Abstract
Many years ago, Manfred Schroeder proved that transfer functions in rooms follow complex Gaussian distributions. This property was extended to impulse responses by the author, following a suggestion by Moorer for simulating impulse responses. More recently, several authors have checked again the later property with modern signal analysis tools. They obtained mixed success, with results that strongly depend on the length of the analysis window. In order to understand these unstable results, the present paper takes a closer look at the statistical distributions of both impulse responses and transfer functions. It shows that an accurate model of both the impulse response and the transfer function is necessary in order to test the distributions. Further, it presents several sources of artefacts that skew the distributions, and show that they can be ascribed to the signal processing methods used to extract the responses. Finally, the conditions for obtaining true Gaussian distributions are specified.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Schroeder, M.R.: Eigenfrequenzstatistik und Anregungsstatistik in Raümen. Acustica 4, 456–465 (1954)
Schroeder, M.R.: Die statistischen Parameter der Frequenzkurven von grossen Raümen. Acustica 4, 594–600 (1954); reprinted in M.R. Schroeder, “Statistical parameters of the frequency response curves of large rooms”, J. Acoust. Eng. Soc. 35 (1987) 307–316
Schroeder, M.R., Kuttruff, H.: On frequency response curves in rooms. Comparison of experimental, theoretical and Monte Carlo results for the average frequency spacing between maxima. J. Acoust. Soc. Am. 34, 76–80 (1962)
Moorer, J.A.: About this reverberation business. Comput. Music J. 3, 13–18 (1979)
Stewart, R., Sandler, M.: Statistical measures of early reflections of room impulse responses. In: Proceedings of the 10th International Conference on Digital Audio Effects (DAFx-07), Bordeaux, France, pp. 59–62 (2007)
Defrance, G., Polack, J.D.: Measuring mixing time in auditoria. J. Acoust. Soc. Am. 123, 3499 (2008)
Figueiredo, F.L.: Indices acoustiques et leurs rapports statistiques: vérification objective et subjective pour un ensemble de salles de spectacles. Ph.D. thesis, Université Pierre et Marie Curie, Paris (2011)
Polack, J.D.: La transmission de l’énergie sonore dans les salles. Thèse d'Etat—Université du Maine, Le Mans (1988)
Jot, J.M.: Etude et realisation d’un spatialisateur de sons par modeles physiques et perceptifs. Ph.D. thesis, Telecom Paris (1992)
Farina, A.: Advancements in impulse response measurements by sine sweeps. In: AES 122nd Convention, Vienna, Austria (2007)
ISO 3382: Acoustics - Measurement of the reverberation time of rooms with reference to other acoustical parameters, (1997)
Acknowledgement
The author wants to thank Xi Zhang, who carried out all the computations used in this paper.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Polack, JD. (2015). Are Impulse Responses Gaussian Noises?. 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_5
Download citation
DOI: https://doi.org/10.1007/978-3-319-05660-9_5
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-05659-3
Online ISBN: 978-3-319-05660-9
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)