Compression Chemical Signal Using Wavelet Transform

Wavelet Transform (WT) had became a popular topic in chemistry and other fields
of science starting from late 1980s, when compactly supported orthonormal wavelets and
fast calculation algorithms were proposed by Mallat (1989) and Daubechies (1988)
respectively. Meanwhile, Fourier transform (FT) plays a very important role in analytical
methods in chemistry through Nuclear Magnetic Resonance (NMR) spectroscopy and
Infrared (IR) spectroscopy (Felinger, 1998). FT localized only in the frequency (or scale)
domain but not in time (or position) domain, while WT is well localized in both.
Furthermore, compared with FT, a large number of basis functions are available with WT,
i.e., Haar, Daubechies, Coiflet, Spline, etc. In this paper, we will discuss the application of
Fast Wavelet Transform (FWT) for data compression in chemistry. Some numerical results
will be presented by using Matlab programming.