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 ...

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