Math for Intelligence

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The Applications of Matrices - What I wish my teachers told me way earlier | MathPrep

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Explained

Siraj Raval

Gilbert Strang (MIT) - Linear Algebra

Fourier Transform (FT), Fourier Series, and Fourier Analysis

Joseph Fourier showed that representing a function as a sum of trigonometric functions greatly simplifies the study of heat transfer. Joseph was a French mathematician and physicist born in Auxerre and best known for initiating the investigation of Fourier series, which eventually developed into Fourier analysis and harmonic analysis, and their applications to problems of heat transfer and vibrations. The Fourier transform and Fourier's law of conduction are also named in his honor. Fourier is also generally credited with the discovery of the greenhouse effect.

  • Fourier Transform (FT) decomposes a function of time (a signal) into its constituent frequencies. This is similar to the way a musical chord can be expressed in terms of the volumes and frequencies of its constituent notes. Fourier Transform | Wikipedia
  • Fourier Series is a periodic function composed of harmonically related sinusoids, combined by a weighted summation. The discrete-time Fourier transform is an example of Fourier series. For functions on unbounded intervals, the analysis and synthesis analogies are Fourier Transform and inverse transform. Fourier Series | Wikipedia
  • Fourier Analysis the study of the way general functions may be represented or approximated by sums of simpler trigonometric functions. Fourier Analysis | Wikipedia

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