https://www.damtp.cam.ac.uk/user/dbs26/ David Skinner University of Cambridge https://www.damtp.cam.ac.uk/user/dbs26/1Bmethods.html Complete PDF File Contents ・Fourier Transforms Simple properties of Fourier transforms. The Fourier inversion theorem. Parseval's theorem for Fourier transforms. Schwartz functions and tempered distributions. Linear systems and transfer functions. The discrete Fourier transform. Cooley and Tukey's algorithm for the fast Fourier transform. https://www.damtp.cam.ac.uk/user/dbs26/1BMethods/FourierT.pdf 8 Fourier Transforms 8.3.1 Fourier transform of the Dirac δ We’ve seen that, if we want to solve a driven pde Ly(x)=f(x) then its often useful to first construct a Green’s function G(x,ξ) obeying LG(x,ξ)= δ(x-ξ). Thus, if we wish to use. Fourier transforms to solve such equations, we'll need to understand the Fourier transform of distributions such as the δ-function.
https://en.wikipedia.org/wiki/Discrete_Fourier_transform Discrete Fourier transform Wikipedia In mathematics, the discrete Fourier transform (DFT) converts a finite sequence of equally-spaced samples of a function into a same-length sequence of equally- ...
