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A Simplified Derivation of Linear Least Square Smoothing and Prediction Theory
Abstract
The central results of the Wiener-Kolmogoroff smoothing and prediction theory for stationary time series are developed by a new method. The approach is motivated by physical considerations based on electric circuit theory and does not involve integral equations or the autocorrelation function. The cases treated are the "infinite lag" smoothing problem, the case of pure prediction (without noise), and the general smoothing prediction problem. Finally, the basic assumptions of the theory are discussed in order to clarify the question of when the theory will be appropriate, and to avoid possible misapplication.
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Cited by
Adaptive noise cancelling: Principles and applications
Widrow, B., Glover, J. R., McCool, J. M., Kaunitz, J., Williams, C. S., Hearn, R. H., Zeidler, J. R., Eugene Dong, Jr., & Goodlin, R. C. (1975) · Proceedings of the IEEE · doi:10.1109/proc.1975.10036 · Cited by 3,939
Least-squares estimation: from Gauss to Kalman
Sorenson, H. W. (1970) · IEEE Spectrum · doi:10.1109/mspec.1970.5213471 · Cited by 746
Cellular Signaling Networks Function as Generalized Wiener-Kolmogorov Filters to Suppress Noise
Hinczewski, M., & Thirumalai, D. (2014) · Physical Review X · doi:10.1103/physrevx.4.041017 · Cited by 30
Noise Control in Gene Regulatory Networks with Negative Feedback
Hinczewski, M., & Thirumalai, D. (2016) · The Journal of Physical Chemistry B · doi:10.1021/acs.jpcb.6b02093 · Cited by 15
Metadata
- Authors
- Bode, H. W., & Shannon, C. E.
- Venue
- Proceedings of the IRE
- Published
- 1950-04
- Volume
- 38
- Issue
- 4
- Pages
- 417-425
- ISSN
- 0096-8390 (ISSN-L)
- OpenAlex
- W2094070726
- Cited by
- 276
- References
- 0
- FWCI
- 11.20
- Type
- journal article
- Language
- en
- Open access
- closed
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- Bode, H. W., & Shannon, C. E. (1950). A Simplified Derivation of Linear Least Square Smoothing and Prediction Theory. Proceedings of the IRE. https://doi.org/10.1109/jrproc.1950.231821
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