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@rnelsonchem
Created September 10, 2013 15:25
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Fourier Intro -- Frequencies, Sines, and Cosines
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"cells": [
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"cell_type": "code",
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"input": [
"%pylab inline\n",
"import plotting2 as pt"
],
"language": "python",
"metadata": {},
"outputs": [
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"output_type": "stream",
"stream": "stdout",
"text": [
"Populating the interactive namespace from numpy and matplotlib\n"
]
}
],
"prompt_number": 29
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"source": [
"# Fourier Transformation of Simple Sine and Cosine Functions\n",
"\n",
"## FT of a Cosine Function\n",
"\n",
"Generate a simulated cosine spectrum. For reasons discussed later, it is best that the frequency is an integer multiple of 2*π. In this case, we need to decide how long we will acquire our data and the number of points that will be collected. Although any number of points can be used with the FFT algorithm, it is most efficient when the number of points is a power of two (See Notebook 2a). \n",
"\n",
"In our simulation, we'll use a single frequency in Hertz. This needs to get converted into radians (rad = 2*π*freq). Then we'll generate a cosine function that spans our time range at the particular frequency that we have defined (cos(rad*time)). We'll make a plot of the full simulation (right) and a zoomed in region (left) at the end of this block, using the *dual\\_plot\\_time* function. The details of this function can be examined in the file *plotting.py*. \n",
"\n",
"<u>Variables</u>:\n",
"\n",
"* *acq\\_time*: The total time in seconds that we will let our sinusoidal functions oscillate.\n",
"\n",
"* *npoints*: This is the total number of points that we will use for our simulations. It's best if this is a multiple of two.\n",
"\n",
"* *time*: This is an array of time data that will be used as our x-axis.\n",
"\n",
"* *frequency*: The frequency in Hertz of our sinusoidal functions. Best to leave this as an integer value.\n",
"\n",
"* *freq\\_rad*: The frequency value converted to radians.\n",
"\n",
"* *cos\\_spec*: The simulated cosine function which has the defined frequency determined at each time point."
]
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"collapsed": false,
"input": [
"acq_time = 1. \n",
"npoints = 2**17 \n",
"time = np.linspace(0, acq_time, npoints) \n",
"frequency = 40 \n",
"freq_rad = 2*np.pi*frequency\n",
"cos_spec = np.cos(freq_rad*time)\n",
"\n",
"pt.dual_plot_time(time, cos_spec, xmin=0, xmax=0.1)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
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DJ1OukASZcpHADw+zm1rFBiNBVfHZtT+ydVT9MSW2OjahxJBfy0UMXZJxjBjyljmRz7xl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"text": [
"<matplotlib.figure.Figure at 0x8b9e400>"
]
}
],
"prompt_number": 30
