{ "metadata": { "name": "", "signature": "sha256:dd1d19ad6fb350777dbafc2a506989bae1e979ce373a166d217a4524679455d4" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "In this notebook, we're going to visualize the data obtained by a Fourier transform in an uncommon way: we will use both the absolute magnitude and the phase in the same plot. I've come across this way of displaying the information associated with Fourier transforms while studying a [non-linear optics course on Coursera](https://class.coursera.org/onl-001).\n", "\n", "In this post, we proceed in the following way:\n", "\n", "- we show what the classical visualization of the Fourier transform is\n", "- we define new functions plotting phase and modulus at the same time\n", "- we apply this to some data and visualize the result interactively (using IPython's wonderful `interact`)" ] }, { "cell_type": "heading", "level": 1, "metadata": {}, "source": [ "Classical visualization of Fourier data" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Below, I show a frequency analysis example found on the internet to generate a time signal, which is then used as input data for the Fourier transform. The time signal is plotted next to the frequency transform." ] }, { "cell_type": "code", "collapsed": false, "input": [ "%matplotlib inline" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 1 }, { "cell_type": "code", "collapsed": false, "input": [ "from pylab import *" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 2 }, { "cell_type": "code", "collapsed": false, "input": [ "# Number of samplepoints\n", "N = 600\n", "# sample spacing\n", "T = 1.0 / 800.0\n", "x = linspace(0.0, N*T, N)\n", "y = sin(100.0 * 2.0 * pi * x) + 0.5*sin(80.0 * 2.0*pi*x)\n", "yf = fft(y)\n", "xf = linspace(0.0, 1.0/(2.0*T), N/2)\n", "\n", "subplot(211)\n", "title(\"time signal\")\n", "plot(x, y)\n", "xlabel(\"time\")\n", "grid()\n", "subplot(212)\n", "title(\"frequency data\")\n", "plot(xf, 2.0/N * abs(yf[0:N/2]))\n", "grid()\n", "xlabel(\"frequency\")\n", "tight_layout()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": { "png": { "height": 282, "width": 424 } }, "output_type": "display_data", "png": 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p8/HmPPggcNJJFPtfJXxjWkUj0tHh5v6FLwA//znw17+Ww9EEXxE1Y0YCICyt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\nf3L7+M1vNrePog2ZOpWOL95Pahtz2WXZ62825hNcc016ftUgTpIEX/t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4onzFlk0Aptke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"text": [ "" ] } ], "prompt_number": 3 }, { "cell_type": "markdown", "metadata": {}, "source": [ "While the time signal is very complex, and yields no information to the naked eye, the Fourier transform shows that the signal is a simple sum of two sinusoids, the first one having a frequency of 50 Hz and the second a frequency of 80 Hz.\n", "\n", "Another comment relating to the previous representation is that only the modulus of the Fourier transform is used in the plot. A more complete representation of the data can be achieved using the phase information. This would look like this:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "subplot(211)\n", "title('modulus of Fourier transform')\n", "plot(xf, 2.0/N * abs(yf[0:N/2]))\n", "grid()\n", "subplot(212)\n", "title('phase of Fourier transform')\n", "plot(xf, angle(yf[0:N/2]))\n", "grid()\n", "tight_layout()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": { "png": { "height": 281, "width": 424 } }, "output_type": "display_data", "png": 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TsVe2VH+f3cGE5HU94OeE7+MiwhDs/0ZoGx+KPbeD1ZR/G0WkvSiJEpFynP7/UlrNX1Er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"text": [ "" ] } ], "prompt_number": 4 }, { "cell_type": "heading", "level": 1, "metadata": {}, "source": [ "A new way of representing modulus and phase on the same plot" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "But we can do better than the last plot! Why not use the phase of the transform to color the module plot (this is what was done during the non-linear optics class)? We will use [this example](http://matplotlib.org/1.2.1/examples/pylab_examples/hist_colormapped.html) as a starting point and build a colored Fourier transform based on polygons built upon the frequency transformed data." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We start with a simple example, where we plot rectangles for each element in a curve. We make use of the `Rectangle` patch that is built-in with `matplotlib`." ] }, { "cell_type": "code", "collapsed": false, "input": [ "import matplotlib.patches as patches\n", "import matplotlib.colors as colors\n", "\n", "fig = plt.figure()\n", "ax = fig.add_subplot(111)\n", "\n", "norm = colors.Normalize(0, 11)\n", "\n", "for i in range(11): # loop for first half of pyramid\n", " color = cm.jet(norm(i))\n", " patch = patches.Rectangle((i, 0), 1, i, facecolor=color, edgecolor=color)\n", " ax.add_patch(patch)\n", " \n", "for i in range(1, 10): # loop for second half of pyramid\n", " color = cm.jet(norm(10 - i))\n", " patch = patches.Rectangle((10 + i, 0), 1, 10 - i, facecolor=color, edgecolor=color)\n", " ax.add_patch(patch)\n", " \n", "# we need to scale the axes to display the figure properly \n", "xlim(0, 21)\n", "ylim(0, 10)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 5, "text": [ "(0, 10)" ] }, { "metadata": { "png": { "height": 255, "width": 364 } }, "output_type": "display_data", "png": 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"text": [ "" ] } ], "prompt_number": 5 }, { "cell_type": "markdown", "metadata": {}, "source": [ "As you can see, the height of each bar is responsible for its color.