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Engineering Mathematics
book

Engineering Mathematics

by Babu Ram
June 2009
Intermediate to advanced content levelIntermediate to advanced
1100 pages
42h 22m
English
Pearson India
Content preview from Engineering Mathematics

18

Fourier Transform

During the study of Fourier series, we confined ourselves to periodic functions. To a periodic function f we assigned Fourier coefficients cn, n ∈ ℤ 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 ∈ ℝ a function F defined on ℝ such that F(ω) ∈ ℂ. This function F will be called Fourier transform of the non-periodic function f. The difference, we note, in a Fourier series and ...

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Publisher Resources

ISBN: 9789332515611