## Wavelets Toolbox

By Prof. Alexander Stoffel (FH Koeln)

The need to have some software free to use for teaching was the main reason to create this toolbox. To have all the mathematical details of the transform algorithms visible looking at the source code and the advantage to adapt and modify the code for special purposes (e.g. for diploma- and master theses) were a further motivation.

An overview of the utilities of the toolbox is given first, then some groups of macros are presented in detail, in particular the macros to calculate the wavelet transform for one-dimensional signals (in the practice audio signals) and two-dimensional signals (images). They are the core of the toolbox. All transforms are implemented using the lifting scheme which is briefly sketched.

A second group of macros concerns calculations with FIR filters or – more mathematically spoken – Laurent polynomials. Their main purpose is to help to construct filters satisfying the conditions of perfect reconstruction for two channel filter banks. Internally the filters are represented as Scilab rationals, but particular output macros allow to show them as z-transform or show the table of the coefficients.

The use of the other groups of utilities as the code experiments, the in- and output of image data and the redundant wavelet transform is only briefly sketched.

The wavelib toolbox in its present form has been used during six years for a master course on wavelets and during a summer term for a research project concerning audio SPAM detection.