Engineering Mathematics, Volume II, Second Edition

7

Fourier Transform

During the study of Fourier series, we confined ourselves to periodic functions. To a periodic function f we assigned Fourier coefficients c_n, n ∈ and then defined the Fourier series as a trigonometric series with coefficients taken as Fourier coefficients. We then discussed the convergence and some other properties of Fourier series. But we generally encounter non-periodic functions in many applications. Our aim in this chapter is to develop a concept, called Fourier transform, in which to a non-periodic function f, we shall assign for each ω ∈ a function F defined on such that F(ω) ∈ . This function F will be called Fourier ...