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Next well use [Numpy's fast Fourier transform routine](http://docs.scipy.org/doc/numpy/reference/generated/numpy.fft.fft.html) to calculate the Fourier transform (FT) of our simulated spectrum. At this point, notice that this function only requires the intenstiy data (y data) and not the time data (x axis). This is a limitation of the Fourier transform: there is no specific time information in the transformation. In addition, there is an assumption that the data are equally spaced in time! If you have unequally spaced data, you need to either [reinterpolate](http://docs.scipy.org/doc/scipy/reference/interpolate.html) the data onto a equally spaced grid or use an alternative method to the FT (e.g. [least squares spectral analysis](http://en.wikipedia.org/wiki/Least-squares_spectral_analysis) which is [implemented in Scipy](http://docs.scipy.org/doc/scipy/reference/tutorial/signal.html#lomb-scargle-periodograms-spectral-lombscargle)).\n",
"\n",
"In order to properly display these data, we also need to calculate the appropriate frequencies for each FT data point. The equation necessary to calculate frequencies is given below (for an even number of data points):\n",
"\n",
"$$f = \\dfrac{[0, 1, ... , n/2 - 1, -n/2, ..., -1]}{n*d}$$\n",
"\n",
"Where n is the number of data points in the time domain and d is the time delay between points. Does this equation look familiar? How about the *m* values for Equation 5 in Notebook 2a. Notice, this is also the first instance where any specific time information about our system is being incorporated. Since Numpy uses the original [Cooley-Tukey FFT algorithm](http://en.wikipedia.org/wiki/Cooley%E2%80%93Tukey_FFT_algorithm), this frequency ordering is necessary to obtain the symmetric FT array that we saw in our 4 point case in Notebook 2a. \n",
"\n",
"Fortunately, Numpy has a convenience function, [*fftfreq*](http://docs.scipy.org/doc/numpy/reference/generated/numpy.fft.fftfreq.html), that can do this calculation for us. This function needs to know the number of points in the original data set and the time step, which is the length of time between each data point.\n",
"\n",
"Again, let's make a nice dual-wide plot of our FT data using the *dual\\_plot\\_ft* function. The FT is a complex transformation, so the computed results contain both real (left plot) and imaginary (right plot) components. In the case of a pure cosine input wave, the FT does not contain any (appreciable) imagainary components. You may see some small contamination because of the discrete nature of the FFT, but this is the most realistic spectroscopic situation. We've zoomed in substantially on the x axis, because the range of frequencies is very high (you can remove the xmin or xmax values from the plotting function to see how high the frequencies go). \n",
"\n",
"Notice that we have two peaks in the real spectrum: one at a positive value and one at the same value but negative. What is going on here? Is there a problem?\n",
"\n",
"<u>Variables</u>:\n",
" \n",
"* *ft\\_cos*: This is the FFT data for our cosine function, which we defined above. (y-axis data)\n",
"\n",
"* *timestep*: This is the delay in seconds between each discrete time point.\n",
"\n",
"* *freqs*: The discrete frequencies for each of our cosine FFT data. (x-axis data)"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"ft_cos = np.fft.fft(cos_spec)\n",
"timestep = acq_time/npoints\n",
