Skip to main content
SpringerLink
Log in

Where Mathematics and Hearing Science Meet: Low Peak Factor Signals and Their Role in Hearing Research

  • Chapter
  • First Online:
Acoustics, Information, and Communication

Part of the book series: Modern Acoustics and Signal Processing ((MASP))

  • 1764 Accesses

Abstract

In his scientific work, Manfred Schroeder touched many different areas within acoustics. Two disciplines repeatedly show up when his contributions are characterized: his strong interest in mathematics and his interest in the perceptual side of acoustics. In this chapter, we focus on the latter. We will first give a compressed account of Schroeder’s direct contributions to psychoacoustics, and emphasize the relation with other acoustics disciplines like speech processing and room acoustics. In the main part of the chapter we will then describe psychoacoustic work being based on or inspired by ideas from Manfred Schroeder. Due to Schroeder’s success in securing a modern online computer for the Drittes Physikalisches Institut after returning to Göttingen in 1969, his research students had a head start in using digital signal processing in room acoustics for digital sound field synthesis and in introducing digital computers into experimental and theoretical hearing research. Since then, the freedom to construct and use specific acoustic stimuli in behavioral and also physiological research has grown steadily, making it possible to test many of Schroeder’s early ideas in behavioral experiments and applications. In parallel, computer models of auditory perception allowed users to analyze and predict how specific properties of acoustic stimuli influence the perception of a listener. As in other fields of physics, the close interplay between experimental tests and quantitative models has been shown to be essential in advancing our understanding of human hearing.

This chapter is an adapted version of a chapter which the authors contributed to a book published on the occasion of the 60th anniversary of the Drittes Physikalisches Institut (DPI) at the Georg-August Universität Göttingen [37].

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    There are alternative ways to determine the envelope of a signal which lead to somewhat different envelopes. We will consider here the Hilbert envelope.

  2. 2.

    In this case, the normalized fourth moment of the waveform.

References

  1. Atal, B.S., Schroeder, M.R.: Predictive coding of speech signals and subjective error criteria. In Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 1978, pp. 573–576 (1978)

    Google Scholar 

  2. Blauert, J.: Spatial Hearing. The Psychophysics of Human Sound Localization. The MIT Press, Cambridge, MA (1997)

    Google Scholar 

  3. Bos, C.E., de Boer, E.: Masking and discrimination. J. Acoust. Soc. Am. 39, 708–715 (1966)

    Article  ADS  Google Scholar 

  4. Breebaart, J., Houtsma, A., Kohlrausch, A., Prijs, V., Schoonhoven, R.: Physiological and Psychophysical Bases of Auditory Function. Shaker Publishers, Maastricht (2001)

    Google Scholar 

  5. Breebaart, J., van de Par, S., Kohlrausch, A.: Binaural processing model based on contralateral inhibition. I. Model structure. J. Acoust. Soc. Am. 110, 1074–1088 (2001)

    Article  ADS  Google Scholar 

  6. Breebaart, J., van de Par, S., Kohlrausch, A.: Binaural processing model based on contralateral inhibition. II. Predictions as a function of spectral stimulus parameters. J. Acoust. Soc. Am. 110, 1089–1104 (2001)

    Article  ADS  Google Scholar 

  7. Breebaart, J., van de Par, S., Kohlrausch, A.: Binaural processing model based on contralateral inhibition. III. Predictions as a function of temporal stimulus parameters. J. Acoust. Soc. Am. 110, 1105–1117 (2001)

    Article  ADS  Google Scholar 

  8. Buss, E., Grose, J.H., Hall III, J.W.: Features of across-frequency envelope coherence critical for comodulation masking release. J. Acoust. Soc. Am. 126, 2455–2466 (2009)

    Article  ADS  Google Scholar 

  9. Carlyon, R.P., Datta, A.J.: Excitation produced by Schroeder-phase complexes: evidence for fast-acting compression in the auditory system. J. Acoust. Soc. Am. 101, 3636–3647 (1997)

    Article  ADS  Google Scholar 

  10. Carlyon, R.P., Datta, A.J.: Masking period patterns of Schroeder-phase complexes: effects of level, number of components, and phase of flanking components. J. Acoust. Soc. Am. 101, 3648–3657 (1997)

    Article  ADS  Google Scholar 

  11. Dau, T., Kollmeier, B., Kohlrausch, A.: Modeling auditory processing of amplitude modulation: I. Detection and masking with narrowband carriers. J. Acoust. Soc. Am. 102, 2892–2905 (1997)

    Article  ADS  Google Scholar 

  12. Dau, T., Kollmeier, B., Kohlrausch, A.: Modeling auditory processing of amplitude modulation: II. Spectral and temporal integration. J. Acoust. Soc. Am. 102, 2906–2919 (1997)

    Article  ADS  Google Scholar 

  13. Dau, T., Püschel, D., Kohlrausch, A.: A quantitative model of the ‘effective’ signal processing in the auditory system: I. Model structure. J. Acoust. Soc. Am. 99, 3615–3622 (1996)

    Article  ADS  Google Scholar 

  14. Dau, T., Püschel, D., Kohlrausch, A.: A quantitative model of the ‘effective’ signal processing in the auditory system: II. Simulations and measurements. J. Acoust. Soc. Am. 99, 3623–3631 (1996)

    Article  ADS  Google Scholar 

  15. Dau, T., Verhey, J., Kohlrausch, A.: Intrinsic envelope fluctuations and modulation-detection thresholds for narrowband noise carriers. J. Acoust. Soc. Am. 106, 2752–2760 (1999)

    Article  ADS  Google Scholar 

  16. Duifhuis, H.: Audibility of high harmonics in a periodic pulse. J. Acoust. Soc. Am. 48, 888–893 (1970)

    Article  ADS  Google Scholar 

  17. Duifhuis, H., Horst, J.W., Wit, H.P. (eds.): Basic Issues in Hearing. Academic Press, London (1988)

    Google Scholar 

  18. Fletcher, H.: Auditory patterns. Rev. Mod. Phys. 12, 47–65 (1940)

    Article  ADS  Google Scholar 

  19. Glasberg, B.R., Moore, B.C.J.: Derivation of auditory filter shapes from notched-noise data. Hear. Res. 47, 103–138 (1990)

    Article  Google Scholar 

  20. Green, D.M., Swets, J.A.: Signal Detection Theory and Psychophysics. Wiley, New York, NY (1974). reprinted by Krieger

    Google Scholar 

  21. Greenwood, D.D.: Auditory masking and the critical band. J. Acoust. Soc. Am. 33, 484–502 (1961)

    Article  ADS  Google Scholar 

  22. Hartmann, W.M., Pumplin, J.: Noise power fluctuation and the masking of sine signals. J. Acoust. Soc. Am. 83, 2277–2289 (1988)

    Article  ADS  Google Scholar 

  23. Hawkins, J.E.J., Stevens, S.S.: The masking of pure tones and of speech by white noise. J. Acoust. Soc. Am. 22, 6–13 (1950)

    Article  ADS  Google Scholar 

  24. Healy, E.W., Bacon, S.P.: Measuring the critical band for speech. J. Acoust. Soc. Am. 119, 1083–1091 (2006)

    Article  ADS  Google Scholar 

  25. Hübner, M., Wiegrebe, L.: The effect of temporal structure on rustling-sound detection in the gleaning bat, Megaderma lyra. J. Comp. Physiol. A 189, 337–346 (2003)

    Google Scholar 

  26. Irino, T., Patterson, R.D.: A time-domain, level-dependent auditory filter: the gammachirp. J. Acoust. Soc. Am. 101, 412–419 (1997)

    Article  ADS  Google Scholar 

  27. Johannesma, P.I.M.: The pre-response stimulus ensemble of neurons in the cochlear nucleus. In: Cardozo, B.L., de Boer, E., Plomp, R. (eds.) Proceedings of the 2nd International Symposium on Hearing, pp. 58–69. Institute for Perception Research, Eindhoven (1972)

    Google Scholar 

  28. Johnston, J.D.: Transform coding of audio signals using perceptual noise criteria. IEEE J. Selected Areas Commun. 6, 314–323 (1988)

    Article  Google Scholar 

  29. Joris, P.X., van der Heijden, M., Louage, D.H., de Sande, B.V., Kerckhoven, C.V.: Dependence of binaural and cochlear “best delays” on characteristic frequency. In: Pressnitzer, D., de Cheveigné, A., McAdams, S., Collet, L. (eds.) Auditory Signal Processing: Physiology. Psychoacoustics, and Models, pp. 477–483. Springer, New York (2005)

