{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "\n\n# Temporal whitening with AR model\n\nHere we fit an AR model to the data and use it\nto temporally whiten the signals.\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "collapsed": false
      },
      "outputs": [],
      "source": [
        "# Authors: Alexandre Gramfort <alexandre.gramfort@inria.fr>\n#\n# License: BSD-3-Clause\n# Copyright the MNE-Python contributors."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "collapsed": false
      },
      "outputs": [],
      "source": [
        "import matplotlib.pyplot as plt\nimport numpy as np\nfrom scipy import signal\n\nimport mne\nfrom mne.datasets import sample\nfrom mne.time_frequency import fit_iir_model_raw\n\nprint(__doc__)\n\ndata_path = sample.data_path()\nmeg_path = data_path / \"MEG\" / \"sample\"\nraw_fname = meg_path / \"sample_audvis_raw.fif\"\nproj_fname = meg_path / \"sample_audvis_ecg-proj.fif\"\n\nraw = mne.io.read_raw_fif(raw_fname)\nproj = mne.read_proj(proj_fname)\nraw.add_proj(proj)\nraw.info[\"bads\"] = [\"MEG 2443\", \"EEG 053\"]  # mark bad channels\n\n# Set up pick list: Gradiometers - bad channels\npicks = mne.pick_types(raw.info, meg=\"grad\", exclude=\"bads\")\n\norder = 5  # define model order\npicks = picks[:1]\n\n# Estimate AR models on raw data\nb, a = fit_iir_model_raw(raw, order=order, picks=picks, tmin=60, tmax=180)\nd, times = raw[0, 10000:20000]  # look at one channel from now on\nd = d.ravel()  # make flat vector\ninnovation = signal.convolve(d, a, \"valid\")\nd_ = signal.lfilter(b, a, innovation)  # regenerate the signal\nd_ = np.r_[d_[0] * np.ones(order), d_]  # dummy samples to keep signal length"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Plot the different time series and PSDs\n\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "collapsed": false
      },
      "outputs": [],
      "source": [
        "plt.close(\"all\")\nplt.figure()\nplt.plot(d[:100], label=\"signal\")\nplt.plot(d_[:100], label=\"regenerated signal\")\nplt.legend()\n\nplt.figure()\nplt.psd(d, Fs=raw.info[\"sfreq\"], NFFT=2048)\nplt.psd(innovation, Fs=raw.info[\"sfreq\"], NFFT=2048)\nplt.psd(d_, Fs=raw.info[\"sfreq\"], NFFT=2048, linestyle=\"--\")\nplt.legend((\"Signal\", \"Innovation\", \"Regenerated signal\"))\nplt.show()"
      ]
    }
  ],
  "metadata": {
    "kernelspec": {
      "display_name": "Python 3",
      "language": "python",
      "name": "python3"
    },
    "language_info": {
      "codemirror_mode": {
        "name": "ipython",
        "version": 3
      },
      "file_extension": ".py",
      "mimetype": "text/x-python",
      "name": "python",
      "nbconvert_exporter": "python",
      "pygments_lexer": "ipython3",
      "version": "3.12.2"
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  "nbformat": 4,
  "nbformat_minor": 0
}