"freqs = np.fft.fftfreq(npoints, d=timestep)\n",
"\n",
"pt.dual_plot_ft(freqs, ft_cos, xmin=-100, xmax=100)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": 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LFiyQx+NRfX29duzYYbTbsGGD2tvbtWnTJs2cOVPl5eXq6uqSJFNt4TyEMZjB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\n",
"text": [
"<matplotlib.figure.Figure at 0x8873358>"
]
}
],
"prompt_number": 31
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## FT of a Sine Function\n",
"\n",
"Next, let's look at the sine function case. Make a new sine function in the same way that we made the previous cosine function, with the same frequency component.\n",
"\n",
"<u>Variable</u>:\n",
"\n",
"* *sin\\_spec*: The simulated sine function which has the defined frequency determined at each time point. "
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"sin_spec = np.sin(freq_rad*time)\n",
"\n",
"pt.dual_plot_time(time, sin_spec, xmin=0.0, xmax=0.1)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": 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Cgmz6wyiP8+eBHTvsJPkAJ/kSO3eKe5jjbBfbtwNLloweJ0GJtjZB0jjO9lqD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\nQVjB/wPcMUExte+BvgAAAABJRU5ErkJggg==\n",
"text": [
"<matplotlib.figure.Figure at 0x8b95be0>"
]
}
],
"prompt_number": 32
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Next, perform the FT of the sine function to see how it differs from a cosine function. In this case, you do not see any (appreciable) real data, but there are two frequencies in the imaginary spectrum: a positive peak at negative frequencies and a negative peak at positive frequencies. What's going on here?\n",
"\n",
"<u>Variable</u>:\n",
"\n",
"* *ft\\_spec*: This is the FFT data for our simple sine function. "
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"ft_sin = np.fft.fft(sin_spec)\n",
"\n",
"pt.dual_plot_ft(freqs, ft_sin, xmin=-100, xmax=100)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": 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ftM2JEx1Xu7p9GIuMjFRQUJAcDocGDhwoSXI4HBo5cuS39v3b3zIVFRXV2UME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\nm8y4owsXLmjt2rV699139b3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"text": [
"<matplotlib.figure.Figure at 0x85d5978>"
]
}
],
"prompt_number": 33
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## FT of Complex Data\n",
"\n",
"Now we've seen both cases where we have real cosine and sine functions; however, the FFT can handle complex inputs as well. What do the FT data of complex inputs look like?\n",
"\n",
"First, let's perform an FT of a mixture of real cosine and imaginary sine functions. As you can see, we now know the exact frequency and the sign of the intensity is correct. How is this possible?\n",
"\n",
"<u>Variable</u>:\n",
"\n",
"* *ft\\_cps*: This is the FFT data for a complex data set containing a real cosine function plus and imaginary sine function. (The *1j* multiplication of *sin\\_spec* is equvalent to multiplying by $\\sqrt{-1}$)"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"ft_cps = np.fft.fft(cos_spec + sin_spec*1j)\n",
"\n",
