{ "cells": [ { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": true }, "outputs": [], "source": [ "%matplotlib inline\n", "\n", "import matplotlib.pyplot as plt\n", "import numpy as np\n", "from astropy.timeseries import LombScargle\n", "\n", "plt.style.use('seaborn-whitegrid')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Convolution" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/Users/jakevdp/anaconda/envs/python3.5/lib/python3.5/site-packages/ipykernel/__main__.py:11: RuntimeWarning: covariance is not positive-semidefinite.\n" ] }, { "data": { "image/png": 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UI2ovw/Pw4cNUK/Dee+8hJCQE06ZNoyjGq1ev0Lt3b+pcZSuEIld3d3eDC1v2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MFzzz2HtWvX6mz5US0LaI5kvIZQKBSQSqUG5dEihOCPP/7Axo0bUVJSok5+7uXlhffeew+PPfYY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\nA8/g4GCIxWJViqPi4mK1Vc/G0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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "from matplotlib import pyplot as plt\n", "\n", "\n", "def generate_smooth_data(size, xlim=(0, 1), coeffs=(0.2, 0.3),\n", " smoothing_length=0.01, rseed=0):\n", " \"\"\"Generate a smooth random curve between 0 and 1\"\"\"\n", " rng = np.random.RandomState(rseed)\n", " x = np.linspace(*xlim, num=size)\n", " C = np.exp(-0.5 * (x - x[:, None]) ** 2 / smoothing_length ** 2)\n", " y = coeffs[0] + coeffs[1] * rng.multivariate_normal(np.zeros(len(x)), C)\n", " return x, y\n", " \n", "\n", "x, y = generate_smooth_data(1000, rseed=5423,\n", " xlim=(-0.2, 1.2),\n", " coeffs=(3, 1.5),\n", " smoothing_length=0.01)\n", "y += 2 + np.sin(2 * np.pi * x) # add larger-scale variation\n", "w = (abs(x - 0.5) < 0.06) / 0.12 # normalized window function\n", "y_w = np.convolve(y, w, mode='same') * (x[1] - x[0]) # convolution\n", "\n", "fig, ax = plt.subplots(2, figsize=(8, 4), sharex=True, sharey=True)\n", "fig.subplots_adjust(hspace=0.1)\n", "\n", "# Plot the data and the smoothed data\n", "ax[0].plot(x, y, '-k', lw=2)\n", "ax[1].plot(x, y_w, '-k', lw=2)\n", "ax[1].plot(x, y, '-', color='gray', alpha=0.8, lw=0.5)\n", "\n", "# Plot the window function at several locations\n", "for window_loc in [0.2, 0.5, 0.8]:\n", " y_loc = y_w[np.searchsorted(x, window_loc)]\n", " ax[0].fill(x + window_loc - 0.5, w, color='gray', alpha=0.5)\n", " ax[1].annotate('', (window_loc, y_loc), (window_loc, 0.0),\n", " textcoords=ax[0].transData,\n", " arrowprops=dict(arrowstyle='->', color='gray', lw=2))\n", "\n", "ax[1].yaxis.set_major_locator(plt.MultipleLocator(2))\n", "ax[1].set(xlim=(0, 1), ylim=(0, 10))\n", "fig.savefig('fig04_Convolution_Diagram.pdf')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Convolution Diagram" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def FT_plotgrid(sharex='col', sharey='col'):\n", " fig, ax = plt.subplots(3, 2, figsize=(10, 6), sharex=sharex, sharey=sharey)\n", " fig.subplots_adjust(left=0.09, bottom=0.19, right=0.95, top=0.95)\n", " for axi in ax[2]:\n", " left, bottom, width, height = axi.get_position().bounds\n", " axi.set_position([left, bottom - 0.05, width, height])\n", " \n", " for axi in ax[:, 1]:\n", " axi.yaxis.set_major_formatter(plt.NullFormatter())\n", "\n", " for xcoord, text in zip([0.30, 0.77], ['$Convolution$', '$Pointwise\\ Product$']):\n", " fig.text(xcoord, 0.42, r'$\\Downarrow$',\n", " size=24, ha='right', va='center')\n", " fig.text(xcoord + 0.01, 0.42, text,\n", " size=14, ha='left', va='center')\n", "\n", "\n", " for ycoord in [0.28, 0.6, 0.87]:\n", " fig.text(0.52, ycoord, \"$FT$\",\n", " size=14, ha='center', va='bottom')\n", " fig.text(0.52, ycoord, r'$\\Longleftrightarrow$',\n", " size=24, ha='center', va='top')\n", " \n", " return fig, ax\n" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/Users/jakevdp/anaconda/envs/python3.5/lib/python3.5/site-packages/ipykernel/__main__.py:11: RuntimeWarning: covariance is not positive-semidefinite.