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, which produces an array of power measurements vs. frequency "bin".
- The modified periodogram is calculated by applying a window function to the time-domain data, computing the discrete Fourier transform, and then computing the squared magnitude of the result.
- Most window functions afford more influence to the data at the center of the set than to data at the edges, which represents a loss of information. To mitigate that loss, the individual data sets are commonly overlapped in time.
The individual periodograms are then time-averaged, which reduces the variance of the individual power measurements.
This method is used by MATLAB's pwelch command to calculate spectral density.
[edit] References
- "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.