"pt.dual_plot_ft(freqs, ft_cps, xmin=-100, xmax=100)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": 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GHA7CGPqH2gUAMFPIwlhcXJwkaebMmca3gdOmTVNNTY3i4+PV1NRk7NvS0iJJ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\nAIAJ/j8ou6y3aWIy+wAAAABJRU5ErkJggg==\n",
"text": [
"<matplotlib.figure.Figure at 0x85a5ef0>"
]
}
],
"prompt_number": 34
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Using this same procedure, we can examine some of the other complex combinations of sine and cosine functions."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"ft_cms = np.fft.fft(cos_spec - sin_spec*1j)\n",
"\n",
"pt.dual_plot_ft(freqs, ft_cms, xmin=-100, xmax=100)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": 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Dp06dqtraWsXHx6u5udnYt7W1VZKUkJCgEydOyOfzqauryyhMLS0tSk9Pl6RB\ntT1bSUmJRowYYSzn5+crPz8/IK8fgcE8Y0Bkq6ysVGVlpbHc0dFhYm/Co3ZJ1C8AMFMwa1fAwtiw\nYcOMb/7OlpaWpvr6emO5oaFBDodD0dHRSk5OVkxMjDwej7KysiRJHo9H2dnZg257NpfLJYfDEZDX\ni+BgnjEgsp0dIrxer7Zs2WJaf8KhdknULwAwUzBrV0CfGcvLy9OuXbv0ySef6KOPPtLu3bt1++23\na9q0aaqrq1NVVZUOHTqkiooK5eXlSZJiY2OVm5ur8vJyNTc3a9u2bfL5fMrJyZGkQbVF+OGZMQCh\nRu0CAJgloPOMzZkzR8ePH9fSpUuVmpqqoqIi41u/ZcuWacOGDfL7/crNzdW9995rtFu8eLHKyso0\nf/58ORwOrVy50rh1Y8yYMZfdFuGHMAYg1KhdAACzRNXW1vaZ3YlgO3bsmGbPnq3W1lZu87C4F1+U\nHntMevJJaelS6S9/MbtHAILJ6/XK6XRqx44dGj16tNndsRzqFwBYTyBrV0BvUwQGiytjAAAAsAvC\nGCzlzKHtCWMAAACIZIQxWMqZV8aYZwwAAACRjDAGS+mfZ4yh7QEAABDpCGOwFJ4ZAwAAgF0QxmAp\nhDEAAADYBWEMlkIYAwAAgF0QxmAphDEAAADYBWEMlkIYAwAAgF0QxmApzDMGAAAAuyCMwVKYZwwA\nAAB2QRiDpTDPGAAAAOyCMAZL4ZkxAAAA2AVhDJZCGAMAAIBdEMZgKYQxAAAA2AVhDJZyZhjr6zv9\nAwAAAEQiwhgs5cwwJhHGAAAAELkIY7CUM+cZ618GAAAAIhFhDJZy9pUx5hoDAABApCKMwVLOnGdM\n4soYAAAAIhdhDJZy9pUxwhgAAAAiFWEMlkIYAwAAgF0QxmAphDEAAADYRVDCWHNzs6ZPn64nn3zS\nWOd2u1VUVKQf//jHWrt2rXrOGJmho6NDv/rVr3TnnXfqgQce0AcffDDgeINpi/BCGANgFmoXACDU\nghLG1q1bp29+85vGclNTk1wulwoKCuRyuVRXV6ft27cb29euXav29natX79eU6ZMUWlpqTo7Owfd\nFuGHoe0BmIXaBQAItYCHsbfeekvDhg3TjTfeaKyrqanRhAkTNGvWLI0bN05z5sxRdXW1JKmrq0tu\nt1vFxcVKTU1VYWGhEhMT5Xa7B90W4Yeh7QGYgdoFADBDQMPYF198ofLycj388MPq6+sz1jc2Nioz\nM9NYzszGoXQxAAAUnklEQVTMlNfrVU9Pj9ra2tTd3a2MjIwB25uami67bWNjYyBfFkKI2xQBhBq1\nCwBgloCGsa1bt+r73/++kpOTFRUVZaz3+/1KSUkxlp1OpyTJ5/PJ7/crISFBsbGxA7b7/f5Bt0X4\nYZ4xAKFG7QIAmGVooA7U2Ngot9ut8vJySRrw7WJ8fLyam5uN5dbWVklSQkKCTpw4IZ/Pp66uLqMw\ntbS0KD09fdBtz1ZSUqIRI0YYy/n5+crPzx/0a0fgcGUMiGyVlZWqrKw0ljs6OkzsTXjULon6BQBm\nCmbtClgYq6ur09GjRzVnzhxJUmdnp3p7e9Xc3KwbbrhB9fX1xr4NDQ1yOByKjo5WcnKyYmJi5PF4\nlJWVJUnyeDzKzs6WJKWlpV1227O5XC45HI5AvWQEAWEMiGxnhwiv16stW7aY1p9wqF0S9QsAzBTM\n2hWwMDZ16lRNmjRJ0ulvFl988UW1tbVpyZIlam9v18svv6yqqiplZWWpoqJCeXl5kqTY2Fjl5uaq\nvLxcS5cuVW1trXw+n3JyciRJ06ZNu+y2CD+EMQChRO0CAJgpYGFs2LBhGjZsmLEcFxen4cOHKz4+\nXvHx8Vq2bJk2bNggv9+v3Nxc3Xvvvca+ixcvVllZmebPny+Hw6GVK1cat26MGTPmstsi/PT2SjEx\nhDEAoUHtAgCYKaq2trbvq3cLb8eOHdPs2bPV2trKbR4W97OfSSNGSKtXSyNHSn/+s3T11Wb3CkCw\neL1eOZ1O7dixQ6NHjza7O5ZD/QIA6wlk7QrKpM/A5WKeMQAAANgFYQyWwjNjAAAAsAvCGCyFecYA\nAABgF4QxWApXxgAAAGAXhDFYSn8Yi4r66zIAAAAQiQhjsJT+MCad/pMwBgAAgEhFGIOlEMYAAABg\nF4QxWEpv718H7yCMAQAAIJIRxmApZ18ZY54xAAAARCrCGCyF2xQBAABgF4QxWEr/PGPS6dsVCWMA\nAACIVIQxWApXxgAAAGAXhDFYCmEMAAAAdkEYg6UQxgAAAGAXhDFYCkPbAwAAwC4IY7AUrowBAADA\nLghjsBTmGQMAAIBdEMZgKVwZAwAAgF0QxmApzDMGAAAAuyCMwVK4MgYAAAC7IIzBUghjAAAAsAvC\nGCyFMAYAAAC7IIzBUphnDAAAAHYxNFAH6u7u1po1a7R//36