Questions tagged [harmonic-analysis]

Harmonic analysis is a branch of mathematics concerned with the representation of functions or signals as the superposition of basic waves, and the study of and generalization of the notions of Fourier series and Fourier transforms.

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Has anyone explored Ptolemy's epicycles as an early form of Fourier analysis?

Whilst researching science in the ancient world, I came across an observation, which unfortunately I did not make a note of, and so cannot credit, that Ptolemy's epicycles were an early form of ...
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4answers
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How was Fourier analysis important to the development of set theory?

I recently read the following quote (unfortunately, I copied it down without attribution): You may be surprised to know that Fourier analysis played a role in the early development of set theory. In ...
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0answers
160 views

Origin of the Fourier transform (1878)

I located Joseph Fourier's book, Analytical Theory of Heat (1878), but at first glance it looks like it is all about heat. What did Fourier call the Fourier transform? When did he first use it?
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Substantiating claimed Fourier quote about “an arbitrarily capricious graph”

The following quote (in English) is fairly widely attributed to Fourier, but I can't substantiate it. An arbitrary function, continuous or with discontinuities, defined in a finite interval by an ...
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0answers
44 views

On the origin of the concept of aliasing & the Discrete Fourier Transform frequency axis

The development of the fast Fourier transform (FFT) is attributed to Cooley & Tukey, both of whom have written a lot about its historical development. However, I am searching for early ...
4
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1answer
1k views

Who came up with the convolution theorem?

I am looking for the earliest reference which proposed the convolution theorem which is often utilized in signal processing (i.e., convolution becomes multiplication in the Fourier domain). The ...
2
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1answer
160 views

First evaluation of $\sum_{n \geq 1} 1/n^2$ by Fourier series

There are many ways to evaluate $\sum_{n \geq 1} 1/n^2$ as $\pi^2/6$, including multiple solutions using Fourier series. A colleague asked me who was the first person to use Fourier series (or Fourier ...