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basic_tools:fourier_transform
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Fourier Transform
Why is it interesting?
The Fourier transform is an essential tool that, for example, makes the music format MP3 possible. With the help of the Fourier transform any given music can be split into the frequencies that it is built of. Then, we can remove those that can't be heard by humans and get an equally sounding, but much smaller music file.
Moreover, the Fourier transform is essential in Quantum Field Theory, where we usually expand any given field configuration in terms of it's Fourier modes and then start analyzing it.
Layman
Explanations in this section should contain no formulas, but instead colloquial things like you would hear them during a coffee break or at a cocktail party.
Student
- The best short introduction is An Interactive Guide To The Fourier Transform by Kalid Azad and the best longer introduction in the book "Who Is Fourier? A Mathematical Adventure"
- Fourier Analysis by Körner is a good book
- A nice description of how the Fourier transformation is used in quantum mechanics, can be found at page 246ff "The Emperor's New Mind" by R. Penrose.
Researcher
The motto in this section is: the higher the level of abstraction, the better.
- Common Question 1
- Common Question 2
Examples
- Example1
- Example2:
History
basic_tools/fourier_transform.1520864089.txt.gz · Last modified: 2018/03/12 14:14 (external edit)
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