## With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, tutorials, and more.

No credit card required

 4 Fourier Transform: Applications

The theory of the Fourier transform is outlined in Chapter 10. Over the interval −∞ < x < ∞ the exponential version of the transform is appropriate, while over the range 0 < x < ∞ the sine or cosine transforms may be useful. We start with several applications of the exponential transform; §4.10 to §4.13 show examples of the use of the sine and cosine transforms.

4.1 Useful formulae for the exponential transform

The exponential Fourier transform is useful to solve linear problems when one or more coordinates range over the entire real line (−∞, ∞). The transform of a function f (x) is defined by*

 (4.1.1)

with inverse

 (4.1.2)

For other definitions in common use see p. 267.

At a point ...

## With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, interactive tutorials, and more.

No credit card required