\n" ] }, { "data": { "image/png": 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EQCQS6W1jLqkMhjAwwdjImIoJJC6pd+/edWiZCkssjPfu3UNdXR1tq7GENwQi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AR2/qWC0Wq14pdffgHgWzDW12EUBIFd73WFpR4/fhwfffQRAODll1+uM5w0JCQE6enprBgMTXhQ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\nmkt9E99UTxiLi4vNPu6DDz6IgoKCOtd3NCW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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x, y = generate_smooth_data(1000, rseed=5423,\n", " xlim=(-0.2, 1.2),\n", " coeffs=(0, 1.5),\n", " smoothing_length=0.01)\n", "y += 0.5 + np.sin(2 * np.pi * x) # add larger-scale variation\n", "w = (abs(x - 0.5) < 0.08) / 0.16 # normalized window function\n", "y_w = np.convolve(y, w, mode='same') * (x[1] - x[0]) # convolution\n", "\n", "#------------------------------------------------------------\n", "# Compute the Fourier transforms of the signal and window\n", "# (-1)^j factors come from FFT shift (see Appendix of astroML text)\n", "y_fft = np.fft.fft(y) * (-1) ** np.arange(len(x))\n", "w_fft = np.fft.fft(w) * (-1) ** np.arange(len(x))\n", "yw_fft = y_fft * w_fft\n", "\n", "#===================================================================\n", "# Now the plots:\n", "\n", "def plot_ft(k, F, ax=None, legend=False, text=None):\n", " \"\"\"plot the real and imaginary part of a Fourier transform\"\"\"\n", " if ax is None:\n", " ax = plt.gca()\n", " F_plot = np.fft.fftshift(F)\n", " ax.plot(k, F_plot.real, '-', color='black', label='real part')\n", " ax.plot(k, F_plot.imag, '-', color='gray', label='imag part')\n", " \n", " if legend:\n", " ax.legend(loc='upper left')\n", " if text:\n", " ax.text(0.98, 0.95, text, ha='right', va='top', size=12,\n", " transform=ax.transAxes)\n", " \n", "\n", "#------------------------------------------------------------\n", "# Set up the plots\n", "fig, axes = FT_plotgrid(sharex=False, sharey=False)\n", "\n", "#----------------------------------------\n", "# Upper left panels: plot the data and window function\n", "ax = axes[0, 0]\n", "ax.plot(x, y, '-k')\n", "ax.text(0.98, 0.95, r\"Data: $D(t)$\",\n", " ha='right', va='top', transform=ax.transAxes, size=12)\n", "ax.xaxis.set_major_formatter(plt.NullFormatter())\n", "ax.set(xlim=(0.01, 0.99),\n", " ylim=(-5, 6))\n", "\n", "ax = axes[1, 0]\n", "ax.plot(x, w, '-k')\n", "ax.text(0.98, 0.95, r\"Window: $W(t)$\",\n", " ha='right', va='top', transform=ax.transAxes, size=12)\n", "ax.xaxis.set_major_formatter(plt.NullFormatter())\n", "ax.set(xlim=(-0.01, 0.99),\n", " ylim=(-0.5, 10))\n", "\n", "#----------------------------------------\n", "# Lower left panel: plot the convolution\n", "ax = axes[2, 0]\n", "\n", "ax.plot(x, y_w, '-k')\n", "\n", "ax.text(0.98, 0.95,\n", " (r'$[D \\ast W](t)$' +\n", " r'$= \\mathcal{F}^{-1}\\{\\mathcal{F}[D] \\cdot \\mathcal{F}[W]\\}$'),\n", " ha='right', va='top', transform=ax.transAxes, size=12)\n", "\n", "ax.set(xlabel='$t$',\n", " xlim=(0.01, 0.99),\n", " ylim=(-4, 4))\n", "\n", "#----------------------------------------\n", "# Upper right panels: plot the Fourier transforms\n", "N = len(x)\n", "dx = (x[1] - x[0])\n", "k = np.arange(-N/2, N/2) / N / dx\n", "\n", "ax1 = axes[0, 1]\n", "ax2 = axes[1, 1]\n", "\n", "plot_ft(k, y_fft, ax=ax1, text=\"Data FT: \" + r'$\\mathcal{F}(D)$')\n", "plot_ft(k, w_fft, ax=ax2, text=\"Window FT: \" + r'$\\mathcal{F}(W)$')\n", "\n", "for ax in [ax1, ax2]:\n", " ax.xaxis.set_major_formatter(plt.NullFormatter())\n", " ax.yaxis.set_major_formatter(plt.NullFormatter())\n", " ax.set_xlim(-30, 30)\n", " \n", "\n", "#----------------------------------------\n", "# Lower right: plot the product of Fourier transforms\n", "ax = axes[2, 1]\n", "plot_ft(k, yw_fft, ax=ax,\n", " text=r'$\\mathcal{F}(D) \\cdot \\mathcal{F}(W)$')\n", "\n", "ax.axis('tight')\n", "ax.set(xlim=(-30, 30),\n", " xlabel='$f$')\n", "\n", "ax.yaxis.set_major_formatter(plt.NullFormatter())\n", "\n", "fig.savefig('fig05_Convolution_Theorem.pdf')" ] } ], "metadata": { "anaconda-cloud": {}, "kernelspec": { "display_name": "Python 3.5", "language": "python", "name": "python3.5" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.5.1" } }, "nbformat": 4, 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