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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,132 @@ | ||
| { | ||
| "cells": [ | ||
| { | ||
| "cell_type": "markdown", | ||
| "metadata": {}, | ||
| "source": [ | ||
| "---\n", | ||
| "title: Coherence Part 1 (Two noise signals)\n", | ||
| "project:\n", | ||
| " type: website\n", | ||
| "format:\n", | ||
| " html:\n", | ||
| " code-fold: false\n", | ||
| " code-tools: true\n", | ||
| "jupyter: python 3\n", | ||
| "number-sections: false\n", | ||
| "---" | ||
| ] | ||
| }, | ||
| { | ||
| "cell_type": "code", | ||
| "execution_count": null, | ||
| "metadata": {}, | ||
| "outputs": [], | ||
| "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" | ||
| ] | ||
| }, | ||
| { | ||
| "cell_type": "markdown", | ||
| "metadata": {}, | ||
| "source": [ | ||
| "## Make two noise signals" | ||
| ] | ||
| }, | ||
| { | ||
| "cell_type": "code", | ||
| "execution_count": null, | ||
| "metadata": {}, | ||
| "outputs": [], | ||
| "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, | ||
| "metadata": {}, | ||
| "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" | ||
| ] | ||
| }, | ||
| { | ||
| "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 = ??? # Spectrum of E1 trials\n", | ||
| "Syy = ??? # ... and E2 trials\n", | ||
| "Sxy = ??? # ... and the cross spectrum\n", | ||
| "\n", | ||
| "# Compute the coherence.\n", | ||
| "cohr = ???\n", | ||
| "\n", | ||
| "# Define a frequency axis.\n", | ||
| "f = np.fft.fftfreq(N, dt)\n", | ||
| "\n", | ||
| "# Plot the result.\n", | ||
| "plt.plot(f, cohr.real)" | ||
| ] | ||
| } | ||
| ], | ||
| "metadata": { | ||
| "kernelspec": { | ||
| "display_name": "Python 3 (ipykernel)", | ||
| "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": "3.12.4" | ||
| } | ||
| }, | ||
| "nbformat": 4, | ||
| "nbformat_minor": 4 | ||
| } |
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,163 @@ | ||
| { | ||
| "cells": [ | ||
| { | ||
| "cell_type": "markdown", | ||
| "metadata": {}, | ||
| "source": [ | ||
| "---\n", | ||
| "title: Coherence Part 2 (Two noise signals, again)\n", | ||
| "project:\n", | ||
| " type: website\n", | ||
| "format:\n", | ||
| " html:\n", | ||
| " code-fold: false\n", | ||
| " code-tools: true\n", | ||
| "jupyter: python 3\n", | ||
| "number-sections: false\n", | ||
| "---" | ||
| ] | ||
| }, | ||
| { | ||
| "cell_type": "code", | ||
| "execution_count": null, | ||
| "metadata": {}, | ||
| "outputs": [], | ||
| "source": [ | ||
| "# Load modules we'll need.\n", | ||
| "\n", | ||
| "from scipy.io import loadmat\n", | ||
| "import matplotlib.pyplot as plt\n", | ||
| "import numpy as np\n", | ||
| "from scipy.signal import spectrogram" | ||
| ] | ||
| }, | ||
| { | ||
| "cell_type": "markdown", | ||
| "metadata": {}, | ||
| "source": [ | ||
| "## Make two noise signals, with multiple trials" | ||
| ] | ||
| }, | ||
| { | ||
| "cell_type": "code", | ||
| "execution_count": null, | ||
| "metadata": {}, | ||
| "outputs": [], | ||
| "source": [ | ||
| "N = 1000;\n", | ||
| "K = 100;\n", | ||
| "dt= 0.001;\n", | ||
| "T = N*dt;\n", | ||
