Appendix 1: The Fourier Transform

**Chapter Contents**

**A1.3 The Complex Fourier Series**

**A1.4 Frequency Analysis of Non-periodic Signals: The Fourier Transform**

**A1.6 A Fourier Transform Example: The Single Pulse**

**A1.7 The Discrete Fourier Transform**

A1.1 Fourier’s Theorem

Jean Baptiste Joseph Fourier (1768–1830) worked on a mathematical model of heat transfer in solid bodies (amongst many other topics). His thesis *On the Propagation of Heat in Solid Bodies* was published in 1807 and contained a novel idea for expanding a continuous function as a trigonometric series. Although Fourier developed this as a part of his model for heat transfer, ...

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