References and further reading ============================== This page lists books and papers that are useful for understanding the algorithms and examples in ``lattice-dsp``. The package documentation does not attempt to replace these sources; it explains how the package uses the ideas. Scalar lattice filters, PARCOR, and AR modeling ----------------------------------------------- .. [Makhoul1975] J. Makhoul, "Linear Prediction: A Tutorial Review," *Proceedings of the IEEE*, 1975. A classic tutorial on linear prediction, AR models, prediction-error filters, and reflection/PARCOR ideas. .. [MarkelGray1976] J. D. Markel and A. H. Gray, Jr., *Linear Prediction of Speech*. Springer, 1976. A classic source for speech linear prediction and PARCOR/lattice structures. .. [Durbin1960] J. Durbin, "The Fitting of Time-Series Models," *Revue de l'Institut International de Statistique*, 1960. Classic Toeplitz/Yule-Walker recursion background. .. [Burg1967] J. P. Burg, "Maximum Entropy Spectral Analysis," presented at the 37th Annual International SEG Meeting, 1967. Original maximum-entropy/Burg spectral estimation work. .. [UlrychBishop1975] T. J. Ulrych and T. N. Bishop, "Maximum entropy spectral analysis and autoregressive decomposition," *Reviews of Geophysics*, 1975. A widely cited review connecting maximum entropy spectral analysis and AR modeling. Schur, Szegő, OPUC, and rational approximation background ----------------------------------------------------------- .. [Pick1916] G. Pick, "Über die Beschränkungen analytischer Funktionen, welche durch vorgegebene Funktionswerte bewirkt werden," *Mathematische Annalen*, 1916. Classical source for the interpolation condition now known as the Pick or Nevanlinna--Pick problem. .. [Dym1989] H. Dym, *J Contractive Matrix Functions, Reproducing Kernel Hilbert Spaces and Interpolation*, American Mathematical Society, 1989. Reference for Schur-class interpolation, reproducing kernels, and contractive matrix-function viewpoints. .. [Schur1917] I. Schur, "Über Potenzreihen, die im Innern des Einheitskreises beschränkt sind," *Journal für die reine und angewandte Mathematik*, 1917. Classical source for the Schur algorithm and Schur functions. .. [Szego1975] G. Szegő, *Orthogonal Polynomials*, 4th ed., American Mathematical Society, 1975. Classical reference for orthogonal polynomial recurrences and Christoffel-Darboux identities. .. [Simon2005] B. Simon, *Orthogonal Polynomials on the Unit Circle*, Parts 1 and 2, American Mathematical Society, 2005. Modern reference for OPUC, Verblunsky coefficients, Szegő recurrences, and unit-circle spectral theory. .. [Bultheel2000] A. Bultheel and M. Van Barel, "Rational approximation in linear systems and control," *Journal of Computational and Applied Mathematics*, 2000. Useful bridge between Schur algorithms, rational approximation, and control-oriented system theory. .. [Potapov1955] V. P. Potapov, "The multiplicative structure of J-contractive matrix functions," *Trudy Moskov. Mat. Obshch.*, 4, 1955. Classical source for Potapov factorization and J-contractive matrix functions. .. [BultheelMuller1998] A. Bultheel and K. Müller, "On several aspects of J-inner functions in Schur analysis," *Bulletin of the Belgian Mathematical Society - Simon Stevin*, 1998. Survey-style discussion of J-inner functions, Potapov factorization, and generalized Schur interpolation context. .. [HanzonOliviPeeters2010] B. Hanzon, M. Olivi, and R. L. M. Peeters, "Balanced realizations of discrete-time stable all-pass systems and the tangential Schur algorithm," arXiv:1012.3272, 2010. Explains the connection between tangential Schur algorithms, RKHS ideas, Schur parameters, and balanced realizations of multivariable lossless systems. .. [OliviMarmoratHanzonPeeters2003] M. Olivi, J.