| "x = np.random.randn(K,N)\n", | ||
| "y = np.random.randn(K,N)\n", | ||
| "t = np.arange(0,N)*dt\n", | ||
| "\n", | ||
| "plt.plot(t,x[0,:])\n", | ||
| "plt.plot(t,y[0,:])\n", | ||
| "plt.xlabel('Time [s]');" | ||
| ] | ||
| }, | ||
| { | ||
| "cell_type": "markdown", | ||
| "metadata": {}, | ||
| "source": [ | ||
| "## Visualize the data across all trials" | ||
| ] | ||
| }, | ||
| { | ||
| "cell_type": "code", | ||
| "execution_count": null, | ||
| "metadata": {}, | ||
| "outputs": [], | ||
| "source": [ | ||
| "plt.imshow(x, # ... and show the image,\n", | ||
| " extent=[min(t), max(t), K, 1], # ... with meaningful axes,\n", | ||
| " aspect='auto') # ... and a nice aspect ratio\n", | ||
| "plt.xlabel('Time [s]')\n", | ||
| "plt.ylabel('Trial #');\n", | ||
| "plt.title('All trials from E1');" | ||
| ] | ||
| }, | ||
| { | ||
| "cell_type": "markdown", | ||
| "metadata": {}, | ||
| "source": [ | ||
| "## Compute the cross-covariance, averaged across trials" | ||
| ] | ||
| }, | ||
| { | ||
| "cell_type": "code", | ||
| "execution_count": null, | ||
| "metadata": {}, | ||
| "outputs": [], | ||
| "source": [ | ||
| "cc_xy = \"SOMETHING\" # Compute cc for each trial, \n", | ||
| "cc_xy = np.mean(cc_xy,0) # ... average over trials,\n", | ||
| "lags = np.arange(-N + 1, N) # ... create a lag axis,\n", | ||
| "plt.plot(lags * dt, cc_xy) # ... and plot the result.\n", | ||
| "plt.xlabel('Lag [s]')\n", | ||
| "plt.ylabel('Trial averaged cross-covariance');\n", | ||
| "plt.ylim([-0.1, 1]);" | ||
| ] | ||
| }, | ||
| { | ||
| "cell_type": "markdown", | ||
| "metadata": {}, | ||
| "source": [ | ||
| "## Compute the coherence" | ||
| ] | ||
| }, | ||
| { | ||
| "cell_type": "code", | ||
| "execution_count": null, | ||
| "metadata": {}, | ||
| "outputs": [], | ||
| "source": [ | ||
| "# Fourier transforms.\n", | ||
| "Xf = \"SOMETHING\" # Compute Fourier transform of x for each trial\n", | ||
| "Yf = \"SOMETHING\" # Compute Fourier transform of y for each trial\n", | ||
| "\n", | ||
| "# Auto- and cross-spectra.\n", | ||
| "Sxx = \"SOMETHING\" # Spectrum of E1 trials\n", | ||
| "Syy = \"SOMETHING\" # ... and E2 trials\n", | ||
| "Sxy = \"SOMETHING\" # ... and the cross spectrum\n", | ||
| "\n", | ||
| "# Trial average.\n", | ||
| "Sxx = np.mean(Sxx,0)\n", | ||
| "Syy = np.mean(Syy,0)\n", | ||
| "Sxy = np.mean(Sxy,0)\n", | ||
| "\n", | ||
| "# Calculate coherence.\n", | ||
| "cohr_squared = \"SOMETHING\"\n", | ||
| "\n", | ||
| "f = np.fft.fftfreq(N, dt) # Define a frequency axis.\n", | ||
| "plt.plot(f, cohr_squared.real) # Plot the coherence.\n", | ||
| "plt.ylim([0, 1.1]) # ... with y-axis scaled,\n", | ||
| "plt.xlabel('Frequency [Hz]') # ... and with axes labeled.\n", | ||
| "plt.ylabel('Coherence')\n", | ||
| "plt.title('Trial averaged coherence between two electrodes');" | ||
| ] | ||
| } | ||
| ], | ||
| "metadata": { | ||
| "kernelspec": { | ||
| "display_name": "Python 3 (ipykernel)", | ||
| "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": "3.12.4" | ||
| } | ||
| }, | ||
| "nbformat": 4, | ||
| "nbformat_minor": 4 | ||
| } |
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