Dirichlet Kernel

The Dirichlet kernel, named for Peter Gustav Lejeune Dirichlet, is a family of periodic functions of period two pi that can be written in several equivalent forms and that play a central role in the study of Fourier series. Convolving the Dirichlet kernel with any two-pi-periodic function produces that function's nth-degree Fourier series approximation, so the convergence behavior of Fourier series can be studied through the properties of the kernel itself, which approaches a Dirac comb as n grows large. This description is adapted from Wikipedia contributors under CC BY-SA 4.0; changes were made. https://creativecommons.org/licenses/by-sa/4.0/