This article is part of the series Frames and Overcomplete Representations in Signal Processing, Communications, and Information Theory.

Open Access Research Article

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

Richard B Reilly

  • Correspondence: Richard B Reilly

Author Affiliations

School of Electrical, Electronic and Mechanical Engineering, University College Dublin, Belfield, Dublin 4, Ireland

EURASIP Journal on Advances in Signal Processing 2006, 2006:065431  doi:10.1155/ASP/2006/65431


The electronic version of this article is the complete one and can be found online at: http://asp.eurasipjournals.com/content/2006/1/065431


Received: 23 August 2004
Revisions received: 22 March 2005
Accepted: 25 March 2005
Published: 5 February 2006

© 2006 Reilly

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.

References

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

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

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

  4. BCJ Moore, An Introduction to the Psychology of Hearing, h (Academic Press, London, UK, 2003)

  5. L Robles, MA Ruggero, NC Rich, Two-tone distortion in the basilar membrane of the cochlea. Nature 349(6308), 413–414 (1991). PubMed Abstract | Publisher Full Text OpenURL

  6. WS Rhode, L Robles, Evidence from Mossbauer experiments for nonlinear vibration in the cochlea. Journal of the Acoustical Society of America 55(3), 588–596 (1974). PubMed Abstract | Publisher Full Text OpenURL

  7. L Robles, MA Ruggero, NC Rich, 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 80(5), 1364–1374 (1986). PubMed Abstract | Publisher Full Text OpenURL

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

  9. MA Ruggero, NC Rich, A Recio, SS Narayan, L Robles, Basilar-membrane responses to tones at the base of the chinchilla cochlea. Journal of the Acoustical Society of America 101(4), 2151–2163 (1997). PubMed Abstract | Publisher Full Text OpenURL

  10. IJ Russell, KE Nilsen, 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 94(6), 2660–2664 (1997). PubMed Abstract | Publisher Full Text | PubMed Central Full Text OpenURL

  11. AJ Oxenham, BCJ Moore, Additivity of masking in normally hearing and hearing-impaired subjects. Journal of the Acoustical Society of America 98(4), 1921–1934 (1995). PubMed Abstract | Publisher Full Text OpenURL

  12. AJ Oxenham, CJ Plack, Suppression and the upward spread of masking. Journal of the Acoustical Society of America 104(6), 3500–3510 (1998). PubMed Abstract | Publisher Full Text OpenURL

  13. CJ Plack, AJ Oxenham, Basilar membrane nonlinearity and the growth of forward masking. Journal of the Acoustical Society of America 103(3), 1598–1608 (1998). PubMed Abstract | Publisher Full Text OpenURL

  14. ML Hicks, SP Bacon, Psychophysical measures of auditory nonlinearities as a function of frequency in individuals with normal hearing. Journal of the Acoustical Society of America 105(1), 326–338 (1999). PubMed Abstract | Publisher Full Text OpenURL

  15. BCJ Moore, DA Vickers, CJ Plack, AJ Oxenham, Inter-relationship between different psychoacoustic measures assumed to be related to the cochlear active mechanism. Journal of the Acoustical Society of America 106(5), 2761–2778 (1999). PubMed Abstract | Publisher Full Text OpenURL

  16. AJ Oxenham, BCJ Moore, DA Vickers, Short-term temporal integration: evidence for the influence of peripheral compression. Journal of the Acoustical Society of America 101(6), 3676–3687 (1997). PubMed Abstract | Publisher Full Text OpenURL

  17. GK Yates, Basilar membrane nonlinearity and its influence on auditory nerve rate-intensity functions. Hearing Research 50(1-2), 145–162 (1990). PubMed Abstract | Publisher Full Text OpenURL

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

  19. BCJ Moore, AJ Oxenham, Psychoacoustic consequences of compression in the peripheral auditory system. Psychological Review 105(1), 108–124 (1998). PubMed Abstract | Publisher Full Text OpenURL

  20. F Bohnke, W Arnold, Nonlinear mechanics of the organ of Corti caused by Deiters cells. IEEE Transactions on Biomedical Engineering 45(10), 1227–1233 (1998). PubMed Abstract | Publisher Full Text OpenURL

