matched_filter.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "matched_filter.ipynb",
      "provenance": [],
      "collapsed_sections": [],
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/xli2522/GW-SignalGen/blob/main/matched_filter.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "qAu1a17f9FyS"
      },
      "source": [
        "\n",
        "<img style=\"float: left;padding: 1.3em\" src=\"https://indico.in2p3.fr/event/18313/logo-786578160.png\">  \n",
        "#  Matched Filtering with Chirp Transform\n",
        "#####(Testing) \n",
        "##### © Xiyuan Li 2021, Department of Physics and Astronomy, Western University (UWO), London, Ontario, Canada\n",
        "##### Resources: \n",
        "[PyCBC](http://github.com/ligo-cbc/pycbc) + additional PyCBC [examples](http://pycbc.org/pycbc/latest/html/#library-examples-and-interactive-tutorials) and module level documentation are [here](http://pycbc.org/pycbc/latest/html/py-modindex.html).\n",
        "\n",
        "##### Code *Reference*:\n",
        "[gw-odw/odw-2020](http://github.com/gw-odw/odw-2020)"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "_B5P5WZT9fZZ"
      },
      "source": [
        "! pip install -q 'lalsuite==6.66' 'PyCBC==1.15.3'"
      ],
      "execution_count": 9,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "TwcnwXFDA5eS"
      },
      "source": [
        "#### Examples: ODW 2020"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ROO2uUf9AoRi"
      },
      "source": [
        "%matplotlib inline\n",
        "import numpy\n",
        "import pylab\n",
        "\n",
        "# specify the sample rate.\n",
        "# LIGO raw data is sampled at 16384 Hz (=2^14 samples/second).\n",
        "# It captures signal frequency content up to f_Nyquist = 8192 Hz.\n",
        "# Here, we will make the computation faster by sampling at a lower rate.\n",
        "sample_rate = 1024 # samples per second\n",
        "data_length = 1024 # seconds\n",
        "\n",
        "# Generate a long stretch of white noise: the data series and the time series.\n",
        "data = numpy.random.normal(size=[sample_rate * data_length])\n",
        "times = numpy.arange(len(data)) / float(sample_rate)"
      ],
      "execution_count": 10,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 869
        },
        "id": "OY5OtyTYAvjq",
        "outputId": "fbe9e105-f9b3-414d-d3ed-a2ba5c1c6341"
      },
      "source": [
        "from pycbc.waveform import get_td_waveform\n",
        "\n",
        "# the \"approximant\" (jargon for parameterized waveform family).\n",
        "# IMRPhenomD is defined in the frequency domain, but we'll get it in the time domain (td).\n",
        "# It runs fast, but it doesn't include effects such as non-aligned component spin, or higher order modes.\n",
        "apx = 'IMRPhenomD'\n",
        "\n",
        "# You can specify many parameters, \n",
        "# https://pycbc.org/pycbc/latest/html/pycbc.waveform.html?highlight=get_td_waveform#pycbc.waveform.waveform.get_td_waveform\n",
        "# but here, we'll use defaults for everything except the masses.\n",
        "# It returns both hplus and hcross, but we'll only use hplus for now.\n",
        "hp1, _ = get_td_waveform(approximant=apx,\n",
        "                         mass1=10,\n",
        "                         mass2=10,\n",
        "                         delta_t=1.0/sample_rate,\n",
        "                         f_lower=25)\n",
        "\n",
        "# The amplitude of gravitational-wave signals is normally of order 1E-20. To demonstrate our method\n",
        "# on white noise with amplitude O(1) we normalize our signal so the cross-correlation of the signal with\n",
        "# itself will give a value of 1. In this case we can interpret the cross-correlation of the signal with white\n",
        "# noise as a signal-to-noise ratio.\n",
        "\n",
        "hp1 = hp1 / max(numpy.correlate(hp1,hp1, mode='full'))**0.5\n",
        "\n",
        "# note that in this figure, the waveform amplitude is of order 1.\n",
        "# The duration (for frequency above f_lower=25 Hz) is only 3 or 4 seconds long.\n",
        "# The waveform is \"tapered\": slowly ramped up from zero to full strength, over the first second or so.\n",
        "# It is zero-padded at earlier times.\n",
        "pylab.figure()\n",
        "pylab.title(\"The waveform hp1\")\n",
        "pylab.plot(hp1.sample_times, hp1)\n",
        "pylab.xlabel('Time (s)')\n",
