Abstract
This chapter focuses on the Fourier transforms. The chapter reviews the Fourier exponential transform and the basic properties of the Fourier transforms. Some elementary Fourier transform pairs are presented in a tabulated form. It may either be used to find the Fourier transform F(ω) of a function f(x) or, conversely, to find the inverse Fourier transform f(x) of a given Fourier transform F(ω). Care is necessary when using general tables of Fourier transform pairs because of the different choices made for the numerical normalization factors multiplying the integrals, and the signs of the exponents in the integrands. The chapter reviews the Fourier cosine and sine transforms, their basic properties, and the Fourier cosine and sine transform pairs. Some elementary Fourier cosine and sine transform pairs are presented in a tabulated form and they may either be used to find the required transform of a function f(x) or, conversely, given either Fc(ω) or Fs(ω), to find the corresponding inverse transform f(x).
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