Smoothing or fitting of experimentally observed curves are the tasks that often arise when experimental data are processed. Thus, it is necessary to do these procedures correctly, with minimum loss of information. The wavelet analysis [1,2,3] seems to be the most suitable tool for this purpose, because it provides information about both various signal frequencies and also the location of these frequencies. The main idea of the wavelet transform is to decompose the function under consideration with respect to a functional basis built by dilations and shifts of a single well localized function, called a basic wavelet.
The lifting scheme [4,5] is a new approach to construct the so-called second generation wavelets, i. e., wavelets which are not necessarily translations and dilations of one function. The latter we refer to as a first generation wavelets or classical wavelets. The lifting scheme has some additional advantages in comparison with the classical wavelets. This transform works for signals of an arbitrary size with correct treatment of the boundaries. Also, all computations can be done in-place. Moreover, the lifting scheme makes them optimal, sometimes increasing the speed of calculations by factor 2.
Our smoothing task is nothing but the wavelet data filtering. It is carried out in three steps: