In this paper we offer a method for constructing functions with many gaps in their supports and in the supports of their Fourier transform. As a result we answer a question of Benedicks [Ben1] and we ...

The Reed-Muller-Fourier Transform was not originated by a Pascal matrix, however it happens to show a strong family resemblance with it, sharing several basic properties. Its area of application is ...

Singularity functions are an important topic in undergraduate studies covered primarily in signal processing. Some of those functions are the step function, the ramp function and the parabolic ...

Fourier transforms are one of the most important algorithms in math, and help our electronics handle visual and audio signals in a sophisticated way.

To help get your mind around the concept, [Jez Swanson] has this interactive Fourier transform visualizer that really drives home the important points.

Transactions of the American Mathematical Society, Vol. 218 (Apr., 1976), pp. 61-87 (27 pages) The main result is an Lp mean convergence theorem for the partial sums of the Fourier series of a class ...