{ "metadata": { "name": "", "signature": "sha256:9199a518b64c13a23d2802b0463de79b4b92bc4a43e810da3b2f5200fbe8262e" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Beating Nyquist\n", "\n", "The [Nyquist-Shannon sampling theorem](http://en.wikipedia.org/wiki/Nyquist%E2%80%93Shannon_sampling_theorem) tells us the frequency above which periodic signals are not detectable in regularly-sampled timeseries measurements. For example, if we observe a star at regular intervals of $\\Delta t = 1 \\rm{hr}$, then the sampling frequency is $f_s = 1 / \\Delta t$ and the Nyquist-Shannon sampling theorem tells us that the data stream is sensitive only to frequencies below the band-limit $B = f_s / 2$. Stated in another way: if our observing cadence is $\\Delta t$, the shortest period we can hope to detect within the data is $2\\Delta t$.\n", "\n", "The above holds for *regularly-sampled* data. What about irregularly-sampled data? A common assumption seems to be that the operative criterion in the above proof is the minimum time $\\Delta t$ between samples, so that for irregularly-sampled data at times $t_i$ the band-limit is at $B = 2\\min_i(t_{i + 1} - t_{i})$. But this is not the case! What is more important is the *window function* of observations; as we'll see, when the sampling is irregular, it is possible to detect periods far smaller than the minimum $\\Delta t$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Fourier Transforms\n", "\n", "To understand why Nyquist doesn't apply in irregular data, we must first understand Fourier transforms and how they relate to this problem.\n", "The [Fourier transform](http://en.wikipedia.org/wiki/Fourier_transform) can be thought of, roughly, as a transormation expressing any function $h(t)$ into a frequency-space representation $H(f)$.\n", "This mapping is one-to-one and reversible, so that $H(f)$ and $h(t)$ in some senses contain the exact same information.\n", "You can read about the math elsewhere, but there are a few important features of the transform that it helps to understand conceptually.\n", "\n", "### Fundamentally, a Fourier transform maps a *sinusoid* to a *delta function*.\n", "This is the first important point to understand. Fourier analysis is constructed around sinusoids as the fundamental building block or basis function of periodic signals.\n", "Because of this, a simple sinusoidal signal maps to a delta-function in frequency space:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "plot_sinusoid_FT() # function defined below" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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2n0MVoDN2BJRBdj/UPhv+eRaEOBEbg5lIpttuRkZ0h5kBnZnKkUk7xguTvgAN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\nx58IqbwkkpR0e3JVW26Fyb3Pl066Dx4bYGgkw8YIr0Q5kRX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"text": [ "" ] } ], "prompt_number": 311 }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Fourier transforms are **linear**\n", "\n", "Sums in time-space translate to sums in frequency-space" ] }, { "cell_type": "code", "collapsed": false, "input": [ "plot_sinusoid_sum_FT()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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1NCc/3SallUqFcrlIMBjCsqye57z5ujEceu9pAAiHIxiGQS4nk1JBOEyM5mbI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"text": [ "" ] } ], "prompt_number": 313 }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Even Non-Periodic Functions can be represented!" ] }, { "cell_type": "code", "collapsed": false, "input": [ "plot_nonperiodic()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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+Zpeg0jqEKfNBYIeZ3QO828yWmlmVf+zIAo5LZNIi41wMmc58p2u7RXJhrO39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\nz2a9CRjotd0d3Ld8K8+7fSWZJVegLSI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"text": [ "" ] } ], "prompt_number": 312 }, { "cell_type": "code", "collapsed": false, "input": [ "plot_nonperiodic_2()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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K+J6B4mJeEAShXPAKbml5Prakc2505FxXGiK+BQHoH8xGqvs8r/NxxHc4ZNtOikR/ej1i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\n4Db3BmNMN/AnwNXW2quAQeDdDRmllGUyW00dHSz9AkCAYMB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"text": [ "" ] } ], "prompt_number": 342 }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Fourier Transforms map multiplication onto convolution" ] }, { "cell_type": "code", "collapsed": false, "input": [ "plot_windowed_sine()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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maibNYsa56KsldErZtbY5Hekem0ri9XhWzV0O+H10tYYYd1qMmX70lYh0uyYE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9AAAg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\nzICSBXzF3Z8KN6q3x8yqgBeBQe7eFHY8Z8LMCoCfAHkEf5d/cvcXw43q9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"text": [ "" ] } ], "prompt_number": 314 }, { "cell_type": "code", "collapsed": false, "input": [ "plot_windowed_sine_sum()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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QnAEaF+vgqnl5tHT0WS7mt9GYgg/GAwp6dcoFM7M4WdVGucUK5TS16R7QQDLU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\nLQdobfNzw+JCivIu4PriAppb2ljj+L3+y2vWuWB6YQaSdwHby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"text": [ "" ] } ], "prompt_number": 327 }, { "cell_type": "markdown", "metadata": {}, "source": [ "## *(Code for Figures found below)*" ] }, { "cell_type": "code", "collapsed": false, "input": [ "%matplotlib inline\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "\n", "# Seaborn sets some nice plotting defaults.\n", "# This can be safely commented-out\n", "import seaborn; seaborn.set()\n", "\n", "# AstroML contains some tools for approximating\n", "# Continuous Fourier transforms. We'll use it below.\n", "from astroML import fourier" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 252 }, { "cell_type": "code", "collapsed": false, "input": [ "def plot_sinusoid_FT():\n", " \"\"\"Plot a single sinusoid and its Fourier power\"\"\"\n", " fig, ax = plt.subplots(1, 2, figsize=(12, 4))\n", " \n", " func = lambda t: np.sin(2 * np.pi * t)\n", " \n", " t = np.linspace(0, 5, 1000)\n", " ax[0].plot(t, func(t))\n", " ax[0].set(ylim=(-1.2, 1.2), xlabel='$t$', ylabel='$h(t)$',\n", " title='Input Data')\n", " \n", " t = np.linspace(0, 20, 10000)\n", " f, H = fourier.FT_continuous(t, func(t))\n", " ax[1].plot(f, abs(H))\n", " ax[1].set(xlim=(-3, 3), xlabel='$f$', ylabel='$|H(f)|$',\n", " title='Spectral Power')\n", " \n", "plot_sinusoid_FT()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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2n0MVoDN2BJRBdj/UPhv+eRaEOBEbg5lIpttuRkZ0h5kBnZnKkUk7xguTvgAN\noc+LlmyQsx5in20RoBshim5bZjTCDDQWLJnREIQ4kYyqmUj9dLs5nrk5RJRSKeC3gS8EmsBrtdaP\nDTz/I8B3AWv+Q9+rtX7koOff2PZ2nAsjA5pyHOYKY8Z/SW+W/T6HIEBnp/KkU47xG+QEYxKW7WDw\nnKYSatbXkj5vbDeYOGaJxIB5SwINQYiTfkZVxJ0xuK4rXnvLMUZ0A18L5LTWL1RKPQ/4Zf+xgGcD\n3661/uRRTh5mphu8L+qHnizR7nTJZtKhnDNsgj7PhdDnVMphfmbM+A1ywrSXzBZypFPmz2iEUaM7\nwIbsflAi8Tg7jg6yYEGfBSFuJNNtHoOWEhHddmKSveRFwDsAtNYfBp5zzfP3A29USn1AKfWGw548\nTDEGgxnBZijni4Kw+7ww4y04M7mE3ka5QT6bPnaJRIB0KkWxkDfaUhNWje6AYiFPynGMXq9QqXvV\nVcL/LJvbZ0GImz0CT/zDRjC4C6VobjsxSXRPA+WB37u+5STgT4HvBb4MeLFS6qsOc/IoMt1gdnZs\nM0QBCoMLC80VoRvbDeZnxo5dIjFgfnqM7WqLjqG7soVVozvACzRyRr+vwyoXGDBbyOM4Zn+WBSFu\nBjPcklU1g8Fx6Mo+8FZikr2kDBQGfk9prQffVb+mtS4DKKX+Bvgi4G9udsLFxd3TlXda5DIp7rp9\nLhRBdseZWQCavb3XSZrBtpSqTZbmxllamg7l3OdOTcOnr9BNpYzs806jzU6zw9PunAutfWdOFNAX\ntyCTYXFhMpRzhkHQv+2LWwDcdnI6tD6fXJjic09sMFucJJsxJy4P+qeveLH5HWdmQuvz/Mw4pWrL\nqPe1ICRJ71rRbaaLcqTYO/uQYEOEI2OS6H4A+Grgz5VSzwceDJ5QSs0ADyqlng7s4GW733KrE66t\nVfo/X93YoTg9xvp6NZTG5nwtcv7yFmtrc6Gc87gsLhb6fW60OlR22tx+srDn73Ac8mkvWHniYolz\n8xOhnPO4DPb50qo3toXxbGh9nsp73zSPPLFOxjUjszDY58+f3wBgIpcOrc/T41lc1+vz0jF3bw2L\nwT4/frEEwFjaCa3Pxakcj17eZvnqNpl08oGGiH8haQYFnvi6zUBmH+wn+W+XXd4GNJRSD+AtovwR\npdQ3K6W+W2u9DbwBeB/wD8BntdbvOOiJm60u1Xqbhel8aI013V6yEWLlkoC5/sYpZvrY1/sWohDH\n2fCNkMIEAAW4AAAgAElEQVS2TYH57+3g/RfGAuGA+ZkxXBe2Kma+twUhbgbdC654uo1AFlLajzGZ\nbq21C3z/NQ8/MvD8n+L5ug9NmJvEBMwV8jiYu/hqM8TKJQFzvpg1dbfCsBeODp7L1HEuVQIBGl6g\nYXo1j0AYFwsRBFflBguGZPcFIUn2+odF4JnAHsuPBEJWYlKmOzI2I8gGZtIpZgt5Y4VJf7FZmKLb\nFzmbhmYD+zW6p8MTTaZvFrMZsQA1kc1Kk0zaYWri+CUSA6RWtyDsRfzD5nGdz16wDmMy3VGyHkHW\nFzxx8viVMt1ej3TKrPhlt0Z3eGIsm0lTmMiOVKZ711JjZp+3Kk1SjsP0RC60c+4KUDOr1GxVm8xO\neaUNw0J2pYwGvwLV7wH3Aj3gu7XWOtlWCQdB/MPmIbMP9mOWUoyIMLfJHmR+Zoye67JVaYV63jCI\nIrsPMFcYY7PSNNLjt1FukE45zEyFJ0Az6RTTkzljs/ulSoPZQo5UKjwBGsxolAzsc7fXY6vaDDWz\nD+b72C3my4FJrfWLgZ8Bfi7h9ggHRPzD5iG10+1nNER3ZALUXHGysd3AcbwaxGEyN52n3elRrbdD\nPW8YbGw3mJsONwMKnnWjZGCg0XNdtqotilPhjnEum2ZqPGvk+7pca+O64dppAGb9v2Gpal6fLacO\nzCilHGAGMC9DIezLnqyqYfe+UUVmH+xnJET3ZmQC1LceVMzLjm2UvSn4sMufmVrBpNPtsV1rMVcI\nN7ACL7hqd3rUGp3Qz30cKrUW3Z4bugAFT9Ruls0LNILPWth9Hs9nGM9njAw0LOcBYAx4GPhd4DeS\nbY5wUAZFnSsCzwgGh0GGxE5GwtMdlQAtGprp7vVcSpUmd50OZ1OcQQYrmNx+0pxawlsRVPEICIT8\nZrnB1Hh4i/eOS5CVDTuYBC/QuLhapd7sMDFmTp93K5dEEFxN5ykZFkwOAT8BPKC1/kml1FngvUqp\nZ2qt9814D1N9ctv7ks3tyoOZ2Qnr+wP2j0m1vVvHMZfLWN+fgGHpx0EYetHtTcE3IxGIporurWqT\nnutGK0AN63OUArQ4vVu15dwJc24OgUCMIrtfnN4dZ5NEdxTVWgKKhTyX12o0Wh3GckN/a4yLSbzd\nhgFKQJab7G0Y1mZHSTO4mZOt1Ou7cdH6RpUxy+fFh2FMNjZq/Z93dlrW9weGY1wCDhI8WP4xujWV\nnXZkU/CmltDbjGBjnIB5Q6t59OtVRyFADQ2udgON8BaOBhjb5whFt8lrNCzml4DnK6U+ALwH+Nda\nazPL4gh7EP+wecguofYz9Omc/nR0yIvNAAqTOdIph5JhAjQq3ysM2EsMEyZBoBGtGDNrnKMMNEwV\noFF+nosDszin5idDP/8oorXeAv5F0u0QDs9e/7AIPBPY47OXMbGSoc909wVoBFaLlOMwO5U3ToBG\nsWNfwMxUDscxr57xVjVC24Ghi0cDQRyVpxvMm9HYrDRxINSykAH97L5h4ywISSA1oc2jK2NiPUMv\nuqPMjIEn5rerLbq93q0PjonNCMVYOpVidipvYHY/QtHtCzzTsr59q0UUAnTaTO/+VqXJ9GQu9EXR\nYO6MhiAkwd7qJQk2ROjjSp1u6xl60V2KMAMK3hd1z3Up18ypWx1kfaOwHYBf5aHSMsrnV6p4G+OE\nuTNjQH8nTsMEaKnSZGo8SzZzw3VpRyYIUk0KNFzXZbMS/sY4AUGgYVKfBSEp9vqHRXWbgPjs7Wf4\nRXeEXt/B85pUq7tUaeI4MD0ZTdWJ+WlvJ87tmjn7XGxVmsxMhbsz4yBzhTFK5YYxPjrX9cpCzkX0\nvs7n0kyOmVW3utbo0On2Ig2gwbzsviAkwaCoE31nBrJLqP0Mv+gOKjxEZS/xs8km+UBLlSYzkznS\nqWiGd7ButQn0ev7OjBGJMfCCq5ZBG+TUm12a7W4kFqIAbydOM8YYdt9vUY3zeD7DWC5tnHdfEJJA\nsqrmIbuE2s/wi25/Cj6XDX8KHsyr8uD6dcmj2DwkoGhYBZPyTrAzY/R9NmWcAzEcVaYbvN1H680u\n9aYZgUaUi2UDTAs0BCEpxD9sHoMuH9kl1E5GQnRHleUG88RYpd6m042mLnmAaX7fUsSLZcG8RXZR\nbgYUUDTMbhHlYtmAuUKeWqNDs92N7BqCYANSKcM8ZEzsZ6hFd73ZodHqRrIzY8DuDo1miLGoq7XA\nrujZMkSMRblhSsCupcaQPke8VmHw3KYEGvG8t8f2XEsQRpXB7LZkVc1g7+xDgg0RjsxQi+5+HeMI\nv6RnJnOkHMeYrO9uucDwq3gE9MVY1Yw+9zeJiTC4Mi3rG3VVnsFzm7JeoZ/pjmCn1QBTN38ShLiR\nOt3mIT57+xkJ0R2l7zWVcpiZyhkjurf6fY5OmExP5nAwz14Sj43IjKzvbnY/SgFqVgm9OGdxTBln\nQUiKQf+weLrNoCc+e+sZCdEdpe8VPFFfqjSN+BDE0edMOsX0ZM6YKfhYFhUatmA2Th+7KVnfUqXJ\nRD5DPhfNomgYqEZkSJ8FISkkq2oeMvtgP8MtumOYgg/O3+25VAyoWx2Hvxk8UV+qNo2oWx1HoJHN\npJkaz5rj6a40yefSjOejE6DBzIEp6xVKEW6ME9APNAwZZ0FICqleYh57dwmVMbGR4RbdMQnQYsGc\nLbP7gUaEGdDg/G1D6laXKk2mJ7KRbA0+SDCjYUqgUZzK4zjRbAYEXt3q8bwZG+Q0mh12mp3oP8uG\nVSMShKSQShnmsWeXUAO+h4TDM9Sieys20W3OF/VWDFPwYE4Fk2Bnxii9zQHFQp5mO/m61a12l2q9\nHfn7GvxAw4Cs74a/MU7UVrGJfIZcNmVMdl8QkmJP9RLRd0bQE8uP9Qy16N6sNMhlU0zkM5FeZ86g\n7NhmDFPwsCt+kq5gUq23aXWi2xp8kKBqRtLWg6h3ZhykOJ1np9mh0Uo20FjfqgPR+vYBHMdhrjBm\nxGdZEJJE/MPmMTgMIrrtZKhF91YMU/BgzrbojWaHegxT8GDOBjkb2zEKUEMCjUCAyjhHQ7GQp7LT\npt2RDXKE0WVPpQwReEawZ3GrTD9YydCK7nanS3knnin4oCZ20mIsril4MMdeIgI0WkwZ543tGMe5\nH1wlvzBaEJJCrAzmIWNiP0Mrujdj2LEvYHYqj0PywqQvQCNeRAnm2EtiFWOG2IiSEKBJLxLeDTTi\n8e5D8p9nQUiSnmRVjaMnO1Jaz9CK7kCAxpH1zaRTFCZzBgkTyfpGwUj22ZC61bHOaPQDDVlMKYwu\n4h82D/HZ28/Qiu7N7WDDlOgzY+B9UW8lXE4uzgzoeD5NPptOPBuYhBhLXID2xzm+rG/iMxrlBtlM\nismxaBdFw2CmW+wlwugi/mHzEHuJ/Qyt6N4o+5nuGKwW4GVBWwnXrY4zA+o4Tn+DnCSJs8/j+Qxj\nuXTiontju0E65VCYyEZ+rb7oTrhiy8ZWPZZF0SCZbkGAa2pCi8AzAlncaj/Rp40SYn3Lz3RPxyS6\nB3ygU+PRi6H9CDLdcVhqAIpTOVY2d2h3emQzycRv69t1XwzH81YuFvL9beeTYmOrzuxUnlQMAnRy\nLEM2k0o0uOp0e2xVm9x7djaW6wUzCEnP4sSBUur1wEGmTFzgV7TWlYibJBiCZFXNQ2Yf7GdoRXdf\ngMaV6R5YcHZ2aSqWa17LxnaDTNqhEJPoD/q8XW2yMDseyzWvZWO7EXnt5kGKhTzLGzu02l1y2Wg3\nINqPXs9ls9LkrlPTsVzPcRw/0EhOgG5XW7huPLMZAIWJLOmUk/iMRhxorX8x6TYIZiILKc1DMt32\nM7z2ku0GKcdhZjIXy/X6me4EM4Ib214GNI4peEi+gkmj1aFWb8eW2YfkPc7btRa9nhubAAXPOlWp\nteh0e7Fdc5BSTDvLBqQch9mp5K1TgpAkvZ5LOuX4PyfcGAHYFdrplCOBkKUMseiuMzOVI5WKR4Am\nvciu2+t5mwHFLMYguT7HLcYGr5WU9SAI6mLt83Qel+QCykD8xh1cbVVaI5dNUkpllVInlVLxrEAX\njKTnurh4lblAsqqmEAQ/2UxKfPaWMrT2ks1yg3MnCrFdb1d0J+P33a626MU4BQ8GCFD/uvHaS/zd\nR0cp0JjareaxMBO/jahUDioRxfve7rku27VWrH/rJFBKfSHw7cA40AJqwIxSygG2gd/VWl9MsIlC\nzAQiO5N2aLbFXmIKwbhkMykarS6u68Y2sy2Ew5FEt1IqC8wDW1prI5f4d7rxTsHP9rO+yZQZKyWQ\nAU3aXhII31gzoFPJBhpJZve9ah4zsV03IKlMN3jZ/WEW3Uqp7wDqwOu11teZCPyM97cppS5ord8V\newOFRAhK32b8BfKSVTWDIPgJChf0XJe0iG6rOLDotjEbEsfOjAHj+Qzj+XRime6gpFucfU7aXtK3\nWsTZ54R3aBxFS02pP6MRn+OhP87lJneeiu2ysaKUGgdeDfwXrXVPKfUUrfVjg8f4SZXfU0rdlUQb\nhWQIRHY2vSvuhOQJxiWT8Rbx93qQHlqT8HByINGtlPo2oIll2ZBiTOUC+9crjCXnb04gGzgzlcNx\nkhdjoyVA/brksQYayVtqUg5MT8ZXitOEhdFRo7WuK6U+BCwppb4UuBd47AbHPh5r44RECbzD4uk2\ni36mW8bFWm4pun1B/R6t9fKNjgkjG6KUSgG/DXwhnsB/7WDWRSn11cD/C3TwMjO/d6tzxilMvOvl\nuLJeS6Sc3FYC2cB0KsX0ZC4xe0kpAXvJ1ESWTNpJPNOdlNUiCUqVJsXpMdKp+FI6I7RBzr8Fvhr4\nCuBrlFKvBpaBTwEfBt6vtT7WwCul/rV/jSzwm1rrPzjO+YToCcSdiG6zGPR0g8xA2Mgtv8W01o1B\nwa2UesHAz8+55tjjZEO+FshprV8IvAH45YHrZIE3Aa8AXgp8j1Jq6VYnjNuLmaTHeVeMxVMiMaA4\nladUafU9gHGyVW2SSadiq0sOu+XkkhSgs1P5/pdhHMxM5kg5yQQaPddlq9pkfibeYhpJz2jEhda6\no7V+m9b6DcAPa61fAPwA8FHgfuC3/JnOI6GUehnwAv++/jJAbCoWsCvunD2/C8lyradbvPb2ceBv\nbqXUXyilfg74Kt8LCPB5pdQ3hdSWFwHvANBafxgYFPRPAx7VWm9rrdvAB4GX3OqEcYvuYBo+iS2z\n+6I77ux+IU+n26PW6MR6XfD6PDczFvvq7WLBE93dmIvXuq5LqdpkfjZeAZpKOcxM5RIRoNWdNp2u\ny3zMVVNmE16vkASBNVBrfVVr/bda658H1oAzxzjtlwOfUUr9JfB24K+O31IhavreYfF0G4Vkuu3n\nMOmybwXeCzwXeLtS6n3ATwLPD6kt00B54PeubzkJntseeK7CAcooJCFAIaFMd7XJbCHeDCgMZPdj\nFifdXo/tWov56fjLCRcLeVwXyrV2rNfdaXZotXvMT8dfti/YlTLum3zwvoo7051J+9apBET3ur+b\nriG8FTjOOp1FvIz51wPfB/xxGI0SosW9xl4iGVUzuE50y7hYx4Grl/i+7fcopVJa67/zvd7PAa6G\n1JYyMFhYOzWwaHP7mucKQOlmJ7v77AxnTs+G1LSDccdZ73qtHiwuxlcj3HVdtipNbjtZiPW6AGdP\nTAOX6aVSsV57Y7uO63piLO4+n14qwEOruOl4+7yz7MWk87Px9/nE/CSPXymTH8/H6id/YrUGwMLM\neOx9XiyOc3GlysLCVKyzKe9/cJmn3X1L99yx8e/h92mt//FGx2itP+of+2Va6/ce4TLrwENa6w7w\niFKqoZRa0Fqv73dw3GMcJTb3peuvn5jwrXvZXMbq/gTY3oeMv1YsCIaKxUkWZuNPwoSN7eNyGA66\nkLJ/Y9Za/53/fwPP5jF47FFvzAAP4C22+XOl1POBBweeexi4RylVxCtV+BLgl252sl/+4ZeytlY5\nYlOORsrfJvvS1XKs167W27Q6XgY07j7n/MT6k5e3uH1hIrbrPn7FF6Az8fd5LO0JsCculpibiM9P\n/tiFTcALNOLu82TOu9k/en6D20/Gd4M8f3kLgPnZ+Me5MJal1e7y5KUSk2PxjfOlq+VbHxQCWuuG\nUqqtlPox4H9rrT83+Lw/0/g8PC/2nx3xMh8Efhh4k1LqNDAJbNzo4LjHOCoWFwtW92W9tANAz/9O\nq9fbVvcH7B8TgIZv4wwy3WtrFdx2/NbOMBmGcQk4SPBwS9Ed040Z4G3AK5RSD/i/v0Yp9c3AlNb6\nzUqp1wHvxLPEvOVm1VSA2LZ/HyQoURi393UroSl4SM5ekpTtAKDoW1qS6nMSu0IWB8Y5TtEdlEhM\nZJyDPpebsYruON9XWuuPK6UeBL5BKfX9wBiQBly82cf3aq3//THO/zdKqZcopT6Cd+/+Aa21zIkb\njtgYzKRfPz2o0y2ebus4kL0k6huzfw0X+P5rHn5k4Pm/Bv76ONeImsJ4MuXkguvFvcAOktsgJ6ge\nkogYS6jPiQYafdEdbwm9PYGGG+/C1cE1GmeXpmK7bpyVcZRSr/BnL/+YiPzWWuvXR3FeITp6spDS\nSKR6if0cxtPd5pobs1IqrbXuRtEwG3ESKifXF6AJLbAbbENc7ArQBLO+0ufI6e9GOTNGeWsn1msX\nE57FiYnXKaVawId9y6AgXF+9RMSdEVxfvSTJ1ghH4cCiO8D3VZ8FHgJerJQa01q/I/SWWUqxkOfR\ny9t0e73YNvNIMgM6ns+Qz6WTzfrGXLpvZiqHQ/ylIQf7XIs54zxotYiTUqXJ1HiWfMybTcHgVvDx\n/a2Dqjwxkgd+CniuUuohvLU1H/T/f7nW+k/ibIxgBkFiOyvVS4ziuhkIGRfrOIoq/Hnge4H3AN+J\nt5OZ4JNEObkkRTcEG+Qkk92fS6BkYL+cXAJZ3/F8mokY/cUB/brVCfQ57tKfAUnM4pRrbWKeyf8x\nrfUrgCXgfcAq8O3Ax4E3x9oSwRj6mW5/c5wkNj8TrqfrujgOpFOyaZGtHCjTrZS6U2v9hP/r/woy\n20qpp3I04T60DG4fHdfmPIEoWJgdjz0DCl6fr27u0O50+ws8oibIgOYSyICCt4D0ynoN13VjKydX\nqjQSE6C5bJqp8WyswVW92aHR6jI3nUyfg791nGs0EtjpdAdAa91USj08uEW7UurfxN0YwQwC73A6\nlcJxJNNtCm7PJZ1y+oUixGtvHwe1l7xTKVUGLgJ1pZQDvFNr/XB0TbOTYJFdnBVMNstN8jkvA5qU\n6AYoVVssxVQztFRtspiAtzlgrpDnyasVao0OUzFsQ99qd6k1OtwRY+WQa5mdyse6cUtSu6wGjOcz\njOfTsX6WE9iM57VKqZ8Y2BNhkLfE3RjBDIIMairlZVVF3JlBt+eSchzJdFvMQbPU36S1fg7wOryt\n2v8F8GGl1P9WSv2ryFpnIUE5ubizY8WEhAkM+n3jEfz1ZodmqxvbTMJ+xF0qMbB1xLkxzbXMTedp\ntLrUm/HUhQ36PJdgn4uFsViFcAKi+1uAS0qpvwZeqZR6gVIq+IPfGXdjBDPoi27HIeU4Iu4Moee6\npAYy3TIDYR8HLRn4Cf//J4AngD8EUEotAfdF1joLiTvT3e50qdbb3BZjSbNrmYu5skUwBV8s5GK5\n3n4Mlg2M428fvJ+KhWR8+zDg6640Gc8feg32oQkWbSYZaBSnclxZr9Fsd2NZzJmAveQH8EqxPht4\nMfBjeIsqV/3n74+7QULydN0g0+2QTjtxr1UXbkDPz3QHolu89vZxrG9OrfUq8K6Q2jIUxF1arVRt\n7bluEsSe9U3YdgDx163e7IvuBDPdA+N8emEy8uuZkukGL+g5MRf9jqtxZ7q11n/p//gR/9+bAJRS\n9wLi6R5R3F7g6fYy3ZJRNYOe6wdCKakqYyuyCDJk4i4nt2WEGIt3h8aSAX2Ou4azCeMcd5/7wdUI\nBZQJZLr3RWv9CPDrSbdDSIbuoL0klZKMqiF0e4G9xPtdvPb2IaI7ZOIuJ7fpZ1rNyPrGbS8ZnT73\nM91GjHM82f0g0Egy0z2XQKAxORa9decgaK0/knQbhGToDdpLUpLpNoWgekmQ6RavvX2YcXcfMuIs\nJ7dVSd5eMjWRJZ1yRtNeEpePPRDdCZXPg71VauJgs9Igl03F4h+/EbGPc7XJfIy155VSrwcOckEX\n+BWtdSXiJgkGsGchpVQvMQaveok3LhD7vnBCCIjojoDiVHzl5EywWqQch2Ihvg1yTOjzWC7DeD4T\na6Y7k3YoxFCe8EbEXaWmVGlSLIzFVgd9P+LcibPR6lBvdmO102itfzG2iwnWECRQg0oZklE1g57r\nkkl7i1tBPN02IvaSCAiykXEIspIBVgvwsvvb1RbdGELvrWqTTDoVS33sm1Es5GOrUrNV9XZmTFKA\njucz5LPpWLK+7U6Pyk6b4lRyFWog3kx3yQALkSAA/ft4YC+RTLcZ9KuXOFK9xFZEdEfAYDm5qNmq\nNEk5DtMTyYqTuUKenutSrrUjv5a3NXguUQEKniCrNTo0291Ir9Pt9bxa7AkHVo7jMBvTjMaubz+5\nEokAU+NZMulULD52ExbLCgKA6+dOgt0PJaNqBkGdbsl024uI7giIc8FZqdJgZirXr9uZFHEtLOz2\nemzXWkYIk7hqspdrbVzXDDE2V8hT2WnT7kQ7o2GChQi8QKNYyMWy2ZUps1aCEIg5x/GEtyvizgh6\nQfUSR7aBtxUR3REQlwDtuS5bVbMEaNSBhkkCNGhD1IIsqFAzl3DWF3YXr0Zd2i747MwluHA0oDiV\np1xt0enGFWgkP87CaBOIOcl0m0XPdUnLNvBWI6I7AuIS3ZWdNt2ea4YA9SsuRC1ATahcEhD83aPO\ndAeL+EwY57mY1isEgYYJfS5Oj+EC5Vq0VVs2y8mXSBQE2Fu9xPN0J9wgAfBmIJyBbeBFdNuHiO4I\niGvx1ZZBC69iE6CG2A4G27AZcXbfhN0oA2ZjWq9Q6gvQ5LO+ca3R6L+3DcjuC6PNYJ1uqV5iDr0e\nfp1u39Mt9hLrENEdAUE5uZESoDEJExM2xgnYDTSizYAGlh0TxFhcm8UY9d6Oqc9BXfKJBOuSCwLs\n3ZFSqpeYQ796iS+6xWtvHyK6IyKOutWBGEtym+yAmakcDvGJMZPsJVFnuvv+ZgOyvnFti96vSz6R\nbFlIiE90m1CXXBBgV8yl/UV7kulOHtd1d6uX+DtSitfePkR0R0RxKhd5ObnAvmKCBzSTTjE9mRup\nDGhQTi7qRYWbZa8s5MxksmUhYTDTHXWg0aBYSLYueUAcorvd6VLZaRvxWRaEwLbgpBzS6ZSIbgMI\nJhtSDviaW7z2FiKiOyKCCgRRWkz6WV9DvqiLhTyblWakBfsDgWtCpjuucnKlSoPZQvJlIQEKkznS\nKSfS9Qqdbo/tasuYKh5xrNEoVT2LkohuwQR612S6XaQ8XdIMVpQJMt0SDNmHiO6IiGMa3qSFlOCJ\nk063R63RiewapUqTqfEs2YwZb92oy8n1euaUhQTP4zk7Fe2Mxna1hYs5AnR6MofjQKkcXXY/OLcJ\nvn1BuLZ6yeBjQjL0a6cPVi+RQMg6zFAuQ0gcC85K1RaTYxly2XRk1zgMfY9zROLEdV1KBuzMOEjU\n5eTKOy26PdcIP3fAbCHPdrUV2ZewSRYiGLBORZnplhrdgkEEH+2UlKczhv7sw8BCSvF024eI7oiY\njWNKutIwxloC0Xtf680OzVbXGDEG0Vdt2TSoRndAsTBGt+dS3okm0DCpRnfAXCFPqdKKzDplUllI\nQditXoJkVQ1hsIxj2pHqJbYiojsi+pnucjRirNHqUG8aJkAjDjT6m4dMm5MNjDrQKPV3ozRonCMO\nNHZ3ozRpnMfodHtU6+1Izl+SjXEEg3D7/uGU2EsMoW/5STmk0pLpthUR3RERdaa7ZJifG3anxqMK\nNIIM6LxBvteoRXc/A2qUAI1HdBsVUEY9o2Fgdl8YXXb9w4OZ7iRbJAz67FOOzD7YiojuiCiMZ8mk\nnZESJlH72DcN2qUwYCQFaOTjbGB2fzqoyR7dOGfSKabGk69LLgh7qpeIf9gIgj9/OuWQTsvsg62I\n6I4Ix3GYncpHVs94oxxkfc0RoFFn94Ns4JyJme7ILDUGCtAYAo10yqFgQF3ygCDTHVUJ0FKlyZwh\ndckFQaqXmEe351XIciTTbTUiuiOkWMizXWv1PyxhUjLQ35zPppkcy0S/qNCgPkddTq5UaeI43o6f\nphCHpWZ2Kt//YjGB3d1Hw+9zp9ujXGsZFUwKo83goj2pXmIGezLdMvtgLSK6I6RYyOO6Xt3hsAky\n3aZ9URcL+chtByb52KMuJ1fyBWiwGYIJzPb9zeEHGt2evzGOge9riCbTvVVt4mKWhShMlFJLSqmL\nSql7k26LcDD2zXRLVjVRdhdS7vrs3Wi2hxAixJxv8iEkSutB33ZgUNYXPItJvdmh3gx/g5zNcpPp\nyZwxG+MERFVOrue6lCpm1SUHyGZSFCay/V0Uw6Rca9NzXaPsNDC42VX4gcYw1+hWSmWB3wVqSbdF\nODiDux/2rQySVU2UXdG9W1GmK4GQdZilXoaMKKt5bPo7M+