    Chapter  Google Scholar 

  30. Kohlrausch, A.: Masking patterns of harmonic complex tone maskers and the role of the inner ear transfer function. In: Duifhuis, H., Horst, J., Wit, H. (eds.) Basic Issues in Hearing, pp. 339–350. Academic Press, Harcourt Brace Jovanovich. Publ, London (1988)

    Google Scholar 

  31. Kohlrausch, A., Fassel, R.: Binaural masking level differences in nonsimultaneous masking. In: Gilkey, R.H., Anderson, T. (eds.) Binaural and Spatial Hearing in Real and Virtual Environments, Chapter 9, pp. 169–190. Lawrence Erlbaum Ass, London (1997)

    Google Scholar 

  32. Kohlrausch, A., Fassel, R., Dau, T.: The influence of carrier level and frequency on modulation and beat-detection thresholds for sinusoidal carriers. J. Acoust. Soc. Am. 108, 723–734 (2000)

    Article  ADS  Google Scholar 

  33. Kohlrausch, A., Fassel, R., van der Heijden, M., Kortekaas, R., van de Par, S., Oxenham, A.J., Püschel, D.: Detection of tones in low-noise noise: further evidence for the role of envelope fluctuations. Acustica United Acta Acustica 83, 659–669 (1997)

    Google Scholar 

  34. Kohlrausch, A., Houtsma, A.J.M.: Edge pitch of harmonic complex tones. IPO Annual Progress Report 26, 39–49 (1991)

    Google Scholar 

  35. Kohlrausch, A., Houtsma, A.J.M.: Pitch related to spectral edges of broadband signals. Phil. Trans. R. Soc. Lond. B 336, 375–382 (1992)

    Article  ADS  Google Scholar 

  36. Kohlrausch, A., Sander, A.: Phase effects in masking related to dispersion in the inner ear. II. Masking period patterns of short targets. J. Acoust. Soc. Am. 97, 1817–1829 (1995)

    Article  ADS  Google Scholar 

  37. Kohlrausch, A., van de Par, S.: On the use of specific signal types in hearing research. In: Kurtz, T., Parlitz, U., Kaatze, U. (eds.) Oscillations, Waves, and Interactions. Sixty Years Drittes Physikalisches Institut. A Festschrift, pp. 37–71. Universitätsverlag Göttingen, Göttingen (2007)

    Google Scholar 

  38. Kollmeier, A., Klump, G., Hohmann, V., Langemann, U., Mauermann, M., Verhey, J. (eds.): Hearing—From Sensory Processing to Perception. Proceedings of the 14th International Symposium on Hearing. Springer, Berlin (2007)

    Google Scholar 

  39. Langhans, A., Kohlrausch, A.: Differences in auditory performance between monaural and diotic conditions. I: Masked thresholds in frozen noise. J. Acoust. Soc. Am. 91, 3456–3470 (1992)

    Article  ADS  Google Scholar 

  40. Lentz, J.J., Leek, M.R.: Psychophysical estimates of cochlear phase response: masking by harmonic complexes. J. Assn. Res. Otolaryngol. 2, 408–422 (2001)

    Article  Google Scholar 

  41. Mehrgardt, S., Schroeder, M.R.: Monaural phase effects in masking with multicomponent signals. In: Klinke, R., Hartmann, R. (eds.) Hearing—Physiological Bases and Psychophysics, pp. 289–295. Springer, New York (1983)

    Chapter  Google Scholar 

  42. Moore, C., Alcántara, J.I., Dau, T.: Masking patterns for sinusoidal and narrow-band noise maskers. J. Acoust. Soc. Am. 104, 1023–1038 (1998)

    Article  ADS  Google Scholar 

  43. Münkner, S., Kohlrausch, A., Püschel, D.: Influence of fine structure and envelope variability on gap-duration discrimination thresholds. J. Acoust. Soc. Am. 99, 3126–3137 (1996)

    Article  ADS  Google Scholar 

  44. Oxenham, A.J., Dau, T.: Reconciling frequency selectivity and phase effects in masking. J. Acoust. Soc. Am. 110, 1525–1538 (2001)

