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An Overcomplete Signal Basis Approach to Nonlinear Time-Tone Analysis with Application to Audio and Speech Processing

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Although a beating tone and the two pure tones which give rise to it are linearly dependent, the ear considers them to be independent as tone sensations. A linear time-frequency representation of acoustic data is unable to model these phenomena. A time-tone sensation approach is proposed for inclusion within audio analysis systems. The proposed approach extends linear time-frequency analysis of acoustic data, by accommodating the nonlinear phenomenon of beats. The method replaces the one-dimensional tonotopic axis of linear time-frequency analysis with a two-dimensional tonotopic plane, in which one direction corresponds to tone, and the other to its frequency of modulation. Some applications to audio prostheses are discussed. The proposed method relies on an intuitive criterion of optimal representation which can be applied to any overcomplete signal basis, allowing for many signal processing applications.


  1. 1.

    Rabiner L, Juang B-H: Fundamentals of Speech Recognition, Signal Processing Series. Prentice-Hall, Englewood Cliffs, NJ, USA; 1993.

  2. 2.

    Gold B, Morgan N: Speech and Audio Signal Processing: Processing and Perception of Speech and Music. John Wiley & Sons, New York, NY, USA; 2000.

  3. 3.

    Beyer RT: Sounds of Our Times: Two Hundred Years of Acoustics. American Institute of Physics, New York, NY, USA; 1998.

  4. 4.

    Moore BCJ: An Introduction to the Psychology of Hearing. 5th edition. Academic Press, London, UK; 2003.

  5. 5.

    Robles L, Ruggero MA, Rich NC: Two-tone distortion in the basilar membrane of the cochlea. Nature 1991, 349(6308):413–414. 10.1038/349413a0

  6. 6.

    Rhode WS, Robles L: Evidence from Mossbauer experiments for nonlinear vibration in the cochlea. Journal of the Acoustical Society of America 1974, 55(3):588–596. 10.1121/1.1914569

  7. 7.

    Robles L, Ruggero MA, Rich NC: Basilar membrane mechanics at the base of the chinchilla cochlea. I. Input-output functions, tuning curves, and response phases. Journal of the Acoustical Society of America 1986, 80(5):1364–1374. 10.1121/1.394389

  8. 8.

    Murugasu E, Russell IJ: Salicylate ototoxicity: the effects on basilar membrane displacement, cochlear microphonics, and neural responses in the basal turn of the guinea pig cochlea. Auditory Neuroscience 1995, 1: 139–150.

  9. 9.

    Ruggero MA, Rich NC, Recio A, Narayan SS, Robles L: Basilar-membrane responses to tones at the base of the chinchilla cochlea. Journal of the Acoustical Society of America 1997, 101(4):2151–2163. 10.1121/1.418265

  10. 10.

    Russell IJ, Nilsen KE: The location of the cochlear amplifier: spatial representation of a single tone on the Guinea pig basilar membrane. Proceedings of the National Academy of Sciences of the United States of America 1997, 94(6):2660–2664. 10.1073/pnas.94.6.2660

  11. 11.

    Oxenham AJ, Moore BCJ: Additivity of masking in normally hearing and hearing-impaired subjects. Journal of the Acoustical Society of America 1995, 98(4):1921–1934. 10.1121/1.413376

  12. 12.

    Oxenham AJ, Plack CJ: Suppression and the upward spread of masking. Journal of the Acoustical Society of America 1998, 104(6):3500–3510. 10.1121/1.423933

  13. 13.

    Plack CJ, Oxenham AJ: Basilar membrane nonlinearity and the growth of forward masking. Journal of the Acoustical Society of America 1998, 103(3):1598–1608. 10.1121/1.421294

  14. 14.

    Hicks ML, Bacon SP: Psychophysical measures of auditory nonlinearities as a function of frequency in individuals with normal hearing. Journal of the Acoustical Society of America 1999, 105(1):326–338. 10.1121/1.424526

  15. 15.

    Moore BCJ, Vickers DA, Plack CJ, Oxenham AJ: Inter-relationship between different psychoacoustic measures assumed to be related to the cochlear active mechanism. Journal of the Acoustical Society of America 1999, 106(5):2761–2778. 10.1121/1.428133

  16. 16.

    Oxenham AJ, Moore BCJ, Vickers DA: Short-term temporal integration: evidence for the influence of peripheral compression. Journal of the Acoustical Society of America 1997, 101(6):3676–3687. 10.1121/1.418328

  17. 17.

    Yates GK: Basilar membrane nonlinearity and its influence on auditory nerve rate-intensity functions. Hearing Research 1990, 50(1–2):145–162. 10.1016/0378-5955(90)90041-M

  18. 18.

    Moore BCJ, Glasberg BR: A model of loudness perception applied to cochlear hearing loss. Auditory Neuroscience 1997, 3: 289–311.

  19. 19.

    Moore BCJ, Oxenham AJ: Psychoacoustic consequences of compression in the peripheral auditory system. Psychological Review 1998, 105(1):108–124.

  20. 20.

    Bohnke F, Arnold W: Nonlinear mechanics of the organ of Corti caused by Deiters cells. IEEE Transactions on Biomedical Engineering 1998, 45(10):1227–1233. 10.1109/10.720200

  21. 21.

