Fourier Series

This chapter gathers the most important formula of the Fourier series and related mathematical subjects. Most of these formulas have been rigorously proofed. Although the purpose of this chapter is to provide a background for chapters 16, 17, 19, and 20, the way in which we present the materials here is more than just as background. The mathematics here is an independent topic by itself, except that we have omitted the proof part in order to remain within the limits of the scope of this book. The chapter includes Fourier series. Fourier integrals, Fourier transforms, convolution, and discrete Fourier transform. It also includes the extension of Fourier series and Fourier transform to the Lorentz shape and correlation function. Emphasis lies on the concept that Fourier series has already been incorporated into the basic common language of physics, chemistry, structural biology and electronic engineering.