":"1990","journal-title":"J. Acoust. Soc. Am."},{"key":"2023073107264956700_c31","doi-asserted-by":"publisher","first-page":"640","DOI":"10.1121\/1.380914","article-title":"Auditory filter shapes derived with noise stimuli","volume":"59","year":"1976","journal-title":"J. Acoust. Soc. Am."},{"key":"2023073107264956700_c32","doi-asserted-by":"crossref","first-page":"123","DOI":"10.1007\/978-1-4613-2247-4","article-title":"Auditory filters and excitation patterns as representations of frequency resolution","volume-title":"Frequency Selectivity in Hearing","author":"Moore","year":"1986"},{"key":"2023073107264956700_c33","doi-asserted-by":"publisher","first-page":"229","DOI":"10.1121\/1.383732","article-title":"Off-frequency listening and auditory-filter asymmetry","volume":"67","year":"1980","journal-title":"J. Acoust. Soc. Am."},{"key":"2023073107264956700_c34","doi-asserted-by":"publisher","first-page":"1529","DOI":"10.1121\/1.1600720","article-title":"Extending the domain of center frequencies for the compressive gammachirp auditory filter","volume":"114","year":"2003","journal-title":"J. Acoust. Soc. Am."},{"key":"2023073107264956700_c35","doi-asserted-by":"publisher","first-page":"369","DOI":"10.1121\/1.1906615","article-title":"A dynamical theory of the cochlea","volume":"22","year":"1950","journal-title":"J. Acoust. Soc. Am."},{"key":"2023073107264956700_c36","doi-asserted-by":"publisher","first-page":"772","DOI":"10.1121\/1.1906688","article-title":"Theory of operation of the cochlea: A contribution to the hydrodynamics of the cochlea","volume":"22","year":"1950","journal-title":"J. Acoust. Soc. Am."},{"key":"2023073107264956700_c37","doi-asserted-by":"crossref","first-page":"1305","DOI":"10.1152\/physrev.2001.81.3.1305","article-title":"Mechanics of the mammalian cochlea","volume":"81","year":"2001","journal-title":"Physiol. Rev."},{"key":"2023073107264956700_c38","doi-asserted-by":"publisher","first-page":"231","DOI":"10.1016\/0378-5955(94)90239-9","article-title":"Characterising auditory filter nonlinearity","volume":"73","year":"1994","journal-title":"Hearing Res."},{"key":"2023073107264956700_c39","doi-asserted-by":"publisher","first-page":"2539","DOI":"10.1121\/1.422775","article-title":"Auditory filter nonlinearity at 2 kHz in normal hearing listeners","volume":"103","year":"1998","journal-title":"J. Acoust. Soc. Am."},{"key":"2023073107264956700_c40","doi-asserted-by":"publisher","first-page":"332","DOI":"10.1121\/1.1378349","article-title":"Intensity-invariance of fine time structure in basilar-membrane click responses: Implications for cochlear mechanics","volume":"110","year":"2001","journal-title":"J. Acoust. Soc. Am."},{"key":"2023073107264956700_c41","first-page":"95","article-title":"On the importance of time\u2014A temporal representation of sound","volume-title":"Visual Representations of Speech Signals","author":"Cooke","year":"1993"},{"key":"2023073107264956700_c42","doi-asserted-by":"publisher","first-page":"2007","DOI":"10.1121\/1.1608963","article-title":"A phenomenological model for the responses of auditory-nerve fibers. II. Nonlinear tuning with a frequency glide","volume":"114","year":"2003","journal-title":"J. Acoust. Soc. Am."},{"key":"2023073107264956700_c43","doi-asserted-by":"publisher","first-page":"1474","DOI":"10.1121\/1.2228539","article-title":"Comparison of the roex and gammachirp filters as representations of the auditory filter","volume":"120","year":"2006","journal-title":"J. Acoust. Soc. Am."},{"key":"2023073107264956700_c44","doi-asserted-by":"publisher","first-page":"147","DOI":"10.1121\/1.1906869","article-title":"The masking and pitch shift of pure tones near abrupt changes in a thermal noise spectrum","volume":"24","year":"1952","journal-title":"J. Acoust. Soc. Am."},{"key":"2023073107264956700_c45","doi-asserted-by":"publisher","first-page":"266","DOI":"10.1103\/PhysRev.23.266","article-title":"The auditory masking of one sound by another and its probable relation to the dynamics of the inner ear","volume":"23","year":"1924","journal-title":"Phys. Rev."},{"key":"2023073107264956700_c46","first-page":"292","article-title":"Continuous-time systems and discrete-time systems","volume-title":"Signals and Systems with MATLAB","year":"2009"},{"key":"2023073107264956700_c47","doi-asserted-by":"publisher","first-page":"648","DOI":"10.1121\/1.1336503","article-title":"A phenomenological model for the responses of auditory-nerve fibers: I. nonlinear tuning with compression and suppression","volume":"109","year":"2001","journal-title":"J. Acoust. Soc. Am."},{"key":"2023073107264956700_c48","doi-asserted-by":"publisher","first-page":"975","DOI":"10.1121\/1.380956","article-title":"The cochlear compromise","volume":"59","year":"1976","journal-title":"J. Acoust. Soc. Am."}],"container-title":["The Journal of the Acoustical Society of America"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/pubs.aip.org\/asa\/jasa\/article-pdf\/130\/6\/3893\/13328540\/3893_1_online.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/pubs.aip.org\/asa\/jasa\/article-pdf\/130\/6\/3893\/13328540\/3893_1_online.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,7,31]],"date-time":"2023-07-31T07:27:40Z","timestamp":1690788460000},"score":1,"resource":{"primary":{"URL":"https:\/\/pubs.aip.org\/jasa\/article\/130\/6\/3893\/904360\/Cascades-of-two-pole-two-zero-asymmetric"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,12,1]]},"references-count":48,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2011,12,1]]}},"URL":"https:\/\/doi.org\/10.1121\/1.3658470","relation":{},"ISSN":["0001-4966","1520-8524"],"issn-type":[{"value":"0001-4966","type":"print"},{"value":"1520-8524","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[2011,12]]},"published":{"date-parts":[[2011,12,1]]}}}