ABSTRACT
This chapter discusses Fourier transform theory for continuous and discrete functions as well as Fourier transform applications. It shows MATLAB's built-in methods for executing forward and inverse Fourier transforms. The transformations from the time domain to the frequency domain and back are called the forward Fourier and inverse Fourier transforms respectively. The transformation is general and can broadly be applied to any variable, not just a time variable. The Fourier transform provides the basis for many filtering and compression algorithms. It is also an indispensable tool for analyzing noisy data. Many differential equations can be solved in the periodic oscillation basis. Additionally, the calculation of convolution integrals of two functions is very fast and simple when it is done in the frequency domain. It is natural to think that a periodic function can be constructed as the sum of other periodic functions. In Fourier series, we do it in the basis of sines and cosines, which are clearly periodic functions.