-P. Marmorat, B. Hanzon, and R. L. M. Peeters, "Schur parametrizations and balanced realizations of real discrete-time stable all-pass systems," CDC, 2003. Real tangential Schur parametrization and balanced-realization context for stable all-pass systems. .. [MarmoratHanzonOliviPeeters2002] J.-P. Marmorat, B. Hanzon, M. Olivi, and R. L. M. Peeters, "Matrix rational H2 approximation: a state-space approach using Schur parameters," CDC, 2002. Uses Schur-parameter coordinates on the manifold of stable all-pass/lossless systems for matrix rational approximation. .. [GonnetGuettelTrefethen2013] P. Gonnet, S. Güttel, and L. N. Trefethen, "Robust Padé Approximation via SVD," *SIAM Review*, 2013. Practical numerical-linear-algebra view of Padé approximation and near-degenerate rational approximants. .. [Trefethen2023] L. N. Trefethen, "Square blocks and equioscillation in the Padé, Walsh, and Carathéodory-Fejér tables," 2023. Modern discussion of Padé/Walsh rational-approximation tables and degeneracy structure. Adaptive filtering ------------------ This section includes the Widrow--Hoff LMS origin, Odile Macchi's transmission-oriented LMS treatment, standard adaptive-filter texts, and the H∞/minimax reinterpretation of LMS. .. [WidrowHoff1960] B. Widrow and M. E. Hoff, Jr., "Adaptive Switching Circuits," 1960 IRE WESCON Convention Record, 1960. Classical origin point for the LMS/delta-rule adaptive-update idea. .. [Macchi1995] Odile Macchi, *Adaptive Processing: The Least Mean Squares Approach with Applications in Transmission*, Wiley, 1995. Focused treatment of LMS-based adaptive processing, transmission/equalization applications, tracking, sign algorithms, and adaptive IIR context. .. [Haykin2002] S. Haykin, *Adaptive Filter Theory*, 4th ed., Prentice Hall, 2002. Standard reference for LMS, NLMS, and RLS families. .. [Haykin2014] S. Haykin, *Adaptive Filter Theory*, 5th ed., Pearson, 2014. Later edition with extensive examples and computer experiments for LMS and RLS adaptive filters. .. [WidrowStearns1985] B. Widrow and S. D. Stearns, *Adaptive Signal Processing*, Prentice Hall, 1985. Foundational adaptive signal processing text. .. [Sayed2008] A. H. Sayed, *Adaptive Filters*, Wiley/IEEE Press, 2008. Modern treatment of adaptive-filter theory and analysis. .. [FarhangBoroujeny2013] B. Farhang-Boroujeny, *Adaptive Filters: Theory and Applications*, 2nd ed., Wiley, 2013. .. [HassibiSayedKailath1996] B. Hassibi, A. H. Sayed, and T. Kailath, "H∞ Optimality of the LMS Algorithm," *IEEE Transactions on Signal Processing*, 44(2), 1996. Shows that LMS and normalized LMS have exact H∞/minimax interpretations, explaining a robustness property that is not visible from the usual least-squares story. Multichannel AR, block Toeplitz systems, and block Levinson recursions ---------------------------------------------------------------------- .. [Whittle1963] P. Whittle, "On the fitting of multivariate autoregressions, and the approximate canonical factorization of a spectral density matrix," *Biometrika*, 1963. Classical source for multivariate autoregression and spectral factorization ideas. .. [WigginsRobinson1965] R. A. Wiggins and E. A. Robinson, "Recursive solution to the multichannel filtering problem," *Journal of Geophysical Research*, 1965. Early multichannel recursive filtering work often associated with the LWR family of algorithms. .. [KailathSayedHassibi2000] T. Kailath, A. H. Sayed, and B. Hassibi, *Linear Estimation*, Prentice Hall, 2000. Modern reference for structured covariance, Toeplitz systems, innovations, and recursive estimation. Multirate DSP, paraunitary systems, and matrix all-pass filters --------------------------------------------------------------- .. [Vaidyanathan1993] P. P. Vaidyanathan, *Multirate Systems and Filter Banks*, Prentice Hall, 1993. Core reference for perfect reconstruction, paraunitary/orthogonal filter banks, polyphase systems, and lattice realizations. .. [StrangNguyen1996] G. Strang and T. Nguyen, *Wavelets and Filter Banks*, Wellesley-Cambridge Press, 1996. Accessible treatment of filter banks and wavelet connections. .. [Mehta2023] P. Mehta, A. S. Bharath, K. Appaiah, R. Velmurugan, and D. Pal, "Lattice All-Pass Filter based Precoder Adaptation for MIMO Wireless Channels," arXiv:2302.11204, 2023. Useful modern example of matrix-lattice all-pass filters as compact unitary MIMO representations. The package uses this as motivation for general matrix-lattice DSP, not as a claim to be a 5G simulator. Model reduction, Hankel operators, Nehari, and AAK ------------------------------------------------------------ .. [Nehari1957] Z. Nehari, "On bounded bilinear forms," *Annals of Mathematics*, 65(1), 1957. Classical source for the Nehari approximation problem and its Hankel-operator interpretation. .. [AdamjanArovKrein1971] V. M. Adamjan, D. Z. Arov, and M. G. Krein, "Analytic properties of Schmidt pairs for a Hankel operator and the generalized Schur-Takagi problem," *Mathematics of the USSR-Sbornik*, 1971. Foundational AAK work connecting Hankel singular structure and rational approximation. .. [Glover1984] K. Glover, "All optimal Hankel-norm approximations of linear multivariable systems and their L∞-error bounds," *International Journal of Control*, 1984. Classic control-theory source for Hankel-norm model reduction. .. [Peller2003] V. V. Peller, *Hankel Operators and Their Applications*, Springer, 2003. Comprehensive operator-theoretic reference for Hankel operators, Nehari-type problems, and AAK theory. .. [Antoulas2005] A. C. Antoulas, *Approximation of Large-Scale Dynamical Systems*, SIAM, 2005. Standard model-reduction reference, useful for balanced truncation, Hankel singular values, and system approximation. Orthogonal convolutions and ML-adjacent unitary systems ---------------------------------------------------------- .. [Wang2020] J. Wang, Y. Chen, R. Chakraborty, and S. X. Yu, "Orthogonal Convolutional Neural Networks," CVPR, 2020. Orthogonality constraints for convolutional layers and stability/regularization motivation. .. [Achour2022] E. M. Achour, F. Malgouyres, and F. Mamalet, "Existence, Stability and Scalability of Orthogonal Convolutional Neural Networks," *Journal of Machine Learning Research*, 2022. Theoretical properties of orthogonal convolutional transforms. .. [Su2022] J. Su, W. Byeon, and F. Huang, "Scaling-up Diverse Orthogonal Convolutional Networks by a Paraunitary Framework," ICML, 2022. Connects orthogonal convolution layers in the spatial domain with paraunitary systems in the spectral domain. How references map to package features -------------------------------------- .. list-table:: :header-rows: 1 :widths: 35 65 * - Package feature - Main references * - Reflection/PARCOR coefficients and Schur/Pick motivation - [Makhoul1975]_, [MarkelGray1976]_, [Pick1916]_, [Schur1917]_, [Dym1989]_ * - Tangential Schur and J-inner/Potapov diagnostics - [Dym1989]_, [Potapov1955]_, [BultheelMuller1998]_, [HanzonOliviPeeters2010]_, [OliviMarmoratHanzonPeeters2003]_, [MarmoratHanzonOliviPeeters2002]_ * - Levinson-Durbin and Burg AR tools - [Durbin1960]_, [Burg1967]_, [UlrychBishop1975]_, [Szego1975]_, [Simon2005]_ * - Multichannel/block Levinson AR tools - [Whittle1963]_, [WigginsRobinson1965]_, [KailathSayedHassibi2000]_ * - NLMS/RLS adaptive filtering - [WidrowHoff1960]_, [Macchi1995]_, [Haykin2002]_, [WidrowStearns1985]_, [Sayed2008]_ * - H∞/minimax LMS interpretation - [WidrowHoff1960]_, [Macchi1995]_, [HassibiSayedKailath1996]_ * - Model reduction and Hankel/AAK theory - [Nehari1957]_, [AdamjanArovKrein1971]_, [Glover1984]_, [Peller2003]_, [Antoulas2005]_, [Bultheel2000]_, [GonnetGuettelTrefethen2013]_ * - Paraunitary and matrix lattice systems - [Vaidyanathan1993]_, [StrangNguyen1996]_, [Mehta2023]_ * - ML unitary convolution motivation - [Wang2020]_, [Achour2022]_, [Su2022]_