        "pylab.ylabel('Normalized amplitude')\n",
        "\n",
        "# Shift the waveform to start at a random time in the Gaussian noise data.\n",
        "waveform_start = numpy.random.randint(0, len(data) - len(hp1))\n",
        "data[waveform_start:waveform_start+len(hp1)] += 10 * hp1.numpy()\n",
        "\n",
        "pylab.figure()\n",
        "pylab.title(\"Looks like random noise, right?\")\n",
        "pylab.plot(hp1.sample_times, data[waveform_start:waveform_start+len(hp1)])\n",
        "pylab.xlabel('Time (s)')\n",
        "pylab.ylabel('Normalized amplitude')\n",
        "\n",
        "pylab.figure()\n",
        "pylab.title(\"Signal in the data\")\n",
        "pylab.plot(hp1.sample_times, data[waveform_start:waveform_start+len(hp1)])\n",
        "pylab.plot(hp1.sample_times, 10 * hp1)\n",
        "pylab.xlabel('Time (s)')\n",
        "pylab.ylabel('Normalized amplitude')"
      ],
      "execution_count": 11,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Text(0, 0.5, 'Normalized amplitude')"
            ]
          },
          "metadata": {},
          "execution_count": 11
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "jSuDccSeBGl7"
      },
      "source": [
        "##### Cross-corelation in the time domain"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 297
        },
        "id": "m48eBjP8BEhb",
        "outputId": "2a9ecf27-b29a-4689-d07c-010001c13c64"
      },
      "source": [
        "cross_correlation = numpy.zeros([len(data)-len(hp1)])\n",
        "hp1_numpy = hp1.numpy()\n",
        "for i in range(len(data) - len(hp1_numpy)):\n",
        "    cross_correlation[i] = (hp1_numpy * data[i:i+len(hp1_numpy)]).sum()\n",
        "\n",
        "# plot the cross-correlated data vs time. Superimpose the location of the end of the signal;\n",
        "# this is where we should find a peak in the cross-correlation.\n",
        "pylab.figure()\n",
        "times = numpy.arange(len(data) - len(hp1_numpy)) / float(sample_rate)\n",
        "pylab.plot(times, cross_correlation)\n",
        "pylab.plot([waveform_start/float(sample_rate), waveform_start/float(sample_rate)], [-10,10],'r:')\n",
        "pylab.xlabel('Time (s)')\n",
        "pylab.ylabel('Cross-correlation')"
      ],
      "execution_count": 12,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Text(0, 0.5, 'Cross-correlation')"
            ]
          },
          "metadata": {},
          "execution_count": 12
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "NwwfBD5YBXRa"
      },
      "source": [
        "##### Colored LIGO Noise"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 275
        },
        "id": "Tx-0TDwMBWYv",
        "outputId": "4fcdce45-58da-4e0a-cd2b-0a09a2216c86"
      },
      "source": [
        "# http://pycbc.org/pycbc/latest/html/noise.html\n",
        "import pycbc.noise\n",
        "import pycbc.psd\n",
        "\n",
        "# The color of the noise matches a PSD which you provide:\n",
        "# Generate a PSD matching Advanced LIGO's zero-detuned--high-power noise curve \n",
        "flow = 10.0\n",
        "delta_f = 1.0 / 128\n",
        "flen = int(sample_rate / (2 * delta_f)) + 1\n",
        "psd = pycbc.psd.aLIGOZeroDetHighPower(flen, delta_f, flow)\n",
        "\n",
        "# Generate colored noise\n",
        "delta_t = 1.0 / sample_rate\n",
        "ts = pycbc.noise.noise_from_psd(data_length*sample_rate, delta_t, psd, seed=127)\n",
        "\n",
        "# Estimate the amplitude spectral density (ASD = sqrt(PSD)) for the noisy data \n",
        "# using the \"welch\" method. We'll choose 4 seconds PSD samples that are overlapped 50%\n",
        "seg_len = int(4 / delta_t)\n",
        "seg_stride = int(seg_len / 2)\n",
        "estimated_psd = pycbc.psd.welch(ts,seg_len=seg_len,seg_stride=seg_stride)\n",
        "\n",
        "# plot it:\n",
        "pylab.loglog(estimated_psd.sample_frequencies, estimated_psd, label='estimate')\n",
        "pylab.loglog(psd.sample_frequencies, psd, linewidth=3, label='known psd')\n",
        "pylab.xlim(xmin=flow, xmax=512)\n",
        "pylab.ylim(1e-47, 1e-45)\n",
        "pylab.legend()\n",
        "pylab.grid()\n",
        "pylab.show()\n",
        "\n",
        "# add the signal, this time, with a \"typical\" amplitude.\n",
        "ts[waveform_start:waveform_start+len(hp1)] += hp1.numpy() * 1E-20"
      ],
      "execution_count": 13,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "HDuBuXWjBpHj"
      },
      "source": [
        "# Generate a PSD for whitening the data\n",