YN2RgnIBBLWyEHGq7rsun7Xk1jdiof\nSTm5yk7b3xjHvD57MxqN0AONXQ+7WQK0b52KINAwsRZ7iPwS8DvActINEQ7O4O6H6bS/5bgIvETp\n7Vc7XQIh68gk3YBhJqpMt+u6bJQbnJybCPW8YRBYDzYrTU7NT4Z23spOm063Z9TC0YBBj3NhIjzv\ndd9OY5gABc/ic2GlSr3ZYWIsvIobJlZrCSgW8n1bV5j065Ib2OfjoJR6NbCmtX6XUupfA7c06S8u\nFiJvV1zY3JdczpMGiwtT+PqOmZkJq/sEdo9JpeV5SaYmd+2GuVzG6j4FDEMfDoqI7giJasFZrdGh\n1TZTgAZ2l7C3gu/XMTbM6wt7x/ncifBuHkYL0GCcK81QRbfJOzPOFvJcWqtRb3YYz4d36zT5vX1M\nXn7HVNAAACAASURBVAO4SqmXA/cBf6CU+hqt9cqNXrC2VomtcVGyuFiwui87/qzdVmmnn+le36gy\nkTFncfNhsX1M1jeqADQa7X6me6fesrpPYP+4DHKQ4EFEd4REVWbM1Cl4gPkZr00b2+GK7o1t82p0\nB0QVXO3uzGieGCv61VS2Kk3OLk6Fdt6SwQJ00DoVpug2caOrMNBavzT4WSn1PuB7bya4BXPYs/uh\nlKczgkGfvZRxtBfxdEfIzFQOh/DLjPUrl8yY9yW94GdAw56GN7FGd0Dfux9RcGVi1jfoc9jvbRM3\nQAqYjWhXyo3tBpl0yqi65MJoM+gf3hV4SbZI2BMISUUZa5FMd4QE5eTCz3R75zPTXuIJk7Az3SbW\nJQ+Iyrtv4gZIAVGV0FvfbpBOOUbVJQ8I3nuhi+5yg/lps+qSh43W+kuTboNwcPZUL5GsqhHsV8ZR\n6nTbh2S6I6ZYyFOqNkOt8rBhsL0km0kzM5mLLtNtYtY3qgxo2ROgswbaDqLaLGaj3GDOUAEaRaa7\n2e5S2Wn3bVmCYAL96iVSp9sY9s10i+i2DiMy3UqpceCPgEWgAnyn1nr9mmN+DXiR/7wLfK3Wuhx3\nWw/L/PQY569WKO+0mQlp+njT0I1xAuZnxnjyaoWe64YmnjbLTVKOmQI0n0szkQ9/J8717QbFQr5/\ngzWJYgSlIdudLuVai6fdXgztnGEyF4F3f9Pg2QxhdNkv0y1Z1WQJ/vwp8XRbjSmZ7u8HPq21fgnw\nh8BP7XPMs4Ev11p/qdb6y2wQ3BDNwkKTBSh4AqLbc0PdiXOz0qBYyBkpQMEb543t8OpWtzvezowL\nhmZAx/MZxvPpUGc0Ngy2TcHu4s4wK/ME9wXJdAsmMZhVlUy3GXQH63T3F7cm2SLhKJgiul8EvMP/\n+R3AywefVEqlgHuANyulPqiUek3M7TsywZfp+nY9tHNulM0XoBBeoNHt9bydGQ0VYwALM2M0293Q\nNsgJ7DSmClCA+enxUAMN0wXoRD5DPpfuBwdhsC6ZbsFAxMpgHruzDynS6WBMZHWrbcRuL1FKfRfw\n/1zz8AoQZK4rwMw1z08Avw68Ca/N71NKfUxr/Zko2xoGCxEI0K1qk7vPXPsnModAQKyX69x93VAe\nnu1qC9c1088dsBtcNULZIGfdcAEK3nv70lqVWqPD1Pjxa3WbvHAUPH/rwswYG+U6ruvihGCdCu4L\nps5oCKPJfov2RHQnS08y3UNB7KJba/0W4C2Djyml/gIIqooXgK1rXrYD/LrWuuEf/17gWcBNRbcJ\nuxzd0/Yi0WqrG0p7Vks7uC6cWpza93wm9Pmuc54nt9FxQ2nPip9ZPHdqxtg+33FmFj52ibbrhNKe\n1uObANx5dtbYPt92appPPbpO10mF0p4d/7PylNuLxvb5zGKBy2s1JqbGmAohuKo1uwDcc+cCiwbu\nMCuMJj13t1SgZLrNYL/ZB/HZ24cRCymBB4BXAR8FvhL4h2ueV8CfKqWeDaSBFwO/f6uTmrDLUarr\nCYnLK5VQ2vP5i148MplPX3c+U3Z2yvjTYBeWy6G059EnPQE6kUsZ2+cxf7rv8Ysl7j19fHF4/pI3\nzjnn+vexKX2ezHrutM+f32BmLH3s811c3gYg7brG9rkw7t0yH35sndtPHn+cL69WcBzotdp7+mdC\ngCGMLt3e7kyO1IQ2g+Dvn0o5OI7j3TdkTKzDFNH9O3hbBH8AaALfAqCU+hHgUa3125VSfwj8H6AN\n/L7W+qHEWnsIJsYyTOQzfbvAcTF5N8qAwB4QlqUm+NstzoyHcr4oWAjZu9+3l8ya2+d5fzzCem9v\nbDdwMNtGNDjOYYhub31GnkzalOU1guCJuSDTnXYkq2oCg5lu8GYiZPbBPowQ3VrrOvAN+zz+KwM/\nvwnP020dCzNjXC3thOIDXQsE6Ky5ontiLMN4PhNaZYv1LU/Imux7XRjwdIfBRtkeARpWcLVRbjBr\nuAANc5w7XW+BsMnrM4TRpNdzSfkfw5T/eZSsarJ0B3z2wf8iuu3D3G+3IWJ+ZoxWuxdKZYtdAWpu\nBhS8bHdYlS3WggyooQvsACbGsl6gEWLW13gBOhtedt+rUNMyeuEo7H7u1reOP85blSaua/ZiWWE0\nGdxjob9oTwReogzWTgcv4y1jYh/mfqMPEQshTsOvWZD1hd0SerVG59jnWt+uM1vIk82Y/XZdmBlj\nPYRAIyiRaLoYm/QDjfUQZjRK5SY912XB4MAKwg00+hYiw/ssjB5epnvXxuA9lmSLhN5+mW6ZfbAO\ns1XMkBBm3er17QYzUzly2eMvXIuSsHzdwRT8ouECFMKr1V2q2CFAIbxAo18u0PBxnvA3BQoj0LCl\nz8LoMSi6ZSGlGQzuSBn8Lz57+xDRHQNh+UC7vR6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"text": [ "" ] } ], "prompt_number": 253 }, { "cell_type": "code", "collapsed": false, "input": [ "def plot_sinusoid_sum_FT():\n", " \"\"\"Plot a sum of sinusoids and their Fourier power\"\"\"\n", " def func(t, coeffs):\n", " frequencies = 2 * np.pi * np.arange(1, len(coeffs) + 1)\n", " return np.dot(coeffs, np.sin(np.outer(frequencies, t)))\n", " \n", " coeffs = [1, 0.5, 0.25]\n", " \n", " fig, ax = plt.subplots(1, 2, figsize=(12, 4))\n", " \n", " t = np.linspace(0, 3, 1000)\n", " ax[0].plot(t, func(t, coeffs))\n", " ax[0].set(ylim=(-1.8, 1.8), xlabel='$t$', ylabel='$h(t)$',\n", " title='Input Data (sum of 3 sinusoids)')\n", " for i, coeff in enumerate(coeffs):\n", " ax[0].plot(t, coeffs[i] * np.sin(2 * np.pi * (i + 1) * t),\n", " color='gray', alpha=0.3)\n", " \n", " t = np.linspace(0, 20, 10000)\n", " f, H = fourier.FT_continuous(t, func(t, coeffs))\n", " ax[1].plot(f, abs(H))\n", " ax[1].set(xlim=(-5, 5), xlabel='$f$', ylabel='$|H(f)|$',\n", " title='Spectral Power')\n", " \n", "plot_sinusoid_sum_FT()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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c27ZZXpYJkCDsd4YvGHLt/8JwMjRCO5mtYNk2Ez2Kh2w2Q71eIx6Pr8kiclUz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"text": [ "" ] } ], "prompt_number": 328 }, { "cell_type": "code", "collapsed": false, "input": [ "def plot_nonperiodic():\n", " window = lambda t: (abs(t - 2.5) < 1.5).astype(float)\n", " \n", " fig, ax = plt.subplots(1, 2, figsize=(12, 4))\n", " \n", " t = np.linspace(0, 5, 1000)\n", " ax[0].plot(t, window(t))\n", " ax[0].set(ylim=(-0.2, 1.5),\n", " xlabel='$t$', ylabel='$h(t)$',\n", " title='Input Data')\n", " \n", " t = np.linspace(-50, 50, 10000)\n", " f, H = fourier.FT_continuous(t, window(t))\n", " ax[1].plot(f, abs(H))\n", " ax[1].set(xlim=(-5, 5), xlabel='$f$', ylabel='$|H(f)|$',\n", " title='Spectral Power')\n", " \n", "plot_nonperiodic()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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CbckTBdoiIiISKMPXaKd3h9SCSMkPBdoiIiISKJka7SG6joC3mY1IPijQFhERkUDJtPcb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\nz2a9CRjotd0d3Ld8K8+7fSWZJVegLSI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"text": [ "" ] } ], "prompt_number": 306 }, { "cell_type": "code", "collapsed": false, "input": [ "def plot_nonperiodic_2():\n", " window = lambda t: (abs(t - 2.5) < 1.5).astype(float)\n", " \n", " fig, ax = plt.subplots(1, 2, figsize=(12, 4))\n", " \n", " t = np.linspace(-50, 50, 10000)\n", " f, H = fourier.FT_continuous(t, t)\n", " H = np.exp(-abs(abs(f) - 3) / 0.3)\n", " \n", " t, h = fourier.IFT_continuous(f, H)\n", " \n", " ax[0].plot(t, h)\n", " ax[0].set(xlim=(-5, 5), #ylim=(-0.2, 1.5),\n", " xlabel='$t$', ylabel='$h(t)$',\n", " title='Input Data')\n", " \n", " ax[1].plot(f, abs(H))\n", " ax[1].set(xlim=(-10, 10), ylim=(0, 1.2), xlabel='$f$', ylabel='$|H(f)|$',\n", " title='Spectral Power')\n", " \n", "plot_nonperiodic_2()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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K+J6B4mJeEAShXPAKbml5Prakc2505FxXGiK+BQHoH8xGqvs8r/NxxHc4ZNtOikR/ej1i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\nn3O3jTV6GB3jzE1DXPumRo+iczW++as0BviVMcab7SW8CniiwWMSEel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"text": [ "" ] } ], "prompt_number": 341 }, { "cell_type": "code", "collapsed": false, "input": [ "def invisible_ticks(ax):\n", " for label in ax.get_xticklabels():\n", " label.set_visible(False)\n", "\n", "def plot_windowed_sine():\n", " window = lambda t: (abs(t - 2.5) < 1.5).astype(float)\n", " func = lambda t: np.sin(2 * np.pi * 2 * t)\n", " \n", " fig = plt.figure(figsize=(12, 8))\n", " gs = plt.GridSpec(4, 2)\n", " \n", " # plot inputs\n", " t = np.linspace(0, 5, 1000)\n", " ax = fig.add_subplot(gs[0, 0])\n", " ax.plot(t, func(t))\n", " ax.set(ylim=(-1.2, 1.2))\n", " invisible_ticks(ax)\n", " ax.set_title('Multiplication in time-space')\n", " \n", " ax = fig.add_subplot(gs[1, 0], sharex=ax)\n", " ax.plot(t, window(t))\n", " ax.set(ylim=(-0.2, 1.2))\n", " invisible_ticks(ax)\n", "\n", " ax = fig.add_subplot(gs[2:, 0], sharex=ax)\n", " ax.plot(t, func(t) * window(t))\n", " ax.set(ylim=(-1.2, 1.2),\n", " xlabel='$t$', ylabel='$h(t)$')\n", " \n", " t = np.linspace(-50, 50, 10000)\n", " ax = fig.add_subplot(gs[0, 1])\n", " f, H = fourier.FT_continuous(t, func(t))\n", " ax.plot(f, abs(H))\n", " ax.set_ylim(0, 60)\n", " invisible_ticks(ax)\n", " ax.set_title('Convolution in frequency-space')\n", " \n", " ax = fig.add_subplot(gs[1, 1], sharex=ax)\n", " f, H = fourier.FT_continuous(t, window(t))\n", " ax.plot(f, abs(H))\n", " invisible_ticks(ax)\n", " \n", " ax = fig.add_subplot(gs[2:, 1], sharex=ax)\n", " f, H = fourier.FT_continuous(t, func(t) * window(t))\n", " ax.plot(f, abs(H))\n", " ax.set(xlim=(-6, 6), xlabel='$f$', ylabel='$|H(f)|$')\n", " \n", " \n", "plot_windowed_sine()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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maibNYsa56KsldErZtbY5Hekem0ri9XhWzV0O+H10tYYYd1qMmX70lYh0uyYE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9AAAg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\nzICSBXzF3Z8KN6q3x8yqgBeBQe7eFHY8Z8LMCoCfAHkEf5d/cvcXw43q9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"text": [ "" ] } ], "prompt_number": 310 }, { "cell_type": "code", "collapsed": false, "input": [ "def invisible_ticks(ax):\n", " for label in ax.get_xticklabels():\n", " label.set_visible(False)\n", "\n", "def plot_windowed_sine_sum():\n", " window = lambda t: (abs(t - 2.5) < 1.5).astype(float)\n", " \n", " def func(t, coeffs=(1, 0.5, 0.25)):\n", " frequencies = 2 * np.pi * np.arange(1, len(coeffs) + 1)\n", " return np.dot(coeffs, np.sin(np.outer(frequencies, t)))\n", " \n", " fig = plt.figure(figsize=(12, 8))\n", " gs = plt.GridSpec(4, 2)\n", " \n", " # plot inputs\n", " t = np.linspace(0, 5, 1000)\n", " ax = fig.add_subplot(gs[0, 0])\n", " ax.plot(t, func(t))\n", " ax.set(ylim=(-1.5, 1.5))\n", " invisible_ticks(ax)\n", " ax.set_title('Multiplication in time-space')\n", " \n", " ax = fig.add_subplot(gs[1, 0], sharex=ax)\n", " ax.plot(t, window(t))\n", " ax.set(ylim=(-0.2, 1.2))\n", " invisible_ticks(ax)\n", "\n", " ax = fig.add_subplot(gs[2:, 0], sharex=ax)\n", " ax.plot(t, func(t) * window(t))\n", " ax.set(ylim=(-1.5, 1.5),\n", " xlabel='$t$', ylabel='$h(t)$')\n", " \n", " t = np.linspace(-50, 50, 10000)\n", " ax = fig.add_subplot(gs[0, 1])\n", " f, H = fourier.FT_continuous(t, func(t))\n", " ax.plot(f, abs(H))\n", " ax.set_ylim(0, 60)\n", " invisible_ticks(ax)\n", " ax.set_title('Convolution in frequency-space')\n", " \n", " ax = fig.add_subplot(gs[1, 1], sharex=ax)\n", " f, H = fourier.FT_continuous(t, window(t))\n", " ax.plot(f, abs(H))\n", " invisible_ticks(ax)\n", " \n", " ax = fig.add_subplot(gs[2:, 1], sharex=ax)\n", " f, H = fourier.FT_continuous(t, func(t) * window(t))\n", " ax.plot(f, abs(H))\n", " ax.set(xlim=(-6, 6), xlabel='$f$', ylabel='$|H(f)|$')\n", " \n", "plot_windowed_sine_sum()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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heg0yT7+Xnz1zgOrGLgDqW7r55v1XRLVB1tnj4cd/3k9Ht15ht73bwxffsyCqDbLqxk5+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\nLQdobfNzw+JCivIu4PriAppb2ljj+L3+y2vWuWB6YQaSdwHby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"text": [ "" ] } ], "prompt_number": 326 }, { "cell_type": "code", "collapsed": false, "input": [ "def plot_regular_window():\n", " window = lambda t: (abs(t - np.round(t)) < 0.01).astype(float)\n", " func = lambda t: np.sin(2 * np.pi * t)\n", " \n", " fig, ax = plt.subplots(1, 2, figsize=(12, 4))\n", " \n", " t = np.linspace(0, 5, 1000)\n", " ax[0].plot(t, func(t) * window(t))\n", " ax[0].set(ylim=(-1.5, 1.5),\n", " xlabel='$t$', ylabel='$h(t)$',\n", " title='Input Data')\n", " \n", " t = np.linspace(-50, 50, 10000)\n", " f, H = fourier.FT_continuous(t, func(t) * window(t))\n", " ax[1].plot(f, abs(H))\n", " ax[1].set(xlim=(-6, 6), xlabel='$f$', ylabel='$|H(f)|$',\n", " title='Spectral Power')\n", " \n", "plot_regular_window()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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QLSIiIiISsazpXjKCO559BvgIUBe+9DF333TcikREREREskzWBN0Mccez0BuAD7n7Sxkp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\nyoq46KzpXH3hqb130kzV//va2t7Fg09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