    Article  ADS  Google Scholar 

  45. Oxenham, J., Dau, T.: Towards a measure of auditory-filter phase response. J. Acoust. Soc. Am. 110, 3169–3178 (2001)

    Article  ADS  Google Scholar 

  46. Patterson, R.D.: Auditory filter shape. J. Acoust. Soc. Am. 55, 802–809 (1974)

    Article  ADS  Google Scholar 

  47. Patterson, R.D.: Auditory filter shapes derived with noise stimuli. J. Acoust. Soc. Am. 59, 640–654 (1976)

    Article  ADS  Google Scholar 

  48. Patterson, R.D., Allerhand, M.H., Giguère, C.: Time-domain modelling of peripheral auditory processing: a modular architecture and a software platform. J. Acoust. Soc. Am. 98, 1890–1894 (1995)

    Article  ADS  Google Scholar 

  49. Patterson, R.D., Nimmo-Smith, I., Weber, D.L., Milroy, R.: The deterioration of hearing with age: frequency selectivity, the critical ratio, the audiogram, and speech threshold. J. Acoust. Soc. Am. 72, 1788–1803 (1982)

    Article  ADS  Google Scholar 

  50. Pierce, J.R.: Some work on hearing. Am. Scientist 48, 40–45 (1960)

    Google Scholar 

  51. Pumplin, J.: Low-noise noise. J. Acoust. Soc. Am. 78, 100–104 (1985)

    Article  ADS  Google Scholar 

  52. Recio, A., Rhode, W.S.: Basilar membrane responses to broadband stimuli. J. Acoust. Soc. Am. 108, 2281–2298 (2000)

    Article  ADS  Google Scholar 

  53. Schneider, P., Andermann, M., Wengenroth, M., Goebel, R., Flor, H., Rupp, A., Diesch, E.: Reduced volume of Heschl’s gyrus in tinnitus. Neuroimage 45, 927–927 (2009)

    Article  Google Scholar 

  54. Schroeder, M.R.: New results concerning monaural phase sensitivity. J. Acoust. Soc. Am. 31, 1579 (1959)

    Article  ADS  Google Scholar 

  55. Schroeder, M.R.: Vocoders: analysis and synthesis speech. Proc. IEEE 54, 720–734 (1966)

    Article  Google Scholar 

  56. Schroeder, M.R.: Relation between critical bands in hearing and the phase characteristics of the cubic difference tones. J. Acoust. Soc. Am. 46, 1488–1492 (1969)

    Article  ADS  Google Scholar 

  57. Schroeder, M.R.: Synthesis of low-peak-factor signals and binary sequences with low autocorrelation. IEEE Transact. Inf. Theor. 16, 85–89 (1970)

    Article  Google Scholar 

  58. Schroeder, M.R.: An integrable model for the basilar membrane. J. Acoust. Soc. Am. 53, 429–434 (1973)

    Article  ADS  Google Scholar 

  59. Schroeder, M.R.: Models of hearing. Proc. IEEE 63, 1332–1350 (1975)

    Article  Google Scholar 

  60. Schroeder, M.R.: New viewpoints in binaural interaction. In: Evans, E.F., Wilson, J.P. (eds.) Psychophysics and Physiology of Hearing, pp. 455–456. Academic Press, New York (1977)

    Google Scholar 

  61. Schroeder, M.R., Atal, B.S.: Computer simulation of sound transmission in rooms. IEEE Int. Convention Record 11, 150–155 (1963)

    Google Scholar 

  62. Schroeder, M.R., Atal, B.S., Hall, J.: Optimizing digital speech coders by exploiting masking properties of the human ear. J. Acoust. Soc. Am. 66, 1647–1652 (1979)

    Article  ADS  Google Scholar 

  63. Schroeder, M.R., Atal, B.S., Sessler, G.M., West, J.E.: Acoustical measurements in Philharmonic Hall (New York). J. Acoust. Soc. Am. 40, 434–440 (1966)

    Article  ADS  Google Scholar 

  64. Schroeder, M.R., Gottlob, D., Siebrasse, K.F.: Comparative study of European concert halls. J. Acoust. Soc. Am. 56, 1195–1201 (1974)

    Article  ADS  Google Scholar 

  65. Schroeder, M.R., Hall, J.L.: Model for mechanical to neural transduction in the auditory receptor. J. Acoust. Soc. Am. 55, 1055–1060 (1974)

    Article  ADS  Google Scholar 

  66. Schroeder, M.R., Strube, H.W.: Flat-spectrum speech. J. Acoust. Soc. Am. 79, 1580–1583 (1986)

    Article  ADS  Google Scholar 

  67. Shamma, S.A., Shen, N., Gopalaswamy, P.: Stereausis: Binaural processing without neural delays. J. Acoust. Soc. Am. 86, 989–1006 (1989)

