References & Further Reading

References

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

    Ch. 10 covers LTI systems with random inputs comprehensively.

  2. S. Haykin, Adaptive Filter Theory, Prentice Hall, 4th ed., 2001

    Ch. 3 (Wiener filter) and Ch. 5 (noise analysis) are primary references.

  3. J. G. Proakis and M. Salehi, Digital Communications, McGraw-Hill, 5th ed., 2008

    Ch. 4 covers matched filters and optimum receivers.

  4. A. V. Oppenheim, A. S. Willsky, and S. H. Nawab, Signals and Systems, Prentice Hall, 2nd ed., 1997

    Ch. 10 provides the signals and systems background for this chapter.

  5. H. L. Van Trees, Detection, Estimation, and Modulation Theory, Part I, John Wiley & Sons, 1968

    Ch. 4 is the definitive treatment of matched filters and optimum detection.

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

    The foundational monograph on optimal linear filtering.

  7. R. M. Gray, Probability, Random Processes, and Ergodic Properties, Springer, 2nd ed., 2009

    Rigorous treatment of spectral theory and linear systems.

  8. A. Leon-Garcia, Probability, Statistics, and Random Processes for Electrical Engineering, Pearson, 3rd ed., 2008

    Accessible treatment of random processes through LTI systems.

  9. H. Stark and J. W. Woods, Probability and Random Processes with Applications to Signal Processing, Prentice Hall, 3rd ed., 2002

    Good coverage of matched filters and noise bandwidth.

  10. G. L. Turin, An Introduction to Matched Filters, 1960

    Classic tutorial on the matched filter principle.

  11. G. Caire, Fundamentals of Stochastic Processes: Lecture Notes, TU Berlin, 2024

    Course material, Ch. 8: Second-Order Processes.

  12. K. Vu, R. Cavalcante, and G. Caire, LMMSE Channel Estimation with Spatial Covariance Side Information, 2018

    LMMSE estimation exploiting spatial structure in massive MIMO.

Further Reading

These resources extend the material in this chapter to adaptive filtering, spectral estimation, and advanced receiver design.

  • Causal Wiener filter and spectral factorization

    Haykin (2001), Ch. 3, §3.7

    The non-causal Wiener filter is unrealizable. The causal version requires spectral factorization — a technique that connects to Hardy spaces and complex analysis.

  • Adaptive filtering (LMS, RLS)

    Haykin (2001), Ch. 5--9

    When the signal and noise statistics are unknown or time-varying, adaptive algorithms converge to the Wiener solution without explicit PSD estimation.

  • Matched filter banks for CDMA and OFDM

    Proakis and Salehi (2008), Ch. 14

    Modern digital communications use banks of matched filters (one per spreading code or subcarrier) to efficiently demodulate multiple simultaneous users.

  • Kalman filter as the state-space Wiener filter

    Haykin (2001), Ch. 10

    The Kalman filter is the recursive, time-varying generalization of the Wiener filter, optimal for state estimation in linear Gaussian systems.

ExercisesCh 16 →