Theory guide

This section gives the conceptual map needed to choose and interpret the algorithms in lattice-dsp. The goal is not to replace a textbook treatment; it is to identify the mathematical objects that appear in the examples and to state the package scope clearly.

Start with the package-positioning page to understand the niche: stable IIR lattice coordinates, model-reduction diagnostics, and SISO/MIMO examples in one workflow. Then use the algorithm-selection page when deciding which API or tutorial to use. Read the causality/data-use page before interpreting online versus offline claims. Read the filtering-relationships page if you want the basic DSP vocabulary behind equalization, echo cancellation, prediction, adaptivity, recursivity, minimum phase, and maximum phase. Read the Hardy/Hankel/state-space page before the finite-Hankel, Nehari/AAK, and MIMO reduction examples. The interpolation/Schur page explains why Pick matrices, inner/outer factors, Kronecker finite-rank structure, and lattice coordinates appear together in the package motivation. The tangential-Schur page gives the finite right-tangential Pick and J-inner baseline used by the matrix/MIMO docs.