dPHlSkyZN0uzZs3X11VdLktxutzZu\n3Kj29nbl5ORowYIFiv7//9fd0dGhsrIy7d+/Xw6HQ0uWLNH48eONYw+mLcILV8YAhBK1CwBgpoBd\nGevp6VFKSorWrVun7du3Ky0tTS6XS5LU1NQkl8ulgoICuVwu1dXVafv27UbbtWvXqr29XevXr9eU\nKVNUWlqqzs7OQbdF+GGeMQChRO0CAJgpYGEsNjZW999/v5KSkhQbG6t77rlHjY2NOnz4sGpqajRh\nwgTNmjVL48aN05w5c1RdXS1J6urqktvtVnFxsVJTU1VYWKjExES53W5JGlRbhJ8zh7bnyhiAYKN2\nAQDMFLRnxg4fPqze3l5dddVVamxsVGZmprEtMzNTXq9XPT09amtrU3d3tzIyMgZsb2pqkqTLatvY\n2Bisl4UgO/PKGPOMAQg1ahcAIJSCEsa++OILrVq1Svfff79Gjhwpv9+vlJQUY7vT6ZQk+Xw++f1+\nJSQkKDY2dsB2v98vSYNqi/DDM2MAzELtAgCEWsAG8Oh36tQprVixQhkZGZozZ44kKT4+Xs3NzcY+\nra2tkqSEhASdOHFCPp9PXV1dRmFqaWlRenr6oNueraSkRCNGjDCW8/PzlZ+fH6iXjgAgjAGRrbKy\nUpWVlcZyR0eHib35KyvXLon6BQBmCmbtCmgY6+3t1cqVKxUdHa1f/OIXxvq0tDTV19cbyw0NDXI4\nHIqOjlZycrJiYmLk8XiUlZUlSfJ4PMrOzh5027O5XC45HI5AvmQEGEPbA5Ht7BDh9Xq1ZcsWE3tk\n/dolUb8AwEzBrF0BvU1xzZo1OnbsmFasWKEhQ/566GnTpqmurk5VVVU6dOiQKioqlJeXJ+n0w9O5\nubkqLy9Xc3Oztm3bJp/Pp5ycnEG3RfjhyhiAUKN2AQDMErArY62traqurtbw4cP1wx/+0Fj/85//\nXD/4wQ+0bNkybdiwQX6/X7m5ubr33nuNfRYvXqyysjLNnz9fDodDK1euNG7dGDNmzGW3RfhhaHsA\noUTtAgCYKaq2trbP7E4E27FjxzR79my1trZym4fFpadL//zPUn6+NHmyNGeO9PDDZvcKQLB4vV45\nnU7t2LFDo0ePNrs7lkP9AgDrCWTtCtrQ9sDlYJ4xAAAA2AVhDJbCPGMAAACwC8IYLIUBPAAAAGAX\nhDFYCmEMAAAAdkEYg6UwzxgAAADsgjAGS+HKGAAAAOyCMAZLYZ4xAAAA2AVhDJbClTEAAADYBWEM\nlsI8YwAAALALwhgshXnGAAAAYBeEMVgKtykCAADALghjsBTCGAAAAOyCMAZLYZ4xAAAA2AVhDJbR\n13f6hytjAAAAsAPCGCyjr+/0n8wzBgAAADsgjMEy+q+CcWUMAAAAdkAYg2X0XwUjjAEAAMAOCGOw\njLOvjDHPGAAAACIZYQyWwW2KAAAAsBPCGCyjP3gxtD0AAADsgDAGy+DKGAAAAOyEMAbLIIwBAADA\nToaa3YFA6OjoUFlZmfbv3y+Hw6ElS5Zo/PjxZncLl+h8YYx5xgBEKmoXACAiroytXbtW7e3tWr9+\nvaZMmaLS0lJ1dnaa3S1cIq6MAbATahcAIOzDWFdXl9xut4qLi5WamqrCwkIlJibK7Xab3TVcIuYZ\nA2AX1C4AgBQBYaytrU3d3d3KyMgw1mVmZqqxsdG8TuGyMM8YALugdgEApAgIY36/XwkJCYqNjTXW\nOZ1O+f1+E3uFy8FtigDsgtoFAJAiYACP+Ph4+Xw+dXV1GUWtpaVF6enp5+z7ox9Jw4ade4yoqPMf\nO1DrI+V3BPt39z8q0R/Ghg6VKiulG244vf+QIef/s/8nHNHv0ArXfkeykyfN7oE5LqV2SV9ev2AN\nUVFScrKUlCS1tkqffmp2jwAEUyBrV9iHseTkZMXExMjj8SgrK0uS5PF4lJ2dfc6+3d0liooaYSx/\n61v5Gj8+/0uP3dd3aesvdxvH+6v8fCkx8fTfFyyQsrJO79/be+E/wxH9Dq1w7Xekqaur1J/+VGks\nd3d3mNgb81xK7ZLOX78mTPjy+oXQ6umRvF7p6FHpm9+UJk/+6xeLAMJfMGtX2Iex2NhY5ebmqry8\nXEuXLlVtba18Pp9ycnLO2bey0iWHw2FCL3E5UlOl++83uxcAAiv///+c5vV65XRuMa87JrmU2iVR\nvwDAXMGrXRHxvc3ixYt1xRVXaP78+XK73Vq5cuWA+/ABALAaahcAIOyvjElSXFycVqxYYXY3AAC4\naNQuAEBEXBkDAAAAgHBDGAMAAAAAExDGAAAAAMAEhDEAAAAAMAFhDAAAAABMQBgDAAAAABMQxgAA\nAADABIQxAAAAADABYQwAAAAATEAYAwAAAAATEMYAAAAAwASEMQAAAAAwAWEMAAAAAExAGAMAAAAA\nExDGAAAAAMAEhDEAAAAAMAFhDAAAAABMQBgDAAAAABMQxgAAAADABIQxAAAAADABYQwAAAAATEAY\nAwAAAAATEMYAAAAAwARDA3GQ48eP6+mnn9b777+voUOHKjs7WwUFBUpNTTX22blzp1566SWdOnVK\neXl5KioqMrZ99tlnWr16terr65WRkaHly5dr7NixAWkLAMD5ULsAAGYLyJWxzs5Ofetb39KGDRtU\nXl6uqKgoPffcc8b2/fv3a/PmzXrooYf06KOPateuXXrjjTeM7Y8//riuuOIKbdiwQddcc41KS0sD\n0hahV1lZaXYXbIHzHBqc58hG7UI/PuuhwXkODc5zeAlIGEtJSdHs2bOVkJCgUaNG6b777tMf//hH\ndXZ2SpJef/115ebmavLkyZo4caJmzZql6upqSVJzc7MOHjyoRYsWKTk5WQsXLtSnn36q//mf/7ns\ntgcOHAjEy8Jl4B+A0OA8hwbnObJRu9CPz3pocJ5Dg/McXoLyzNj//u//avTo0YqLi5MkNTU1KTMz\n09iekZGhxsZGSVJjY6MSEhKUmJgoSYqKitLXv/51Y/tg2gIAcLGoXQCAUAt4GDt+/Lj+6Z/+SQ8+\n+KCxzu/3KyUlxVh2Op3y+XzGNqfTOeAYTqdTfr//stu2t7cH9kUBACIatQsAYIaLGsCjpKRE77//\n/nm33XbbbSopKZEk/d///Z+WLVum22+/XVOnTjX2iY+PV3Nzs7Hc2tqqhIQEY5vX6x1wzJaWFn33\nu9+9rLatra1G27MdPXr0Yl4