# The use of fast Fourier transform for the estimation of power spectra: A method based on time averaging over short, modified periodograms

@article{Welch1967TheUO, title={The use of fast Fourier transform for the estimation of power spectra: A method based on time averaging over short, modified periodograms}, author={Peter D. Welch}, journal={IEEE Transactions on Audio and Electroacoustics}, year={1967}, volume={15}, pages={70-73} }

The use of the fast Fourier transform in power spectrum analysis is described. Principal advantages of this method are a reduction in the number of computations and in required core storage, and convenient application in nonstationarity tests. The method involves sectioning the record and averaging modified periodograms of the sections.

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## 3 References

### A Direct Digital Method of Power Spectrum Estimation

- Computer ScienceIBM J. Res. Dev.
- 1961

A method of digital power spectrum estimation involving the direct combination of the sample time function with sines and cosines and the practical design details necessary for the planning of a spectral estimation program are treated.

### Discussion, Emphasizing the Connection Between Analysis of Variance and Spectrum Analysis*

- Mathematics
- 1961

Abstract : The case of a function of time is considered which is periodic with known period. A classical analysis of variance, based on a pattern involving d observations in each of the r.c cells…

### AN EXPLORATORY STUDY OF THE BI-SPECTRUM OF ECONOMIC TIME SERIES

- Mathematics
- 1965

The main motivation of the analysis presented here is to investigate certain non-linear properties of the mechanism which may be supposed to generate a time series. I investigate specifically…