The DOI matches its Crossref record; 5 of the 5 references it cites were found in a registry or an index.
Spectrum estimation and harmonic analysis
Abstract
In the choice of an estimator for the spectrum of a stationary time series from a finite sample of the process, the problems of bias control and consistency, or "smoothing," are dominant. In this paper we present a new method based on a "local" eigenexpansion to estimate the spectrum in terms of the solution of an integral equation. Computationally this method is equivalent to using the weishted average of a series of direct-spectrum estimates based on orthogonal data windows (discrete prolate spheroidal sequences) to treat both the bias and smoothing problems. Some of the attractive features of this estimate are: there are no arbitrary windows; it is a small sample theory; it is consistent; it provides an analysis-of-variance test for line components; and it has high resolution. We also show relations of this estimate to maximum-likelihood estimates, show that the estimation capacity of the estimate is high, and show applications to coherence and polyspectrum estimates.
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Cites
A Mathematical Theory of Communication
Shannon, C. E. (1948) · Bell System Technical Journal · doi:10.1002/j.1538-7305.1948.tb01338.x · Cited by 88,486
An algorithm for the machine calculation of complex Fourier series
Cooley, J. W., & Tukey, J. W. (1965) · Mathematics of Computation · doi:10.1090/s0025-5718-1965-0178586-1 · Cited by 13,154
Prolate Spheroidal Wave Functions, Fourier Analysis and Uncertainty - I
Slepian, D., & Pollak, H. O. (1961) · Bell System Technical Journal · doi:10.1002/j.1538-7305.1961.tb03976.x · Cited by 2,492
Prolate Spheroidal Wave Functions, Fourier Analysis and Uncertainty - II
Landau, H. J., & Pollak, H. O. (1961) · Bell System Technical Journal · doi:10.1002/j.1538-7305.1961.tb03977.x · Cited by 839
Landau, H. J., & Pollak, H. O. (1962) · Bell System Technical Journal · doi:10.1002/j.1538-7305.1962.tb03279.x · Cited by 839
Cited by
Delorme, A., & Makeig, S. (2004) · Journal of Neuroscience Methods · doi:10.1016/j.jneumeth.2003.10.009 · Cited by 24,371
A Pervasive Millennial-Scale Cycle in North Atlantic Holocene and Glacial Climates
Bond, G., Showers, W., Cheseby, M., Lotti, R., Almasi, P., deMenocal, P., Priore, P., Cullen, H., Hajdas, I., & Bonani, G. (1997) · Science · doi:10.1126/science.278.5341.1257 · Cited by 2,720
Westerhold, T., Marwan, N., Drury, A. J., Liebrand, D., Agnini, C., Anagnostou, E., Barnet, J. S. K., Bohaty, S. M., De Vleeschouwer, D., Florindo, F., et al. (2020) · Science · doi:10.1126/science.aba6853 · Cited by 1,946
Delorme, A., Sejnowski, T., & Makeig, S. (2007) · NeuroImage · doi:10.1016/j.neuroimage.2006.11.004 · Cited by 1,759
Theta rhythms coordinate hippocampal-prefrontal interactions in a spatial memory task
Jones, M. W., & Wilson, M. A. (2005) · PLoS Biology · doi:10.1371/journal.pbio.0030402 · Cited by 1,036
Metadata
- Authors
- Thomson, D. J.
- Venue
- Proceedings of the IEEE
- Published
- 1982
- Volume
- 70
- Issue
- 9
- Pages
- 1055-1096
- ISSN
- 0018-9219 (ISSN-L)
- OpenAlex
- W2155722796
- Cited by
- 4,418
- References
- 5
- FWCI
- 8.78
- Type
- journal article
- Language
- en
- Open access
- closed
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