Theoretical Background
======================

Overview
--------

Semi-Classical Signal Analysis (SCSA) is a signal processing method inspired by 
quantum mechanics. It treats signals as "potentials" and uses eigenvalue decomposition 
of associated differential operators for reconstruction and denoising.

Mathematical Foundation
-----------------------

For a 1D signal V(x), SCSA constructs the operator:

.. math::

   \mathcal{L} = -\gamma^2 \frac{d^2}{dx^2} + V(x)

where γ is the semi-classical parameter controlling smoothness.

Key Parameters
--------------

Gamma Parameter
~~~~~~~~~~~~~~~

The parameter γ controls smoothing:

* Small γ (< 1): More smoothing
* Large γ (> 1): Less smoothing, preserves details

Cutoff Parameter h
~~~~~~~~~~~~~~~~~~

The cutoff h determines reconstruction quality:

* Small h: More smoothing
* Large h: Less smoothing

Use ``filter_with_c_scsa()`` for automatic optimization.
