Spectral Estimation and the Open Window
John C. Burgess · The Journal of the Acoustical Society of America · 1974
The usual artifice used in spectral estimation is to visualize a finite data record as the product of a boxcar data window and a data record of infinite length. This has led to the concept that leakage results from the lobe structure observed in the Fourier transform of a boxcar data window. Use of the true artifice for finite discrete time series, that both the data window and the sample time series are periodically extended, leads to the concept of an open data window. The open window makes no contribution to leakage. There is no leakage when the open window is used with a sample from an ideal random process. Leakage results from modification of an open window (smoothing) or from Procrustean truncation of coherent components in a data record. Augmenting a data record with zeros and tapering the ends with short half-cosine bells are equivalent to modifying an open window. The latter practice is not effective in counteracting leakage from truncated periodic components and has little value for improving the stability of estimates for random processes.