uBqGjo+Oc/yYIPM5zaHCegy+Y/y5HSu2SqF/Bxmc9NDjPocF5Dr5A\n/pt8UWHM5XJ95T5ffPGF/uEf/kHXXnut5s2bN2Db2LFj5fF4jGWPx6O0tDRj2/Hjx3X8+HElJiaq\nr69Pn3zyiTGq1KW2PXz48DkjUsXFxSk5OVnXXXfdxbxcDNKWLVvM7oItcJ5Dg/McfMnJycatgYEU\n7rVLon6FEp/10OA8hwbnOfgCVbsCMrT9qVOntGLFCl111VVasmTJOdvvuOMOPf7447rpppsUHx+v\nyspKzZ07V5KUmpqq66+/XuvWrdMDDzygl156SUlJSZo4ceKg2/aLi4vTpk2bjIeyAQDWERcXF5Qw\n9lWsXrsk6hcAWFWgaldUbW1t32APcuDAAS1dulTDhw9XVFSUsf7JJ580vs175ZVX9OKLL6q7u1v5\n+fkD5ls5duyYVq1apfr6emVmZmrZsmUDviEcTFsAAM6H2gUAMFtAwhgAAAAA4NIEZWh7AAAAAMCF\nEcYAAAAAwAQBGcDDSjZu3Kg9e/boyJEjKikp0R133DFg+86dO/XSSy/p1KlTysvLG3AP/2effabV\nq1ervr5eGRkZWr58OffwX6R77rlHx48f15Ahp/P91KlT9cgjjxjbL3TecfE6OjpUVlam/fv3y+Fw\naMmSJRo/frzZ3Qp7S5Ys0Ycffqjo6GhJ0oQJE1RWViZJcrvd2rhxo9rb25WTk6MFCxYY++HCdu7c\nqerqajU0NKiwsHDA5/5C59Wu73PqV+hRu0LDrp/pUKB+BV6oa1fEXRkbO3asFi5cqKysrAEPZEvS\n/v37tXnzZj300EN69NFHtWvXLr3xxhvG9scff1xXXHGFNmzYoGuuuUalpaWh7n7YioqK0pNPPqnq\n6mpVV1cPKGZfdd5x8dauXav29natX79eU6ZMUWlpKaOsBUBUVJSWLl1qvH/7C1lTU5NcLpcKCgrk\ncrlUV1en7du3m9zb8JGUlKR58+YpOzt7wPqvOq92fZ9Tv0KP2hUadv1MhwL1K/BCXbsiLozdfvvt\nuvHGGzVs2LBztr3++uvKzc3V5MmTNXHiRM2aNUvV1dWSpObmZh08eFCLFi1ScnKyFi5cqE8//VQH\nDhwI9UsIW3195x8L5kLnHRevq6tLbrdbxcXFSk1NVWFhoRITE+V2u83uWkQ43/u3pqZGEyZM0KxZ\nszRu3DjNmTOH9+4lmDx5sm655RaNHDlywPoLnVc7v8+pX+agdgWXnT/ToUL9CqxQ166IC2MX0tTU\npMzMTGM5IyNDjY2NkqTGxkYlJCQoMTFR0ulvGr7+9a8b2/HVnnjiCRUWFmrz5s369NNPjfUXOu+4\neG1tberu7lZGRoaxLjMzk3MZIM8995zuuece/fa3vx3w78KZ793MzEx5vV719PSY1c2IcKHzyvv8\n/KhfwUPtCi4+08FH/QqNYNUuW4Uxv9+vlJQUY9npdMrn8xnbnE7ngP2dTqfa29tD2sdw9dhjj6mi\nokIrV65UU1OTnn76aWPbhc47Lp7f71dCQoJiY2ONdU6nU36/38ReRYa///u/1wsvvKB169ZJOn3L\nl3T+964k3r+DdKHzyvv8/KhfwUHtCj4+08FF/QqdYNWusBrAo6SkRO+///55t912220qKSm5YPv4\n+Hg1Nzcby62trUpISDC2eb3eAfu3trbqu9/97iB7Hf4u5rz3P6CYlpam+fPn67777lN7e7uuuOKK\nC553XLz4+Hj5fD51dXUZH/aWlhalp6eb3LPwl5WVJUmKjY3Vz372M911111qaGg473tXEu/fQbrQ\neT1x4kREvs+pX6FH7bIGaldwUb9CJ1i1K6zCmMvlGlT7sWPHyuPxGMsej0dpaWnGtuPHj+v48eNK\nTExUX1+fDh8+zGhUuvzz3tvbK+nC5x0XLzk5WTExMfJ4PMY/vh6P55wHTDE4/ffe9/X1KS0tTfX1\n9ca2hoYGOZ1ORqMapPOdV4fDoejo6Ih9n1O/Qo/aZQ2R+pm2IupXcAWrdkXcbYo9PT06efKkent7\nderUKePvknTHHXdoz549euutt/T++++rsrJSM2bMkCSlpqbq+uuv17p16+T1evXss88qKSlJEydO\nNPPlhIW2tjb96U9/0qlTp9Tc3KznnntOkyZNMr59udB5x8WLjY1Vbm6uysvL1dzcrG3btsnn8ykn\nJ8fsroW1EydO6N1339XJkyf12WefaePGjXI6nfrGN76hadOmqa6uTlVVVTp06JAqKio0c+ZMs7sc\nNvr/Pe7p6Rnw9/Od17y8PEn2fp9Tv0KL2hUadv5MBxv1KzhCXbuiamtrzz+MUJhavXq1ampqFBUV\nZXxDsHz5ck2fPl2S9Morr+jFF19Ud3e38vPzB8wdcOzYMa1atUr19fXKzMzUsmXLbP/N4sXweDx6\n4okn1NLSIqfTqVtvvVV5eXlKSkoy9rnQecfF6+zsVFlZmfbt28dcLQHi8/m0fPlyHTlyRF/72tc0\nefJkzZw507i1YM+ePdqwYYP8fr9yc3O1cOFCY04iXNimTZv0/PPPD1hXVFSkoqKiC55Xu77PqV+h\nRe0KHbt+poON+hUcoa5dERfGAAAAACAcEI8BAAAAwASEMQAAAAAwAWEMAAAAAExAGAMAAAAAExDG\nAAAAAMAEhDEAAAAAMAFhDAAAAABMQBgDAAAAABMQxgAAAADABIQxAAAAADDB/wOq8CM4ww6ypAAA\nAABJRU5ErkJggg==\n",
"text": [
"<matplotlib.figure.Figure at 0x8484780>"
]
}
],
"prompt_number": 35
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"ft_spc = np.fft.fft(sin_spec + cos_spec*1j)\n",
"\n",
"pt.dual_plot_ft(freqs, ft_spc, xmin=-100, xmax=100)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": 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H6+TJk/J6vWpvbzcKU3Nzs9LS0iTJUt+zFRYWauTIkcZ2bm6ucnNzA/L8AQAX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\nAAAIg/8PBT1aSbw95BoAAAAASUVORK5CYII=\n",
