Abstract
Many kinds of Wavelets are used to investigate different kinds of data series (Mallat 2009). Still all are based on the same ground of the scaling law and the possibility of free spacing. Wavelets can be placed arbitrarily in a time series at any place, and therefore differ from a Fourier Transform which always needs to be performed between the two boundaries of the time series. Therefore Wavelets may have any frequency with arbitrary precision, which again differs from Fourier Transforms which need to be multiples of the fundamental frequency of the series length.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Bader, R.: Reconstruction of radiating sound fields using minimum energy method. J. Acoust. Soc. Am. 127(1), 300–308 (2010)
Bader, R., Münster, M., Richter, J., Timm, H.: Microphone Array Measurements of Drums and Flutes. In: Bader, R. (ed. / Hrsg) Musical Acoustics, Neurocognition, and Psychology of Music / Musikalische Akustik, Neurokognition und Musikpsychologie, vol. 25, pp. 13–54. Hamburger Jahrbuch für Musikwissenschaft (2009)
Bai, M.R.: Application of BEM (boundary element method)-based acoustic holography to radiation analysis of sound sources with arbitrarily shaped geometries. J. Acoust. Soc. Am. 92(1), 533–549 (1992)
Bouchet, L., Loyau, T.: Calculation of acoustic radiation using equivalent-sphere methods. J. Acoust. Soc. Am. 170(5), 2387–2397 (2000)
Fletcher, N., Rossing, T.D.: Physics of Musical Instruments. Springer (2000)
Granqvist, S., Hammabert, B.: The Correlogram: a visual display of periodicity. TMH-QPSR 4, 13–22 (1998)
Haase, M., Widjajakusuma, J., Bader, R.: Scaling Laws and Frequency Decomposition from Wavelet Transform Maxima Lines and Ridges. In: Novak, M.M. (ed.) Emergent Nature, pp. 365–374. World Scietific (2002)
Jansson, E.V.: A study of acoustical and hologram interferometric measurements of the top plate vibrations of a guitar. Acustica 25, 95–100 (1971)
Magalhães, M.B.S., Tenenbaum, R.A.: Sound Source Reconstruction Techniques: A Review of Their Evolution and New Trends. Acta Acustica United with Acustica 90, 199–220 (2004)
Mallat, S.: A Wavelet Tour of Signal Processing: The Sparse Way, 3rd edn. Elsevier, Amsterdam (2009)
Meynard, J.D., Williams, E.G., Lee, Y.: Nearfield acoustic holography: I. Theory of generalized holography and the development of NAH. J. Acoust. Soc. Am. 78(4), 1395–1413 (1985)
Ochmann, M.: The source simulation technique for acoustic radiation problems. Acustica 81, 512–527 (1995)
Ochmann, M.: The full-field equations for acoustic radiation and scattering. J. Acoust. Soc. Am. 105(5), 2574–2584 (1999)
Rayess, N., Wu, S.F.: Experimental validations of the HELS method for reconstructing acoustic radiation from a complex vibrating structure. J. Acoust. Soc. Am. 107(6), 2955–2964 (1999)
Richardson, B.E., Roberts, G.W.: The adjustment of mode frequencies in guitars: a study by means of holographic interferometry and finite element analysis. In: Proceedings of the Stockhom Musical Acoustics Conference, pp. 285–302 (1983)
Rossing, T.D.: Science of Percussion Instruments. World Scientific (2001)
Rossing, T.D.: Physics of Guitars: An Introduction. J. of Guitar Acoustics 4, 45–67 (1981)
Wang, Z., Wu, S.F.: Helmholtz equation-least-squares method for reconstructing the acoustic pressure field. J. Acoust. Soc. Am. 102(4), 2020–2032 (1995)
Williams, E.G.: Fourier Acoustics. Sound Radiation and Nearfield Acoustic Holography. Academic Press, San Diego (1999)
Williams, E.G., Maynard, J.D., Skurdzyk, E.: Sound source reconstructions using a microphone array. J. Acoust. Soc. Am. 6(1), 341–344 (1980)
Wu, S.F.: On reconstruction of acoustic pressure fields using the Helmholtz equation least squares method. J. Acoust. Soc. Am. 107(5), 2511–2522 (1999)
Wu, S.F., Lu, H., Bajwa, M.S.: Reconstruction of transient acoustic radiation from a sphere. J. Acoust. Soc. Am. 117(4), 2065–2077 (2005)
Zipser, L., Franke, H.: Refractoscopic visualisation of sound in musical instruments. In: Bresin, R. (ed.) Proceedings of SMAC 2003, pp. 763–766 (2003)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Bader, R. (2013). Frequency Representations. In: Nonlinearities and Synchronization in Musical Acoustics and Music Psychology. Current Research in Systematic Musicology, vol 2. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-36098-5_2
Download citation
DOI: https://doi.org/10.1007/978-3-642-36098-5_2
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-36097-8
Online ISBN: 978-3-642-36098-5
eBook Packages: EngineeringEngineering (R0)