\n", "\n", "We can now move on to a more general function that will use `Polygon` as a drawing primitive, so that we can position each polygon at different left and right heights." ] }, { "cell_type": "code", "collapsed": false, "input": [ "import matplotlib.patches as patches\n", "import matplotlib.colors as colors\n", "\n", "def plot_fft_with_phase(ax, xf, yf):\n", " phases = angle(yf)\n", " norm = colors.Normalize(phases.min(), phases.max())\n", " \n", " for left, right, ampl_left, ampl_right, phase in zip(xf[:-1], xf[1:], yf[:-1], yf[1:], phases):\n", " color = cm.jet(norm(phase))\n", " xy = array([[left, 0], [left, abs(ampl_left)], [right, abs(ampl_right)], [right, 0]])\n", " patch = patches.Polygon(xy, facecolor=color, edgecolor=color)\n", " ax.add_patch(patch)\n", " \n", " return (xf.min(), xf.max(), abs(yf).min(), abs(yf).max())" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 6 }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can test this function on our example data:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "fig = plt.figure()\n", "ax = fig.add_subplot(111)\n", "xmin, xmax, ymin, ymax = plot_fft_with_phase(ax, xf, 2.0/N * (yf[0:N/2]))\n", "xlim(xmin, xmax)\n", "ylim(ymin, ymax)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 7, "text": [ "(3.8487731520338761e-17, 0.96980162341340059)" ] }, { "metadata": { "png": { "height": 251, "width": 376 } }, "output_type": "display_data", "png": 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fUjoQEU8D3gA8G/gp4B6yG1MvTyl1m36yM8E8Pl8OAa/u8VafBQzxWrU6tNPY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\nqSmG9+2jdfQoQ/v3M3/kCEN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"text": [ "" ] } ], "prompt_number": 7 }, { "cell_type": "markdown", "metadata": {}, "source": [ "As one can see, an interesting property of the phase is shown in the plot above: there is a phase change at the first frequency in the signal as well as in the second one." ] }, { "cell_type": "heading", "level": 1, "metadata": {}, "source": [ "Application to interactive data analysis" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's apply our visualization technique to some time signals. Below, we generated a frequency modulated pulse and interactively select its parameters." ] }, { "cell_type": "code", "collapsed": false, "input": [ "from IPython.html.widgets import interact" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 8 }, { "cell_type": "code", "collapsed": false, "input": [ "def impulse_signal(t, f, tau, phase=0):\n", " return cos(2 * pi * f * t + phase) * exp(-t**2/tau**2)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 9 }, { "cell_type": "code", "collapsed": false, "input": [ "t = linspace(-10, 10, 200)\n", "s = impulse_signal(t, 1, 2)\n", "plot(t, s)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 10, "text": [ "[]" ] }, { "metadata": { "png": { "height": 255, "width": 381 } }, "output_type": "display_data", "png": 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U1p1WQd+MPn0AkAoO+s65u+Wn1jxA0jkz7v6w/Em1lznntkmSmQ2Y2cFmtrzxgbXbdqrY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\n+gCQkyKDfpI+/Sq07lDRB1AFBH0AyEm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"text": [ "" ] } ], "prompt_number": 10 }, { "cell_type": "code", "collapsed": false, "input": [ "def plot_with_colors(f, tau, userxmax=None, phase=0):\n", " fig = figure()\n", " ax = fig.add_subplot(211)\n", " t = linspace(-10, 10, 500)\n", " s = impulse_signal(t, f, tau, phase=phase)\n", " ax.plot(t, s)\n", " \n", " ax2 = fig.add_subplot(212)\n", " yf = fft(s)\n", " xf = fftfreq(yf.size, t[1] - t[0])\n", " \n", " xmin, xmax, ymin, ymax = plot_fft_with_phase(ax2, xf, yf)\n", " if userxmax != None:\n", " xlim(0, userxmax)\n", " else: \n", " xlim(xmin, xmax)\n", " ylim(ymin, ymax)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 13 }, { "cell_type": "code", "collapsed": false, "input": [ "interact(plot_with_colors, \n", " f=(1, 3, 0.1),\n", " tau=(.1, 3, 0.1),\n", " userxmax=(1, 5, 0.1),\n", " phase=(0, 3.14, 0.1))" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": { "png": { "height": 255, "width": 381 } }, "output_type": "display_data", "png": 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Yn3RS9ecV4fyggxpf7rKRjn6rgj7A//yf+eTmWbPgTW9q3X4lqRcY9CWpS514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\n7Bm+kUbqU8exCrBr1yFmzVrHrbdu4Nr7G5g8/lx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"text": [ "" ] } ], "prompt_number": 14 }, { "cell_type": "markdown", "metadata": {}, "source": [ "This is it. This way of visualizing Fourier transforms can be helpful, depending on your data.\n", "\n", "This post was entirely written using the IPython notebook. You can see a static view or download this notebook with the help of nbviewer at [20141217_PhaseColoredFFT.ipynb](http://nbviewer.ipython.org/urls/raw.github.com/flothesof/posts/master/20141217_PhaseColoredFFT.ipynb)." ] } ], "metadata": {} } ] }