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AlephZero

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You can understand the basics of what it means and how to use it for some practical applications with very little maths (i.e. high school level), if you are happy to use computer software to crunch the numbers for you.

At the other end of the scale, Springer publish the Journal of Fourier Analysis and Applications, for new research papers.

A random selection of applications for it are image processing, signal processing, data compression (e.g. MP3 audio and and JPG video), and advanced methods for solving ODEs and PDEs.

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jasonRF

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jason

edit: linear algebra is also helpful for understanding Fourier - it was a prereq. for our signals class and the ideas from linear algebra are natural to use to think about fourier series, both in continuous and discrete time.

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analogdesign

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An application is filtering. A noisy signal looks like a clean signal, but has lots of tiny spikes and troughs on it. Using Fourier analysis, we can find the coefficients for the sum, then set them equal to zero beyond a certain frequency threshold. Then the tiny spikes-which correspond to very high frequencies- aren't added into our sum, so when we put everything back together we get a nice smooth and clear signal.

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