Non-stationary RRi series
============

In some situations like physical exercise, the RRi series might present
a non-stationary behavior. In cases like these, classical approaches are not
recommended once the statistical properties of the signal vary over time.

The following figure depicts the RRi series recorded on a subject riding a bicycle.
Without running analysis and only visually inspecting the time series, is possible
to tell that the average and the standard deviation of the RRi are not constant
as a function of time.

.. image:: ../figures/exercise_rri.png
    :width: 500 px

In order to extract useful information about the dynamics of non-stationary RRi series,
the following methods applies the classical metrics in shorter running adjacent segments, 
as illustrated in the following image:

.. image:: ../figures/sliding_segments.png
    :width: 500 px

For example, for a segment size of **30s** (S) and **15s** (O) overlap a signal with **300s** (D) will have P segments:

P = int((D - S) / (S - O)) + 1

P = int((300 - 30) / (30 - 15)) + 1 = 19 segments

Time Varying
############

Time domain indices applied to shorter segments

.. code-block:: python

    from hrv.sampledata import load_exercise_rri
    from hrv.nonstationary import time_varying

    rri = load_exercise_rri()
    results = time_varying(rri, seg_size=30, overlap=0)
    results.plot(index="rmssd", marker="o", color="r")


.. image:: ../figures/tv_rmssd.png
    :width: 500 px


Plot the results from **time varying** together with its respective RRi series


.. code-block:: python

    from hrv.sampledata import load_exercise_rri
    from hrv.nonstationary import time_varying

    rri = load_exercise_rri()
    results = time_varying(rri, seg_size=30, overlap=0)
    results.plot_together(index="rmssd", marker="o", color="k")

.. image:: ../figures/tv_together.png
    :width: 500 px

Short Time Fourier Transform
############################

To be implemented.