"text": [
"<matplotlib.figure.Figure at 0x8341390>"
]
}
],
"prompt_number": 36
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"ft_smc = np.fft.fft(sin_spec - cos_spec*1j)\n",
"\n",
"pt.dual_plot_ft(freqs, ft_smc, xmin=-100, xmax=100)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": 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f/xPqEaE7/s5dQSnWzI6EBwDmE+pizezIXYA1DBsmLV9+rlj73/+V7r471CNC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\nCBAqnFkDAAAAABOiWAMAAAA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"text": [
"<matplotlib.figure.Figure at 0x8859128>"
]
}
],
"prompt_number": 37
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Multiple Frequencies\n",
"\n",
"What happens when there are multiple sinusoidal components in the same spectrum? \n",
"\n",
"To test this out, let's make a new function that is a mixture of a couple of frequencies.\n",
"\n",
"Varibles:\n",
"\n",
"* *frequency2*: This is our second frequency in Hertz. Again it is best that this is an integer value.\n",
"\n",
"* *freq\\_rad2*: Convert the second frequency into radians.\n",
"\n",
"* *cos\\_spec2*: Create our simulated spectrum, which is an addition of the two cosine functions at different frequencies."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"frequency2 = 55 \n",
"freq_rad2 = 2*np.pi*frequency2\n",
"cos_spec2 = np.cos(freq_rad*time) + np.cos(freq_rad2*time)\n",
"\n",
"pt.dual_plot_time(time, cos_spec2, xmin=0.0, xmax=0.1)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": 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snNHRwf4elKnsIdj8AvKAbdsY6Y+jTAHl29GPunL6JFNAaI+eF+wTZIoSLVmS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\nTkSuQmCC\n",
"text": [
"<matplotlib.figure.Figure at 0x8b8c710>"
]
}
],
"prompt_number": 38
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now, do the FT of this data and look at the resulting frequency spectrum. As you might expect, there are now multiple frequency componenents, and because this spectrum is only composed of real cosine functions, we see both positive and negative frequency compoenent in only the real portion of the FT data."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"ft_cos2 = np.fft.fft(cos_spec2)\n",
"\n",
"pt.dual_plot_ft(freqs, ft_cos2, xmin=-100, xmax=100)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": 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+t2JbhDEAABAtwhjCsmNoe3rGEI2RPWNWDW1PGAMAANEijCEsK8OYldtC4rHj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\ngg==\n",
"text": [
"<matplotlib.figure.Figure at 0x85d5a58>"
]
}
],
"prompt_number": 39
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let's look at another related situtation. What happens when the intensities of the compenents are different? \n",
"\n",
"This can also be simulated fairly easily. Let's multiply one of our cosine functions by a constant."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"cos_spec3 = 5*np.cos(freq_rad*time) + np.cos(freq_rad2*time)\n",
"\n",
