Welch's method

Welch's method, named after Peter D. Welch, is an approach to spectral density estimation, meaning the estimation of how the power of a signal is spread across frequencies. It improves on the standard periodogram and on Bartlett's method by trading some frequency resolution for lower noise in the estimated power spectrum. The signal is split into L segments of length M that overlap by D points, with a 50 percent overlap when D equals M divided by two and no overlap, which is the same as Bartlett's method, when D is zero. Each segment is multiplied by a window function, which is why the result is called a modified periodogram, the discrete Fourier transform of every windowed segment is taken and its squared magnitude computed, and the individual spectrum estimates are averaged to reduce variance. The method is used in physics, engineering and applied mathematics.