        "from pycbc.types import TimeSeries\n",
        "\n",
        "# The PSD, sampled properly for the noisy data\n",
        "flow = 10.0\n",
        "delta_f = 1.0 / data_length\n",
        "flen = int(sample_rate / (2 * delta_f)) + 1\n",
        "psd_td = pycbc.psd.aLIGOZeroDetHighPower(flen, delta_f, 0)\n",
        "\n",
        "# The PSD, sampled properly for the signal\n",
        "delta_f = sample_rate / float(len(hp1))\n",
        "flen = int(sample_rate / (2 * delta_f)) + 1\n",
        "psd_hp1 = pycbc.psd.aLIGOZeroDetHighPower(flen, delta_f, 0)\n",
        "\n",
        "# The 0th and Nth values are zero. Set them to a nearby value to avoid dividing by zero.\n",
        "psd_td[0] = psd_td[1]\n",
        "psd_td[len(psd_td) - 1] = psd_td[len(psd_td) - 2]\n",
        "# Same, for the PSD sampled for the signal\n",
        "psd_hp1[0] = psd_hp1[1]\n",
        "psd_hp1[len(psd_hp1) - 1] = psd_hp1[len(psd_hp1) - 2]\n",
        "\n",
        "# convert both noisy data and the signal to frequency domain,\n",
        "# and divide each by ASD=PSD**0.5, then convert back to time domain.\n",
        "# This \"whitens\" the data and the signal template. \n",
        "# Multiplying the signal template by 1E-21 puts it into realistic units of strain.\n",
        "data_whitened = (ts.to_frequencyseries() / psd_td**0.5).to_timeseries()\n",
        "hp1_whitened = (hp1.to_frequencyseries() / psd_hp1**0.5).to_timeseries() * 1E-21"
      ],
      "execution_count": 14,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 297
        },
        "id": "E2AIN1bnBqqE",
        "outputId": "ad900cc5-b045-4223-efdc-b98255fd453e"
      },
      "source": [
        "# Now let's re-do the correlation, in the time domain, but with whitened data and template.\n",
        "cross_correlation = numpy.zeros([len(data)-len(hp1)])\n",
        "hp1n = hp1_whitened.numpy()\n",
        "datan = data_whitened.numpy()\n",
        "for i in range(len(datan) - len(hp1n)):\n",
        "    cross_correlation[i] = (hp1n * datan[i:i+len(hp1n)]).sum()\n",
        "\n",
        "# plot the cross-correlation in the time domain. Superimpose the location of the end of the signal.\n",
        "# Note how much bigger the cross-correlation peak is, relative to the noise level,\n",
        "# compared with the unwhitened version of the same quantity. SNR is much higher!\n",
        "pylab.figure()\n",
        "times = numpy.arange(len(datan) - len(hp1n)) / float(sample_rate)\n",
        "pylab.plot(times, cross_correlation)\n",
        "pylab.plot([waveform_start/float(sample_rate), waveform_start/float(sample_rate)],\n",
        "           [(min(cross_correlation))*1.1,(max(cross_correlation))*1.1],'r:')\n",
        "pylab.xlabel('Time (s)')\n",
        "pylab.ylabel('Cross-correlation')"
      ],
      "execution_count": 15,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Text(0, 0.5, 'Cross-correlation')"
            ]
          },
          "metadata": {},
          "execution_count": 15
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ywPPoivMDPWD"
      },
      "source": [
        "#### Reference: ODW 2020 Matched Filtering in Action\n"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Package outdated - will update later"
      ],
      "metadata": {
        "id": "vhELbVqgpx-t"
      }
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 543
        },
        "id": "daxHiwQPDdL6",
        "outputId": "f659d40b-668b-46b8-f151-edcc2bc4579b"
      },
      "source": [
        "import pylab\n",
        "from pycbc.catalog import Merger\n",
        "from pycbc.filter import resample_to_delta_t, highpass\n",
        "\n",
        "# As an example we use the GW150914 data\n",
        "merger = Merger(\"GW150914\")\n",
        "\n",
        "# Get the data from the Hanford detector\n",
        "strain = merger.strain('H1')\n",
        "\n",
        "# Remove the low frequency content and downsample the data to 2048Hz\n",
        "strain = highpass(strain, 15.0)\n",
        "strain = resample_to_delta_t(strain, 1.0/2048)\n",
        "\n",
        "pylab.plot(strain.sample_times, strain)\n",
        "pylab.xlabel('Time (s)')\n",
        "pylab.show()"
      ],
      "execution_count": 16,
      "outputs": [
        {
          "output_type": "error",
          "ename": "ModuleNotFoundError",
          "evalue": "ignored",
          "traceback": [
            "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
