Examples tutorials¶
These pages are generated from the runnable scripts in examples/. Each tutorial page explains the context, shows the main equations, states what the example verifies when applicable, embeds generated figures/data, and includes the source code. For terminology across the package, start with The lattice DSP concept map; for MIMO claims, see MIMO verification map.
Build the full tutorial gallery with results:
./scripts/build_docs_with_results.sh
Orientation tutorials¶
Interoperability recipes¶
Core scalar lattice tutorials¶
- Reflection coefficients and denominator coefficients
- Lattice-ladder realization versus direct numerator coefficients
- Reflection coefficients as a stability coordinate system
- Why direct-form adaptive IIR updates can become unstable
- OpenMP batch processing for independent streams
- Million-sample IIR throughput for long acoustic-like tails
- Large echo-scale recursive model stress
Model-reduction tutorials¶
- MIMO long-signal state-space stress
- Reachability, observability, and Hankel singular values
- Finite Hankel SISO model reduction
- Nehari and AAK intuition from a finite SISO Hankel matrix
- Finite Nehari tail to rational model
- Exact rational-tail validation for finite Nehari candidates
- AAK Schmidt-pair diagnostics for SISO Hankel approximation
- Finite-section SISO AAK/Nehari certificate
- Selecting a finite SISO AAK/Nehari rational candidate
- Finite-section AAK/Nehari reduction on a non-exact tail
- Finite-section AAK/Nehari reduction of a stable IIR filter
- Finite block-Hankel MIMO model reduction
- Coupled MIMO finite-Hankel model reduction
- MIMO model-reduction stress cases
- MIMO block-Hankel to matrix-lattice bridge diagnostics
- Experimental MIMO state-space to matrix-lattice realization
- Calibrating matrix-lattice static gain diagnostics
Adaptive and AR tutorials¶
Applications and signal-model tutorials¶
Spectral diagnostic tutorials¶
Adaptive and robust filtering tutorials¶
Multichannel and matrix tutorials¶
- Diagonal MIMO equals independent SISO
- Causal online MIMO lattice prediction
- Online coupled MIMO prediction versus independent SISO
- Multichannel AR with block Levinson-Durbin
- Matrix-valued AR spectral estimation
- MIMO lattice response versus block Levinson AR
- Matrix lattice all-pass response
- Coupled MIMO matrix-lattice filtering
- Multichannel audio decorrelation with energy preservation
- Compressing a frequency-dependent unitary response
- Paraunitary filter-bank behavior
- Unitary convolution block for ML-style stability