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By Francis Weston Sears

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Rolf-Inge Godoy, who I own many inspirations and ideas in the fields of music psychology, musical gestures, philosophy, and neurophysiology. In terms of Musical Signal Processing I learned a lot, and was very much encouraged by Prof. Julius Smith or Prof. Jim Beauchamp, who I want to thank for all their support and ideas. In terms of Musical Acoustics a great lot of support and inspiration I own to Prof. Tom Rossing, Prof. Uwe Hansen, Prof. Jim Cottingham, Prof. Antoine Chaigne, and Prof. Johan Sundberg, among many others, which I want to thank for all their encouragement and work.

Bader: Nonlinearities & Synchronization in Musical Acoustics, CRSM 2, pp. 13–56. 1007/978-3-642-36098-5_2 14 2 Frequency Representations with the Wavelet kernel Ψ(x) = e−(x−α) 2 / β eiγ/ ax . 2) The scaling law assumes that y is analyzed with different scaling length a. As parameter a appears in the exponential complex function of the kernel, the analyzing length changes the analyzing frequency, too. So for a given fixed wavelet parameter γ, the window of the frequency dependent analyzing frame changes.

G. violin ’scratching’ and trumpet ’spitting’ as being caused by the same iterative process. In the first part of the book basic Signal Processing tools are presented as most suitable for investigating sounds of Musical Instruments. Very basic methods like FFT or autocorrelation are omitted as many excellent textbooks are available here. The section splits into time series and embedding methods. Wavelet analysis, correlograms, and spectral entropy are methods to derive periodicities and Gestalt patterns while at the same time allow zooming into sounds both temporally and in terms of frequency.

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