    Friedman DH: Implementation of a nonlinear wave-digital-filter cochlear model. Proceedings of IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP~'90), April 1990, Albuquerque, NM, USA 1: 397–400.

  22. 22.

    Hirahara T, Komakine T: A computational cochlear nonlinear preprocessing model with adaptive Q circuits. Proceedings of IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP '89), May 1989, Glasgow, UK 1: 496–499.

  23. 23.

    Deng L, Kheirallah I: Dynamic formant tracking of noisy speech using temporal analysis on outputs from a nonlinear cochlear model. IEEE Transactions on Biomedical Engineering 1993, 40(5):456–467. 10.1109/10.243416

  24. 24.

    Heil P, Rajan R, Irvine DRF: Topographic representation of tone intensity along the isofrequency axis of cat primary auditory cortex. Hearing Research 1994, 76(1–2):188–202. 10.1016/0378-5955(94)90099-X

  25. 25.

    Reale RA, Imig TJ: Tonotopic organization in auditory cortex of the cat. Journal of Comparative Neurology 1980, 192(2):265–291. 10.1002/cne.901920207

  26. 26.

    Morel A, Garraghty PE, Kaas JH: Tonotopic organization, architectonic fields, and connections of auditory cortex in macaque monkeys. Journal of Comparative Neurology 1993, 335(3):437–459. 10.1002/cne.903350312

  27. 27.

    Cansino S, Williamson SJ, Karron D: Tonotopic organization of human auditory association cortex. Brain Research 1994, 663(1):38–50. 10.1016/0006-8993(94)90460-X

  28. 28.

    Pantev C, Bertrand O, Eulitz C, et al.: Specific tonotopic organizations of different areas of human auditory cortex revealed by simultaneous magnetic and electric recordings. Electroencephalography and Clinical Neurophysiology 1995, 94(1):26–40. 10.1016/0013-4694(94)00209-4

  29. 29.

    Lauter JL, Herscovitch P, Formby C, Raichle ME: Tonotopic organization in human auditory cortex revealed by positron emission tomography. Hearing Research 1985, 20(3):199–205. 10.1016/0378-5955(85)90024-3

  30. 30.

    Lockwood AH, Salvi RJ, Coad ML, et al.: The functional anatomy of the normal human auditory system: responses to 0.5 and 4.0 kHz tones at varied intensities. Cerebral Cortex 1999, 9(1):65–76. 10.1093/cercor/9.1.65

  31. 31.

    Wessinger CM, Buonocore MH, Kussmaul CL, Mangun GR: Tonotopy in human auditory cortex examined with functional magnetic resonance imaging. Human Brain Mapping 1997, 5(1):18–25. 10.1002/(SICI)1097-0193(1997)5:1<18::AID-HBM3>3.0.CO;2-Q

  32. 32.

    Bilecen D, Scheffler K, Schmid N, Tschopp K, Seelig J: Tonotopic organization of the human auditory cortex as detected by BOLD-FMRI. Hearing Research 1998, 126(1–2):19–27. 10.1016/S0378-5955(98)00139-7

  33. 33.

    Talavage TM, Ledden PJ, Benson RR, Rosen BR, Melcher JR: Frequency-dependent responses exhibited by multiple regions in human auditory cortex. Hearing Research 2000, 150(1–2):225–244. 10.1016/S0378-5955(00)00203-3

  34. 34.

    Schönwiesner M, von Cramon DY, Rübsamen R: Is it tonotopy after all? NeuroImage 2002, 17(3):1144–1161. 10.1006/nimg.2002.1250

  35. 35.

    Lee N, Schwartz SC: Robust transient signal detection using the oversampled Gabor representation. IEEE Transactions on Signal Processing 1995, 43(6):1498–1502. 10.1109/78.388862

  36. 36.

    Dallos P, Cheatham MA: Nonlinearities in cochlear receptor potentials and their origins. Journal of the Acoustical Society of America 1989, 86(5):1790–1796. 10.1121/1.398611

  37. 37.

    Wegel RL, Lane CE: The auditory masking of one pure tone by another and its probable relation to the dynamics of the inner ear. Physical Review 1924, 23(2):266–285. 10.1103/PhysRev.23.266

  38. 38.

    Lim HH, Anderson DJ: Feasibility experiments for the development of a midbrain auditory prosthesis. Proceedings of 1st Annual International IEEE EMBS Conference on Neural Engineering, March 2003, Capri Island, Italy 193–196.

  39. 39.

    Snyder RL, Sinex DG, McGee JD, Walsh EW: Acute spiral ganglion lesions change the tuning and tonotopic organization of the cat inferior colliculus neurons. Hearing Research 2000, 147(1–2):200–220. 10.1016/S0378-5955(00)00132-5

  40. 40.

    Mallat SG, Zhang Z: Matching pursuits with time-frequency dictionaries. IEEE Transactions on Signal Processing 1993, 41(12):3397–3415. 10.1109/78.258082

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Correspondence to Richard B. Reilly.

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Reilly, R.B. An Overcomplete Signal Basis Approach to Nonlinear Time-Tone Analysis with Application to Audio and Speech Processing. EURASIP J. Adv. Signal Process. 2006, 065431 (2006) doi:10.1155/ASP/2006/65431

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  • Information Technology
  • Signal Processing
  • Quantum Information
  • Basis Approach
  • Optimal Representation