            "\u001b[0;31mModuleNotFoundError\u001b[0m                       Traceback (most recent call last)",
            "\u001b[0;32m<ipython-input-16-de736b6379e2>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m      7\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      8\u001b[0m \u001b[0;31m# Get the data from the Hanford detector\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 9\u001b[0;31m \u001b[0mstrain\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mmerger\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mstrain\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'H1'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     10\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     11\u001b[0m \u001b[0;31m# Remove the low frequency content and downsample the data to 2048Hz\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;32m/usr/local/lib/python3.7/dist-packages/pycbc/catalog/__init__.py\u001b[0m in \u001b[0;36mstrain\u001b[0;34m(self, ifo, duration, sample_rate)\u001b[0m\n\u001b[1;32m     88\u001b[0m         \"\"\"\n\u001b[1;32m     89\u001b[0m         \u001b[0;32mfrom\u001b[0m \u001b[0mastropy\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mutils\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdata\u001b[0m \u001b[0;32mimport\u001b[0m \u001b[0mdownload_file\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 90\u001b[0;31m         \u001b[0;32mfrom\u001b[0m \u001b[0mpycbc\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mframe\u001b[0m \u001b[0;32mimport\u001b[0m \u001b[0mread_frame\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     91\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     92\u001b[0m         \u001b[0;31m# Information is currently wrong on GWOSC!\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;32m/usr/local/lib/python3.7/dist-packages/pycbc/frame/__init__.py\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m from . frame import (locations_to_cache, read_frame, datafind_connection,\n\u001b[0m\u001b[1;32m      2\u001b[0m                      \u001b[0mquery_and_read_frame\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mframe_paths\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mwrite_frame\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      3\u001b[0m                      DataBuffer, StatusBuffer)\n\u001b[1;32m      4\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      5\u001b[0m \u001b[0;32mfrom\u001b[0m \u001b[0;34m.\u001b[0m \u001b[0mstore\u001b[0m \u001b[0;32mimport\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0mread_store\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;32m/usr/local/lib/python3.7/dist-packages/pycbc/frame/frame.py\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m     22\u001b[0m \u001b[0;32mimport\u001b[0m \u001b[0mnumpy\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     23\u001b[0m \u001b[0;32mimport\u001b[0m \u001b[0mos\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mpath\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mglob\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mtime\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 24\u001b[0;31m \u001b[0;32mimport\u001b[0m \u001b[0mglue\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdatafind\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     25\u001b[0m \u001b[0;32mfrom\u001b[0m \u001b[0mpycbc\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mtypes\u001b[0m \u001b[0;32mimport\u001b[0m \u001b[0mTimeSeries\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mzeros\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     26\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;31mModuleNotFoundError\u001b[0m: No module named 'glue.datafind'",
            "",
            "\u001b[0;31m---------------------------------------------------------------------------\u001b[0;32m\nNOTE: If your import is failing due to a missing package, you can\nmanually install dependencies using either !pip or !apt.\n\nTo view examples of installing some common dependencies, click the\n\"Open Examples\" button below.\n\u001b[0;31m---------------------------------------------------------------------------\u001b[0m\n"
          ],
          "errorDetails": {
            "actions": [
              {
                "action": "open_url",
                "actionText": "Open Examples",
                "url": "/notebooks/snippets/importing_libraries.ipynb"
              }
            ]
