What is the salient uses of Fourier analysis in machine learning? What subjects of Fourier analysis have had more effect on machine learning?
Please mention the references. 



What subjects of Fourier analysis have had more effect on machine learning?
Here is a [summary](http://www.mathcs.duq.edu/~jackson/tutorial.html) that could provide a good entry point into the literature:



> 
> Since Linial, Mansour, and Nisan introduced the use of discrete
>  Fourier analysis in machine learning in 1989, it has been a powerful
>  tool for proving both positive and negative theoretical learnability
>  results and has also helped to spawn fruitful applied machine learning
>  research. Several learning-theoretic results rely on this technique,
>  such as the Kushilevitz-Mansour algorithm for learning (parity)
>  decision trees. Key algorithmic ideas based on Fourier analysis include the membership-query algorithm for finding weak-approximating parities and use of Fourier coefficients to estimate the influence of a variable. An open learning problem
>  that seem particularly amenable to Fourier techniques is the problem to learn monotone functions with respect to the uniform distribution from examples alone.
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