Theoretical Description of the Fourier Transform of the Absolute Amplitude Spectra and Its Applications

Speaking in a very broad sense, the Fourier transform (FT) can be treated as a systematic way to decompose arbitrary function into a superposition of harmonic (“symmetrical”) functions. It is a fundamental tool for studying of various processes and for this reason it is present in basically every scientific discipline. In last decades, the Fourier transformation was used in distinctive fields such as geophysics (Maus 1999, Skianis et al. 2006), image decomposition in neuroscience (Guyader et al. 2004), imaging in medical applications (Lehmann et al., 1999) just to mention a few. Recently, FT was successfully applied in wood sciences (Fujita et al. 1996; Midorikawa et al. 2005, Midorikawa and Fujita 2005). For example, Fujita and co-workers (Midorikawa et al. 2005, Midorikawa and Fujita 2005) used two-dimensional Fourier transform method to analyze the cell arrangements within the xylem ground tissues. In our recent papers (Csoka et al. 2005, Csoka et al. 2007), we made one step forward and try to analyze the wood anatomy via FT of the density function of the tree. Method is based on a forwarded Fourier transformation of the absolute amplitude spectra. Since the comprehensive literature survey of the accessible studies did not reveal any similar results based on this method, in this chapter we will discuss the basic theorem of FT of an absolute amplitude spectrum and a possibility to generate higher order FT defined as,