    Article  ADS  Google Scholar 

  68. Smith. Der Einfluß des Vorzeichens des Momentanfrequenzverlaufes von Maskierern auf die Detektion von reinen Tönen (The influence of the sign of the change in the instantaneous frequency of a masker on the detectability of pure tones). Master’s Thesis, Georg-August-Universität Göttingen (1984)

    Google Scholar 

  69. Smith, K., Sieben, U., Kohlrausch, A., Schroeder, M.R.: Phase effects in masking related to dispersion in the inner ear. J. Acoust. Soc. Am. 80, 1631–1637 (1986)

    Article  ADS  Google Scholar 

  70. Strube, H.W.: A computationally efficient basilar-membrane model. Acustica 58, 207–214 (1985)

    Google Scholar 

  71. Summers, V.: Effects of hearing impairment and presentation level on masking period patterns for Schroeder-phase harmonic complexes. J. Acoust. Soc. Am. 108, 2307–2317 (2000)

    Article  ADS  Google Scholar 

  72. Summers, V., Leek, M.R.: Masking of tones and speech by Schroeder-phase harmonic complexes in normally hearing and hearing-impaired listeners. Hear. Res. 118, 139–150 (1998)

    Article  Google Scholar 

  73. van de Par, S., Kohlrausch, A.: A new approach to comparing binaural masking level differences at low and high frequencies. J. Acoust. Soc. Am. 101, 1671–1680 (1997)

    Article  ADS  Google Scholar 

  74. van de Par, S., Kohlrausch, A.: Diotic and dichotic detection using multiplied-noise maskers. J. Acoust. Soc. Am. 103, 2100–2110 (1998)

    Article  ADS  Google Scholar 

  75. van de Par, S., Kohlrausch, A.: The role of intrinsic masker fluctuations on the spectral spread of masking. In Forum Acusticum 2005, Budapest, pp. 1635–1640, European Acoustics Association (2005)

    Google Scholar 

  76. van der Heijden, M., Kohlrausch, A.: The role of envelope fluctuations in spectral masking. J. Acoust. Soc. Am. 97, 1800–1807 (1995)

    Article  ADS  Google Scholar 

  77. von Klitzing, R., Kohlrausch, A.: Effect of masker level on overshoot in running- and frozen-noise maskers. J. Acoust. Soc. Am. 95, 2182–2201 (1994)

    Google Scholar 

Download references

Acknowledgments

The work described in this chapter reflects the close and fruitful cooperations that I (AK) had over the past more than 30 years with friends and colleagues at the DPI in Göttingen and later on in Eindhoven where I was joined at the IPO by SvdP in 1992. We both would like to thank all our colleagues for the creative atmosphere, never-ending curiosity and great fun, which helped to generate some interesting scientific insights. A part of the Göttingen atmosphere was in 1991 exported to Eindhoven, and as can be seen from the reference list, this has become a similarly fruitful period.

Author information

Authors and Affiliations

  1. Behavior, Cognition, & Perception Group, Philips Research Europe, High Tech Campus 36 (MS WO 02), Eindhoven, 5656AE, The Netherlands

    Armin Kohlrausch

  2. Human-Technology Interaction, Eindhoven University of Technology, Eindhoven, The Netherlands

    Armin Kohlrausch

  3. Acoustics Group, Institute of Physics, Carl von Ossietzky Universität, Oldenburg, Germany

    Steven van de Par

Authors
  1. Armin Kohlrausch
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Steven van de Par
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Armin Kohlrausch .

Editor information

Editors and Affiliations

  1. The School of Architecture, Rensselaer Polytechnic Institute, Troy, New York, USA

    Ning Xiang

  2. Darmstadt University of Technology, Darmstadt, Germany

    Gerhard M. Sessler

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer International Publishing Switzerland

About this chapter

Cite this chapter

Kohlrausch, A., van de Par, S. (2015). Where Mathematics and Hearing Science Meet: Low Peak Factor Signals and Their Role in Hearing Research. In: Xiang, N., Sessler, G. (eds) Acoustics, Information, and Communication. Modern Acoustics and Signal Processing. Springer, Cham. https://doi.org/10.1007/978-3-319-05660-9_7

Download citation

Publish with us

Policies and ethics

Search

Navigation