References

References

  1. N. Wiener, Extrapolation, Interpolation, and Smoothing of Stationary Time Series, MIT Press, 1949

    Declassified version of the 1942 NDRC report. The foundational document of the Wiener filter.

  2. A. N. Kolmogorov, Stationary Sequences in Hilbert Space, 1941

    Independent discrete-time derivation, including the Kolmogorov-Szego formula.

  3. G. Szego, Beitrage zur Theorie der Toeplitzschen Formen, 1920

    The original limit theorem for Toeplitz determinants; source of the geometric-mean formula.

  4. T. Kailath, A. H. Sayed, and B. Hassibi, Linear Estimation, Prentice Hall, 2000

    Chapter 7 is the standard modern treatment of Wiener filtering and spectral factorization.

  5. M. H. Hayes, Statistical Digital Signal Processing and Modeling, Wiley, 1996

    Accessible engineering-oriented account with many worked examples of Wiener filter design.

  6. S. Haykin, Adaptive Filter Theory, Pearson, 5th ed., 2014

    Definitive reference on LMS and RLS as adaptive Wiener filters.

  7. A. Papoulis and S. U. Pillai, Probability, Random Variables, and Stochastic Processes, McGraw-Hill, 4th ed., 2002

    Chapters 10-11 cover WSS processes, PSDs, and the Wiener filter at a broad engineering level.

  8. B. D. O. Anderson and J. B. Moore, Optimal Filtering, Prentice Hall, 1979

    Classical reference bridging Wiener and Kalman filtering through the innovations framework.

  9. C. W. Therrien, Discrete Random Signals and Statistical Signal Processing, Prentice Hall, 1992

    Clear presentation of discrete-time Wiener filtering and linear prediction.

  10. H. Wold, A Study in the Analysis of Stationary Time Series, Almqvist & Wiksell, 1938

    Source of the Wold decomposition and the innovations representation.

  11. M. B. Khalilsarai, S. Haghighatshoar, X. Yi, and G. Caire, Channel Extrapolation via Subspace-Based Prediction in Massive MIMO with Mobility, 2021

    Application of Wiener-Kolmogorov prediction to massive MIMO channel aging.

  12. B. Widrow and S. D. Stearns, Adaptive Signal Processing, Prentice Hall, 1985

    Original comprehensive treatment of LMS and its analysis.

Further Reading

For the advanced reader who wants to go beyond this chapter, we suggest a mix of classical texts and modern research directions.

  • Spectral factorization algorithms for rational PSDs

    Kailath, Sayed, Hassibi — Linear Estimation (2000), Appendix E

    Comprehensive numerical methods for factoring high-order rational spectra reliably.

  • Hardy spaces and outer functions

    Hoffman — Banach Spaces of Analytic Functions (1962)

    Mathematical underpinning of the Paley-Wiener condition and minimum-phase factors as outer functions.

  • Toeplitz operators and Szego's theorem

    Grenander and Szego — Toeplitz Forms and Their Applications (1958)

    The deep link between Toeplitz eigenvalue distributions and PSDs.

  • Minimax Wiener filters under uncertainty

    Verdu and Poor — IEEE Trans. Info. Theory, 1984

    Robust Wiener design when PSDs are known only to lie in uncertainty sets.

  • Innovations representation of non-Gaussian processes

    Kailath — IEEE Trans. Info. Theory, 1970 (classic tutorial)

    Extends the innovations idea beyond the Gaussian case via nonlinear filtering.

ExercisesCh 10 →