Basic system identification sanity check
========================================

.. admonition:: Tutorial goal

   Run a minimal identification example to check package wiring and API behavior.

.. note::

   New to the terminology? See the :doc:`lattice DSP concept map <../../algorithms/concept_map>` and the :doc:`causality/data-use guide <../../theory/causality_and_data_use>` for how online, offline, block, and MIMO examples should be read.

Context
-------

This page is intentionally simple.  It is a first script to run after installation to make
sure the compiled extension and Python package import correctly.

Key idea and equations
----------------------

The desired signal is generated by a known system from a reference input:

.. math::

   d[n] = H(q^{-1})x[n].

The model output :math:`\widehat d[n]` is compared with :math:`d[n]`.
This is the two-signal identification form, not causal self-prediction of
``x[n]`` from its own past.

Causality and data use
----------------------

The example is a small causal system-identification sanity check: output is formed from the reference input and current filter state, then compared with the desired signal.

How to read the result
----------------------

A successful run should complete without import/build errors and should report a finite identification error.

Run command
-----------

.. code-block:: bash

   python examples/system_identification.py

Source code
-----------

.. literalinclude:: ../../../examples/system_identification.py
   :language: python
   :linenos: