Fourier series | Wikipedia audio article
Channel: wikipedia tts
Date: 07/05/2019

This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Fourier_series


00:00:38 1 History
00:03:13 2 Definition
00:13:33 2.1 Complex-valued functions
00:20:38 2.2 Other common notations
00:26:49 3 Convergence
00:28:24 4 Examples
00:28:33 4.1 Example 1: a simple Fourier series
00:31:04 4.2 Example 2: Fourier's motivation
00:34:37 4.3 Other applications
00:34:58 5 Beginnings
00:37:54 5.1 Birth of harmonic analysis
00:38:53 6 Extensions
00:39:02 6.1 Fourier series on a square
00:41:12 6.2 Fourier series of Bravais-lattice-periodic-function
01:14:44 6.3 Hilbert space interpretation
01:21:15 7 Properties
01:21:28 7.1 Table of basic properties
01:21:37 7.2 Symmetry properties
01:22:15 7.3 Riemann–Lebesgue lemma
01:24:59 7.4 Derivative property
01:26:11 7.5 Parseval's theorem
01:29:05 7.6 Plancherel's theorem
01:30:15 7.7 Convolution theorems
01:30:51 7.8 Compact groups
01:35:27 7.9 Riemannian manifolds
01:36:20 7.10 Locally compact Abelian groups
01:37:54 8 Table of common Fourier series
01:39:19 9 Approximation and convergence of Fourier series
01:39:50 9.1 Least squares property
01:41:19 9.2 Convergence
01:43:13 9.3 Divergence
01:48:18 10 See also
01:49:08 11 Notes



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SUMMARY
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In mathematics, a Fourier series () is a periodic function composed of harmonically related sinusoids, combined by a weighted summation.  With appropriate weights, one cycle (or period) of the summation can be made to approximate an arbitrary function in that interval (or the entire function if it too is periodic).  As such, the summation is a synthesis of another function.  The discrete-time Fourier transform is an example of synthesis.  The process of deriving the weights that describe a given function is a form of Fourier analysis.  For functions on unbounded intervals, the analysis and synthesis analogies are Fourier transform and inverse transform.