Welch's method, named after Peter D. Welch, is an approach for spectral density estimation. It is used in physics, engineering, and applied mathematics for estimating the power of a signal at different frequencies. The method is based on the concept of using periodogram spectrum estimates, which are the result of converting a signal from the time domain to the frequency domain. Welch's method is an improvement on the standard periodogram spectrum estimating method and on Bartlett's method, in that it reduces noise in the estimated power spectra in exchange for reducing the frequency resolution. Due to the noise caused by imperfect and finite data, the noise reduction from Welch's method is often desired.
The Welch method is based on Bartlett's method and differs in two ways:
After doing the above, the periodogram is calculated by computing the discrete Fourier transform, and then computing the squared magnitude of the result, yielding power spectrum estimates for each segment. The individual spectrum estimates are then averaged, which reduces the variance of the individual power measurements. The end result is an array of power measurements vs. frequency "bin".
Other overlapping windowed Fourier transforms include:
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