Coherence_Lab_Part_1.ipynb

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    "---\n",
    "title: Coherence Part 1 (Two noise signals)\n",
    "project:\n",
    "  type: website\n",
    "format:\n",
    "  html:\n",
    "    code-fold: false\n",
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    "---"
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   "source": [
    "# Load modules we'll need.\n",
    "from scipy.io import loadmat\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "from scipy.signal import spectrogram"
   ]
  },
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Make two noise signals"
   ]
  },
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   "source": [
    "N = 1000;\n",
    "dt= 0.001;\n",
    "T = N*dt;\n",
    "x = np.random.randn(N)\n",
    "y = np.random.randn(N)\n",
    "t = np.arange(0,N)*dt\n",
    "\n",
    "plt.plot(t,x)\n",
    "plt.plot(t,y)\n",
    "plt.xlabel('Time [s]');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Compute the cross-covariance"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
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   "outputs": [],
   "source": [
    "cc_xy = \"SOMETHING\"                          # Compute the covariance.\n",
    "lags = np.arange(-N + 1, N)                  # Create a lag axis,\n",
    "plt.plot(lags * dt, cc_xy)                   # ... and plot the result.\n",
    "plt.ylim([-0.1, 1])\n",
    "plt.xlabel('Lag [s]')\n",
    "plt.ylabel('Cross-covariance');\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Compute the coherence"
   ]
  },
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   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "Xf = np.fft.fft(x - x.mean())           # Compute Fourier transform of x\n",
    "Yf = np.fft.fft(y - y.mean())           # Compute Fourier transform of y\n",
    "\n",
    "# Compute the spectra\n",
    "Sxx = \"SOMETHING\"  # Spectrum of x\n",
    "Syy = \"SOMETHING\"  # ... and y\n",
    "Sxy = \"SOMETHING\"  # ... and the cross spectrum\n",
    "\n",
    "# Compute the coherence.\n",
    "cohr = \"SOMETHING\"\n",
    "\n",
    "# Define a frequency axis.\n",
    "f = np.fft.fftfreq(N, dt)\n",
    "\n",
    "# Plot the result.\n",
    "plt.plot(f, cohr.real)"
   ]
  }
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