Notes on the Fourier Transform — Eli Bendersky

The Fourier series is a great tool for analyzing periodic functions. But what about functions that don’t repeat? We’ve seen that we can compute Fourier series for a non-periodic function defined on a finite interval, as long as we don’t care about its behavior beyond that interval. Let’s extend this idea to functions that never repeat; that is, non-periodic functions defined on the interval (-\infty,\infty). Visualizing Fourier series for non-repeating functions To motivate the subject ahead,…