"pt.dual_plot_time(time, cos_spec3, xmin=0.0, xmax=0.1)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": 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np07JV6iHh8WkTNcXjcncuWFykEwE6ZFHgN/+bSHRqzaYC2Wxo/HZu3dkTNMx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aAQJEoIoq6whM4+VFIn54WKIMkxq6r8URWkU6doBJIVpORH2ASJK9jRMGMG8NxzwQpmvPQS0K+f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\nTkSuQmCC\n",
"text": [
"<matplotlib.figure.Figure at 0x84a1c50>"
]
}
],
"prompt_number": 40
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The FT of this new simulated data still contains two frequency components; however, the intensity of the two peaks is different by the ratio defined in our simulation. As it turns out, the integrated area under these peaks also has the same ratio. In real systems, the areas and not intensities are much better indicators of the relative amounts of each frequency componenent."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"ft_cos3 = np.fft.fft(cos_spec3)\n",
"\n",
"pt.dual_plot_ft(freqs, ft_cos3, xmin=-100, xmax=100)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": 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0v/93f69YWZl0331m7xGG09bWJqfTqb1792rChAlm747lUL8AwHrCWbuCmsAD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\nR5JCanspl8slh8MRkfc72kV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+vyG63HHlcz406ldkULsij+90ZFG/oidStctWE3iUlJTo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\nJiCMAQAAAIAJ/j/gCzruQzQqXQAAAABJRU5ErkJggg==\n",
"text": [
"<matplotlib.figure.Figure at 0x8493278>"
]
}
],
"prompt_number": 41
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Inverse FT\n",
"\n",
"The FT is a reversible process, so if you are given a spectrum of frequencies, you can convert those into a time-domain spectrum as well. The Numpy inverse Fourier Transform functions all begin with 'i', so [*ifft*](http://docs.scipy.org/doc/numpy/reference/generated/numpy.fft.ifft.html) will reverse our eariler FT data. However, the FT and its reverse are both complex transformations. Even though we started with purely real data, the reverse transform returns a complex data set. The imaginary component has a very small, but non-zero, intensity because of floating point errors. (Notice the y axis limits on the lower plot of imaginary data, though. They are very small (1e-14) relative to the real data.)"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"rev_cos3 = np.fft.ifft(ft_cos3)\n",
"\n",
"pt.dual_plot_time(time, rev_cos3.real, xmin=0.0, xmax=0.1) # Plot real data first\n",
"pt.dual_plot_time(time, rev_cos3.imag, xmin=0.0, xmax=0.1) # Plot imaginary data second"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": 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261BMtqSb2xDCBXofU2LuWj+214LeF6azpDikjubHpbRxFaQQ64ejINnILMG1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\n",
"text": [
"<matplotlib.figure.Figure at 0x8864ac8>"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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N3qrG6v0g5HPWWfaTVkC4lCoW8fT++4HmzQMVRRjRyVo7rMZLTuOvMN1bIwcP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\n",
"text": [
"<matplotlib.figure.Figure at 0x8864898>"
]
}
],
"prompt_number": 42
},
{
"cell_type": "code",
"collapsed": false,
"input": [],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 42
}
],
"metadata": {}
}
]
}
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