ABSTRACT
Fourier series in science and engineering has practical applications in the resolution of sound waves into their different frequencies, for example, in an MP3 player, in telecommunications and Wi-Fi, in computer graphics and image processing, in climate variation, and in water waves. This chapter provides students to show that Fourier expansions of non-periodic functions have limited range and describes Fourier series for non-periodic functions over a range of 2π. However, it is possible to determine a Fourier series to represent the function over any range of width 2π. Given a non-periodic function, a new function may be constructed by taking the values of a function in the given range and then repeating them outside of the given range at intervals of 2π.
