Created
December 18, 2012 16:38
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iPython Notebook demonstration of how to find Fourier coefficients.
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{ | |
"metadata": { | |
"name": "WaveFilter1" | |
}, | |
"nbformat": 3, | |
"nbformat_minor": 0, | |
"worksheets": [ | |
{ | |
"cells": [ | |
{ | |
"cell_type": "code", | |
"collapsed": false, | |
"input": [ | |
"# Demonstration of how to find Fourier coefficients\n", | |
"import numpy, pylab, math\n", | |
"x = numpy.linspace(0,2*math.pi, 100)\n", | |
"\n", | |
"def wave1(x):\n", | |
" b1 = 5\n", | |
" b3 = 2\n", | |
" return b1 * math.sin(x) + b3 * math.sin(3*x)\n", | |
"\n", | |
"wave = map(wave1, x)\n", | |
"pylab.plot(x,wave)" | |
], | |
"language": "python", | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"output_type": "pyout", | |
"prompt_number": 17, | |
"text": [ | |
"[<matplotlib.lines.Line2D at 0xb15404c>]" | |
] | |
}, | |
{ | |
"output_type": "display_data", | |
"png": 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Jkf/1B3wCJ/JSnTrSz+3dG/j5Z++u9dtvsr9Jt272Dm9APrn8859AfDxw/Lj3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\nAElFTkSuQmCC\n" | |
} | |
], | |
"prompt_number": 17 | |
}, | |
{ | |
"cell_type": "code", | |
"collapsed": false, | |
"input": [ | |
"def integrate(f, start, end, step=0.1):\n", | |
" return sum(map(lambda x: f(x), numpy.arange(start, end, step)))*step\n" | |
], | |
"language": "python", | |
"metadata": {}, | |
"outputs": [], | |
"prompt_number": 2 | |
}, | |
{ | |
"cell_type": "code", | |
"collapsed": false, | |
"input": [ | |
"integrate(math.sin, 0, math.pi) # Testing integration function (should come out to 2)\n" | |
], | |
"language": "python", | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"output_type": "pyout", | |
"prompt_number": 6, | |
"text": [ | |
"1.999547959712598" | |
] | |
} | |
], | |
"prompt_number": 6 | |
}, | |
{ | |
"cell_type": "code", | |
"collapsed": false, | |
"input": [ | |
"pylab.plot(x, map(lambda x: math.sin(x)*wave1(x), x))\n", | |
"pylab.show()\n" | |
], | |
"language": "python", | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"output_type": "display_data", | |
"png": 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8ykraF/KWW2RHwrwx2utKTYZO5DxixRiM1nI6dozGj4eFyY6EecOllesMn8i5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\n" | |
} | |
], | |
"prompt_number": 9 | |
}, | |
{ | |
"cell_type": "code", | |
"collapsed": false, | |
"input": [ | |
"pylab.plot(x, map(lambda x: math.sin(3*x)*wave1(x), x))\n", | |
"pylab.show()" | |
], | |
"language": "python", | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"output_type": "display_data", | |
"png": 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jBg7ob6PYEvDVq1djxIgRGDZsGJ577rl23xcIAIsXAwUFdnqTQ5cuQN++tM+D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\nhmE0hQWcYRhGU1jAGYZhNOX/AcH3K8FT9ZOFAAAAAElFTkSuQmCC\n" | |
} | |
], | |
"prompt_number": 14 | |
}, | |
{ | |
"cell_type": "code", | |
"collapsed": false, | |
"input": [ | |
"T = 2 * math.pi # Fundamental period\n", | |
"ang_velocity = 1 # Radian/sec\n", | |
"n = 1\n", | |
"b1 = (2/T) * integrate(lambda x: math.sin(n * ang_velocity * x) * wave1(x), 0, T)\n", | |
"print \"Fourier coefficient b1:\", b1" | |
], | |
"language": "python", | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"output_type": "stream", | |
"stream": "stdout", | |
"text": [ | |
"Fourier coeffitient b1: 5.00005433925\n" | |
] | |
} | |
], | |
"prompt_number": 12 | |
}, | |
{ | |
"cell_type": "code", | |
"collapsed": false, | |
"input": [ | |
"n = 3\n", | |
"b3 = (2/T) * integrate(lambda x: math.sin(n * ang_velocity * x) * wave1(x), 0, T)\n", | |
"print \"Fourier coefficient b3:\", b3\n" | |
], | |
"language": "python", | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"output_type": "stream", | |
"stream": "stdout", | |
"text": [ | |
"Fourier coeffitient b3: 2.00016363946\n" | |
] | |
} | |
], | |
"prompt_number": 13 | |
}, | |
{ | |
"cell_type": "code", | |
"collapsed": false, | |
"input": [], | |
"language": "python", | |
"metadata": {}, | |
"outputs": [] | |
} | |
], | |
"metadata": {} | |
} | |
] | |
} |
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