  21. DH Friedman, 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. T Hirahara, T Komakine, 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. L Deng, I Kheirallah, Dynamic formant tracking of noisy speech using temporal analysis on outputs from a nonlinear cochlear model. IEEE Transactions on Biomedical Engineering 40(5), 456–467 (1993). PubMed Abstract | Publisher Full Text OpenURL

  24. P Heil, R Rajan, DRF Irvine, Topographic representation of tone intensity along the isofrequency axis of cat primary auditory cortex. Hearing Research 76(1-2), 188–202 (1994). PubMed Abstract | Publisher Full Text OpenURL

  25. RA Reale, TJ Imig, Tonotopic organization in auditory cortex of the cat. Journal of Comparative Neurology 192(2), 265–291 (1980). PubMed Abstract | Publisher Full Text OpenURL

  26. A Morel, PE Garraghty, JH Kaas, Tonotopic organization, architectonic fields, and connections of auditory cortex in macaque monkeys. Journal of Comparative Neurology 335(3), 437–459 (1993). PubMed Abstract | Publisher Full Text OpenURL

  27. S Cansino, SJ Williamson, D Karron, Tonotopic organization of human auditory association cortex. Brain Research 663(1), 38–50 (1994). PubMed Abstract | Publisher Full Text OpenURL

  28. C Pantev, O Bertrand, C Eulitz, et al. Specific tonotopic organizations of different areas of human auditory cortex revealed by simultaneous magnetic and electric recordings. Electroencephalography and Clinical Neurophysiology 94(1), 26–40 (1995). PubMed Abstract | Publisher Full Text OpenURL

  29. JL Lauter, P Herscovitch, C Formby, ME Raichle, Tonotopic organization in human auditory cortex revealed by positron emission tomography. Hearing Research 20(3), 199–205 (1985). PubMed Abstract | Publisher Full Text OpenURL

  30. AH Lockwood, RJ Salvi, ML Coad, 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 9(1), 65–76 (1999). PubMed Abstract | Publisher Full Text OpenURL

  31. CM Wessinger, MH Buonocore, CL Kussmaul, GR Mangun, Tonotopy in human auditory cortex examined with functional magnetic resonance imaging. Human Brain Mapping 5(1), 18–25 (1997). PubMed Abstract | Publisher Full Text OpenURL

  32. D Bilecen, K Scheffler, N Schmid, K Tschopp, J Seelig, Tonotopic organization of the human auditory cortex as detected by BOLD-FMRI. Hearing Research 126(1-2), 19–27 (1998). PubMed Abstract | Publisher Full Text OpenURL

  33. TM Talavage, PJ Ledden, RR Benson, BR Rosen, JR Melcher, Frequency-dependent responses exhibited by multiple regions in human auditory cortex. Hearing Research 150(1-2), 225–244 (2000). PubMed Abstract | Publisher Full Text OpenURL

  34. M Schönwiesner, DY von Cramon, R Rübsamen, Is it tonotopy after all? NeuroImage 17(3), 1144–1161 (2002). PubMed Abstract | Publisher Full Text OpenURL

  35. N Lee, SC Schwartz, Robust transient signal detection using the oversampled Gabor representation. IEEE Transactions on Signal Processing 43(6), 1498–1502 (1995). Publisher Full Text OpenURL

  36. P Dallos, MA Cheatham, Nonlinearities in cochlear receptor potentials and their origins. Journal of the Acoustical Society of America 86(5), 1790–1796 (1989). PubMed Abstract | Publisher Full Text OpenURL

  37. RL Wegel, CE Lane, The auditory masking of one pure tone by another and its probable relation to the dynamics of the inner ear. Physical Review 23(2), 266–285 (1924). Publisher Full Text OpenURL

  38. HH Lim, DJ Anderson, 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. RL Snyder, DG Sinex, JD McGee, EW Walsh, Acute spiral ganglion lesions change the tuning and tonotopic organization of the cat inferior colliculus neurons. Hearing Research 147(1-2), 200–220 (2000). PubMed Abstract | Publisher Full Text OpenURL

  40. SG Mallat, Z Zhang, Matching pursuits with time-frequency dictionaries. IEEE Transactions on Signal Processing 41(12), 3397–3415 (1993). Publisher Full Text OpenURL