Acoustics and Psychoacoustics, 4th Edition

Appendix 1: The Fourier Transform

Chapter Contents

A1.1   Fourier’s Theorem

A1.1.1  Frequency spectrum

A1.2   Fourier Analysis

A1.3   The Complex Fourier Series

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

A1.5   The Convolution Theorem

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, ...