Welch method

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In physics, engineering, and applied mathematics, Welch's method, named after P.D. Welch, is used for estimating power spectra.

The Welch method, based on Barlett's procedure, splits a set of data into smaller sets of data and calculates the modified periodogram (the power spectrum) of each set. The modified periodogram is calculated by applying a window function to the time-domain data, computing the discrete fourier transform, and then computing the magnitude square of the result. Then the frequency domain coefficients arising from calculating the modified periodograms are averaged over the frequency components of each data set to reduce the variance. Due to the windowing, the Welch method provides a smoothed periodogram estimate.

This method is used by MATLAB's PSD command to calculate spectral density.

Reference

• "The Use of Fast Fourier Transform for the Estimation of Power Spectra: A Method Based on Time Averaging Over Short, Modified Periodograms", IEEE Transactions on Audio Electroacoustics, Volume AU-15 (June 1967), pages 70-73.

• Oppenheim, A.V., and R.W. Schafer, Digital Signal Processing, Englewood Cliffs, NJ: Prentice-Hall, 1975, pp 548-554.