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "pKdVDm2MDglq"
      },
      "source": [
        "\n",
        "# Remove 2 seconds of data from both the beginning and end\n",
        "conditioned = strain.crop(2, 2)\n",
        "\n",
        "pylab.plot(conditioned.sample_times, conditioned)\n",
        "pylab.xlabel('Time (s)')\n",
        "pylab.show()"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "BkiRXtwrDhhy"
      },
      "source": [
        "from pycbc.psd import interpolate, inverse_spectrum_truncation\n",
        "# Estimate the power spectral density\n",
        "\n",
        "# We use 4 second samples of our time series in Welch method.\n",
        "psd = conditioned.psd(4)\n",
        "\n",
        "# Now that we have the psd we need to interpolate it to match our data\n",
        "# and then limit the filter length of 1 / PSD. After this, we can\n",
        "# directly use this PSD to filter the data in a controlled manner\n",
        "psd = interpolate(psd, conditioned.delta_f)\n",
        "\n",
        "# 1/PSD will now act as a filter with an effective length of 4 seconds\n",
        "# Since the data has been highpassed above 15 Hz, and will have low values\n",
        "# below this we need to inform the function to not include frequencies\n",
        "# below this frequency. \n",
        "psd = inverse_spectrum_truncation(psd, 4 * conditioned.sample_rate,\n",
        "                                  low_frequency_cutoff=15)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "XwF0q_6DDoEL"
      },
      "source": [
        "from pycbc.waveform import get_td_waveform\n",
        "# In this case we \"know\" what the signal parameters are. In a search\n",
        "# we would grid over the parameters and calculate the SNR time series\n",
        "# for each one\n",
        "\n",
        "# We'll assume equal masses, and non-rotating black holes which is within the posterior probability\n",
        "# of GW150914. \n",
        "m = 36 # Solar masses\n",
        "hp, hc = get_td_waveform(approximant=\"SEOBNRv4_opt\",\n",
        "                     mass1=m,\n",
        "                     mass2=m,\n",
        "                     delta_t=conditioned.delta_t,\n",
        "                     f_lower=20)\n",
        "\n",
        "# We will resize the vector to match our data\n",
        "hp.resize(len(conditioned))\n",
        "\n",
        "# The waveform begins at the start of the vector, so if we want the\n",
        "# SNR time series to correspond to the approximate merger location\n",
        "# we need to shift the data so that the merger is approximately at the \n",
        "# first bin of the data.\n",
        "\n",
        "# The cyclic_time_shift method shifts the timeseries by a given amount of time.\n",
        "# It treats the data as if it were on a ring so points shifted off the end\n",
        "# of the series reappear at the start. Note that time stamps are *not* in\n",
        "# general affected (as the start time of the full array is shifted),\n",
        "# but the index of each point in the vector is.\n",
        "#\n",
        "# By convention waveforms returned from `get_td_waveform` have their\n",
        "# merger stamped with time zero, so we can use the start time to \n",
        "# shift the merger into position\n",
        "pylab.figure()\n",
        "pylab.title('Before shifting')\n",
        "pylab.plot(hp.sample_times, hp)\n",
        "pylab.xlabel('Time (s)')\n",
        "pylab.ylabel('Strain')\n",
        "\n",
        "template = hp.cyclic_time_shift(hp.start_time)\n",
        "\n",
        "pylab.figure()\n",
        "pylab.title('After shifting')\n",
        "pylab.plot(template.sample_times, template)\n",
        "pylab.xlabel('Time (s)')\n",
        "pylab.ylabel('Strain')"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "LOcWcKPwDsEr"
      },
      "source": [
        "##### Signal to Noise Time Series\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "EG_MyhfqDo7r"
      },
      "source": [
        "from pycbc.filter import matched_filter\n",
        "import numpy\n",
        "\n",
        "snr = matched_filter(template, conditioned,\n",
        "                     psd=psd, low_frequency_cutoff=20)\n",
        "\n",
        "# Remove time corrupted by the template filter and the psd filter\n",
        "# We remove 4 seonds at the beginning and end for the PSD filtering\n",
        "# And we remove 4 additional seconds at the beginning to account for\n",
