The Fourier Transform

The Fourier Transform is one of the key tools in solving and studying partial differential equations. The Fourier transform decomposes a function of time into the frequencies that make it up, similarly to how a musical chord can be expressed as the amplitude of its constituent notes. The Fourier Transform is a tool that breaks a waveform into an alternate representation, characterized by sine and cosines. The Fourier Transform shows that any waveform can be re-written as the sum of sinusoidal functions. The Fourier transform is important in mathematics, engineering, and the physical sciences.

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  • Fourier integral operator
  • Laplace transform & Linear canonical transform
  • Special functions and generalized functions

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