Transformations,Implementations, and Pitfalls

Transformations are ubiquitous in practically every field of signal processing and the choice of the right transformation can be crucial for extracting the information from the data. In computational practice, however, the fact that one tries to implement an infinite transformation defined on a continuum for finite discrete data can lead to unwanted and often also unexpected effects. Using the example of the continuous wavelet transform, this note points to some of these effects and gives explanation why this happens and how it can be avoided. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)