Frequency representations

pp. 13-56

in: Rolf Bader, Nonlinearities and synchronization in musical acoustics and music psychology, Berlin, Springer, 2013

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.