        "# the template length (this is somewhat generous for \n",
        "# so short a template). A longer signal such as from a BNS, would \n",
        "# require much more padding at the beginning of the vector.\n",
        "snr = snr.crop(4 + 4, 4)\n",
        "\n",
        "# Why are we taking an abs() here?\n",
        "# The `matched_filter` function actually returns a 'complex' SNR.\n",
        "# What that means is that the real portion correponds to the SNR\n",
        "# associated with directly filtering the template with the data.\n",
        "# The imaginary portion corresponds to filtering with a template that\n",
        "# is 90 degrees out of phase. Since the phase of a signal may be \n",
        "# anything, we choose to maximize over the phase of the signal.\n",
        "pylab.figure(figsize=[10, 4])\n",
        "pylab.plot(snr.sample_times, abs(snr))\n",
        "pylab.ylabel('Signal-to-noise')\n",
        "pylab.xlabel('Time (s)')\n",
        "pylab.show()\n",
        "\n",
        "peak = abs(snr).numpy().argmax()\n",
        "snrp = snr[peak]\n",
        "time = snr.sample_times[peak]\n",
        "\n",
        "print(\"We found a signal at {}s with SNR {}\".format(time, \n",
        "                                                    abs(snrp)))"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "0_pvOx_-DvU7"
      },
      "source": [
        "from pycbc.filter import sigma\n",
        "# The time, amplitude, and phase of the SNR peak tell us how to align\n",
        "# our proposed signal with the data.\n",
        "\n",
        "# Shift the template to the peak time\n",
        "dt = time - conditioned.start_time\n",
        "aligned = template.cyclic_time_shift(dt)\n",
        "\n",
        "# scale the template so that it would have SNR 1 in this data\n",
        "aligned /= sigma(aligned, psd=psd, low_frequency_cutoff=20.0)\n",
        "\n",
        "# Scale the template amplitude and phase to the peak value\n",
        "aligned = (aligned.to_frequencyseries() * snrp).to_timeseries()\n",
        "aligned.start_time = conditioned.start_time"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "z_94x_URD0tr"
      },
      "source": [
        "# We do it this way so that we can whiten both the template and the data\n",
        "white_data = (conditioned.to_frequencyseries() / psd**0.5).to_timeseries()\n",
        "white_template = (aligned.to_frequencyseries() / psd**0.5).to_timeseries()\n",
        "\n",
        "white_data = white_data.highpass_fir(30., 512).lowpass_fir(300, 512)\n",
        "white_template = white_template.highpass_fir(30, 512).lowpass_fir(300, 512)\n",
        "\n",
        "# Select the time around the merger\n",
        "white_data = white_data.time_slice(merger.time-.2, merger.time+.1)\n",
        "white_template = white_template.time_slice(merger.time-.2, merger.time+.1)\n",
        "\n",
        "pylab.figure(figsize=[15, 3])\n",
        "pylab.title('PyCBC Matched Filtering Result of GW150914 Signal from the Hanford Detector')\n",
        "pylab.plot(white_data.sample_times, white_data, label=\"Data\")\n",
        "pylab.plot(white_template.sample_times, white_template, label=\"Template\")\n",
        "pylab.xlabel('Time (s)')\n",
        "pylab.legend()\n",
        "pylab.show()"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ZvWgmC5yD37D"
      },
      "source": [
        "subtracted = conditioned - aligned\n",
        "\n",
        "# Plot the original data and the subtracted signal data\n",
        "\n",
        "for data, title in [(conditioned, 'Original H1 Data'),\n",
        "                    (subtracted, 'Signal Subtracted from H1 Data')]:\n",
        "\n",
        "    t, f, p = data.whiten(4, 4).qtransform(.001,\n",
        "                                                  logfsteps=100,\n",
        "                                                  qrange=(8, 8),\n",
        "                                                  frange=(20, 512))\n",
        "    pylab.figure(figsize=[15, 3])\n",
        "    pylab.title(title)\n",
        "    pylab.pcolormesh(t, f, p**0.5, vmin=1, vmax=6)\n",
        "    pylab.yscale('log')\n",
        "    pylab.xlabel('Time (s)')\n",
        "    pylab.ylabel('Frequency (Hz)')\n",
        "    pylab.xlim(merger.time - 2, merger.time + 1)\n",
        "    pylab.show()"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "CoYnfuSvEMIL"
      },
      "source": [
        "#### End of ODW 2020 Examples"
      ]
    }
  ]
}