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.
- Package positioning
- Choosing an algorithm
- Causality, data use, and signal roles
- Filtering relationships and signal-processing vocabulary
- Hardy, Hankel, reachability, and observability
- Interpolation, Schur stability, and why lattice coordinates help
- Tangential Schur, Pick matrices, and J-inner factors