Chapter 11 - Functional Series and Integral Transforms

Abstract

A Fourier series is a type of functional series with terms that consist of coefficients times sine and cosine functions. It can represent almost any periodic function. The sine and cosine functions can be replaced by complex exponential functions. A Fourier transform is a representation of a function using an integral instead of a sum. Many modern instruments use Fourier transforms to produce spectra from raw data in another form. A Laplace transform is a representation of a function that is similar to a Fourier transform except that it uses real exponential functions instead of complex exponential functions.