{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Residual analysis to determine the optimal cutoff frequency\n", "\n", "> Marcos Duarte \n", "> Laboratory of Biomechanics and Motor Control ([http://pesquisa.ufabc.edu.br/bmclab](http://pesquisa.ufabc.edu.br/bmclab)) \n", "> Federal University of ABC, Brazil" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "A common problem in signal processing is to automatically determine the optimal cutoff frequency that should be employed in a low-pass filter to attenuate as much as possible the noise without compromising the signal content of the data. \n", "\n", "Before we continue, see [this Jupyter notebook](http://nbviewer.ipython.org/github/demotu/BMC/blob/master/notebooks/DataFiltering.ipynb) for an overview about data filtering if needed.\n", "\n", "Unfortunately, there is no definite solution for this problem, but there are some techniques, with different degrees of success, to try to determine the optimal cutoff frequency. \n", "\n", "David Winter, in his classic book *Biomechanics and motor control of human movement*, proposed a method to find the optimal cutoff frequency based on residual analysis of the difference between filtered and unfiltered signals over a range of cutoff frequencies. The optimal cutoff frequency is the one where the residual starts to change very little because it is considered that from this point, it's being filtered mostly noise and minimally signal, ideally. This concept is straightforward to implement. \n", "\n", "The function `optcutfreq.py` from Python module `optcutfreq` is an implementation of this method and it is divided in three parts (after the help section): first, the residuals over a range of cutoff frequencies are calculated; second, an algorithm tries to find the noisy region (with a supposed linear behavior in the frequency domain) of the residuals versus cutoff frequencies plot and finds the optimal cutoff frequency; and third, the results are plotted. The code is lengthy relatively to the simplicity of the idea because of the long help section, the implementation of the automatic search and a rich plot. Here is the function signature:\n", "\n", "```python\n", "fc_opt = optcutfreq(y, freq=1, fclim=[], show=False, ax=None):\n", "```\n", "\n", "Let's test this function with benchmark data. \n", "\n", "In 1977, Pezzack, Norman and Winter published a paper where they investigated the effects of differentiation and filtering processes on experimental data (the angle of a bar manipulated in space). Since then, these data have became a benchmark to test new algorithms. Let's work with these data (available at [http://isbweb.org/data/pezzack/index.html](http://isbweb.org/data/pezzack/index.html)). The data have the angular displacement measured by video and the angular acceleration directly measured by an accelerometer, which we will consider as the true acceleration. \n", "Part of these data are showing next:" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Installation\n", "\n", "```bash\n", "pip install optcutfreq\n", "```\n", "\n", "Or\n", "\n", "```bash\n", "conda install -c duartexyz optcutfreq\n", "```" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "ExecuteTime": { "end_time": "2017-12-29T19:22:46.907564Z", "start_time": "2017-12-29T19:22:46.688392Z" } }, "outputs": [], "source": [ "# Import the necessary libraries\n", "import numpy as np\n", "%matplotlib inline\n", "import matplotlib.pyplot as plt" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "ExecuteTime": { "end_time": "2017-12-29T19:22:48.275312Z", "start_time": "2017-12-29T19:22:47.904032Z" } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# load data file\n", "time, disp, disp2, aacc = np.loadtxt('./../data/Pezzack.txt', skiprows=6, unpack=True)\n", "dt = np.mean(np.diff(time))\n", "# plot data\n", "fig, (ax1,ax2) = plt.subplots(1, 2, sharex = True, figsize=(11, 4))\n", "plt.suptitle(\"Pezzack's benchmark data\", fontsize=20)\n", "ax1.plot(time, disp, 'b')\n", "ax1.set_xlabel('Time [s]'); ax1.set_ylabel('Angular displacement [rad]')\n", "ax2.plot(time, aacc, 'g')\n", "ax2.set_xlabel('Time [s]'); ax2.set_ylabel('Angular acceleration [rad/s$^2$]')\n", "plt.subplots_adjust(wspace=0.3)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "And using the residual analsysis code:" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "ExecuteTime": { "end_time": "2017-12-29T19:22:53.522401Z", "start_time": "2017-12-29T19:22:52.929965Z" } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "from optcutfreq import optcutfreq\n", "\n", "freq = np.mean(1/np.diff(time))\n", "fc_opt = optcutfreq(disp, freq=freq, show=True)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The optimal cutoff frequency found is 5.6 Hz. Note that the filtering process is relevant only for the derivative of the data; we cannot distinguish the unfiltered and unfiltered displacements (see that the RMSE residual is very small). \n", "Let's employ this filter, differentiate the data twice and compare with the true acceleration as we did before:" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "ExecuteTime": { "end_time": "2017-12-29T19:23:32.085684Z", "start_time": "2017-12-29T19:23:31.936581Z" } }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "from scipy.signal import butter, filtfilt\n", "# Butterworth filter\n", "# Correct the cutoff frequency for the number of passes in the filter\n", "C = 0.802 # for dual pass; C = (2**(1/npasses) - 1)**0.25\n", "b, a = butter(2, (fc_opt/C)/(freq/2))\n", "dispf = filtfilt(b, a, disp)\n", "aaccBW = np.diff(dispf, 2)*freq*freq\n", "# RMSE:\n", "rmseBW = np.sqrt(np.mean((aaccBW-aacc[1:-1])**2))\n", "# plot data\n", "fig, ax1 = plt.subplots(1, 1, figsize=(11, 4))\n", "plt.suptitle(\"Pezzack's benchmark data\", fontsize=20)\n", "ax1.plot(time[1:-1], aacc[1:-1], 'g', label='Analog acceleration: (True value)')\n", "ax1.plot(time[1:-1], aaccBW, 'r', \n", " label='Butterworth %.3g Hz: RMSE = %0.2f' %(fc_opt,rmseBW))\n", "ax1.set_xlabel('Time [s]');\n", "ax1.set_ylabel('Angular acceleration [rad/s$^2$]');\n", "plt.legend(frameon=False, fontsize=12, loc='upper left');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The performance seems satisfactory (see [this Jupyter notebook](http://nbviewer.ipython.org/github/demotu/BMC/blob/master/notebooks/DataFiltering.ipynb) for a comparison using other filters), but it is known that this residual analysis algorithm results in oversmoothing the kinematic data (see [http://www.clinicalgaitanalysis.com/faq/cutoff.html](http://www.clinicalgaitanalysis.com/faq/cutoff.html))." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To read more about the determination of the optimal cutoff frequency, see the following papers: \n", "\n", "- Pezzack, Norman, & Winter (1977). [An assessment of derivative determining techniques used for motion analysis](http://www.health.uottawa.ca/biomech/courses/apa7305/JB-Pezzack-Norman-Winter-1977.pdf). Journal of Biomechanics, 10, 377-382.\n", "- Giakas & Baltizopoulos (1997) [A comparison of automatic filtering techniques applied to biomechanical walking data](http://www.pe.uth.gr/sk_cms/scriptlib/getblob.php?redir=../sk_cms/images/notfound.htm&table=pepublications&field=doc&id=30). J. Biomech. 30, 847-850.\n", "- Alonso, Salgado, Cuadrado & Pintado (2009) [Automatic smoothing of raw kinematic signals using SSA and cluster analysis](http://lim.ii.udc.es/docs/proceedings/2009_09_EUROMECH_Automatic.pdf). 7th EUROMECH Solid Mechanics Conference.\n", "- Kristianslund, Krosshaug & Bogert (2012) [Effect of low pass filtering on joint moments from inverse dynamics: Implications for injury prevention](http://www.klokavskade.no/upload/Publication/Kristianslund_2012_J%20Biomechan_Effect%20of%20low-pass%20filtering%20on%20joint%20moments%20from%20inverse%20dynamics.pdf). J. Biomech. 45, 666-671." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## References\n", "\n", "- Pezzack JC, Norman RW, & Winter DA (1977). [An assessment of derivative determining techniques used for motion analysis](http://www.health.uottawa.ca/biomech/courses/apa7305/JB-Pezzack-Norman-Winter-1977.pdf). Journal of Biomechanics, 10, 377-382. [PubMed](http://www.ncbi.nlm.nih.gov/pubmed/893476).\n", "- Winter DA (2009) [Biomechanics and motor control of human movement](http://books.google.com.br/books?id=_bFHL08IWfwC&printsec=frontcover&source=gbs_ge_summary_r&cad=0#v=onepage&q&f=false). 4 ed. Hoboken, EUA: Wiley." ] } ], "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": "3.8.10" }, "varInspector": { "cols": { "lenName": 16, "lenType": 16, "lenVar": 40 }, "kernels_config": { "python": { "delete_cmd_postfix": "", "delete_cmd_prefix": "del ", "library": "var_list.py", "varRefreshCmd": "print(var_dic_list())" }, "r": { "delete_cmd_postfix": ") ", "delete_cmd_prefix": "rm(", "library": "var_list.r", "varRefreshCmd": "cat(var_dic_list()) " } }, "types_to_exclude": [ "module", "function", "builtin_function_or_method", "instance", "_Feature" ], "window_display": false } }, "nbformat": 4, "nbformat_minor": 4 }