CHAPTER 2 The Fourier Kingdom
The story begins in 1807 when Fourier presents a memoir to the Institut de France, where he claims that any periodic function can be represented as a series of harmonically related sinusoids. This idea had a profound impact in mathematical analysis, physics, and engineering, but it took a century and a half to understand the convergence of Fourier series and complete the theory of Fourier integrals.
Fourier was motivated by the study of heat diffusion, which is governed by a linear differential equation. However, the Fourier transform diagonalizes all linear time-invariant operators—the building blocks of signal processing. It therefore is not only the starting point of our exploration but also the basis of all ...
Get A Wavelet Tour of Signal Processing, 3rd Edition now with the O’Reilly learning platform.
O’Reilly members experience books, live events, courses curated by job role, and more from O’Reilly and nearly 200 top publishers.
