Lanczos sigma factor

Summary

The Lanczos sigma factors are the weights $\sigma_k = \frac{\sin(\pi k/m)}{\pi k/m}$ by which one multiplies the terms of a truncated Fourier series of order $m$. The weighted sum, called the sigma approximation, equals the average of the partial sum over a window of length $2\pi/m$ around each point. This local averaging greatly reduces the overshoot near jumps known as the Gibbs phenomenon. The factors are named after Cornelius Lanczos.