Better description of white noise.

This commit is contained in:
Roger Labbe committed 2015-07-19 12:44:35 -07:00
1 parent c258d429b4
commit 364a2357d7
1 file changed
+117 -75
+117 -75
View File
@@ -329,7 +329,7 @@
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truncated
"text/plain": [
"<matplotlib.figure.Figure at 0x718e470>"
"<matplotlib.figure.Figure at 0x708d208>"
]
},
"metadata": {},
@@ -433,7 +433,7 @@
"name": "stdout",
"output_type": "stream",
"text": [
"Average of measurements is 165.0006\n"
"Average of measurements is 165.0192\n"
]
}
],
@@ -464,7 +464,7 @@
"name": "stdout",
"output_type": "stream",
"text": [
"Average of measurements is 164.9314\n"
"Average of measurements is 165.0368\n"
]
}
],
@@ -497,7 +497,7 @@
"data": {
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truncated
"text/plain": [
"<matplotlib.figure.Figure at 0x4340358>"
"<matplotlib.figure.Figure at 0x40ef5c0>"
]
},
"metadata": {},
@@ -535,7 +535,7 @@
"data": {
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truncated
"text/plain": [
"<matplotlib.figure.Figure at 0x4340160>"
"<matplotlib.figure.Figure at 0x40ef3c8>"
]
},
"metadata": {},
@@ -564,7 +564,7 @@
"data": {
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truncated
"text/plain": [
"<matplotlib.figure.Figure at 0x7354080>"
"<matplotlib.figure.Figure at 0x72071d0>"
]
},
"metadata": {},
@@ -595,7 +595,7 @@
"data": {
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truncated
"text/plain": [
"<matplotlib.figure.Figure at 0x72f7898>"
"<matplotlib.figure.Figure at 0x72bc438>"
]
},
"metadata": {},
@@ -627,7 +627,7 @@
"data": {
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truncated
"text/plain": [
"<matplotlib.figure.Figure at 0x743d320>"
"<matplotlib.figure.Figure at 0x7266518>"
]
},
"metadata": {},
@@ -662,7 +662,7 @@
"data": {
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"text/plain": [
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},
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@@ -691,7 +691,7 @@
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truncated
"text/plain": [
"<matplotlib.figure.Figure at 0x7201f60>"
"<matplotlib.figure.Figure at 0x72d5278>"
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},
"metadata": {},
@@ -733,7 +733,7 @@
"data": {
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truncated
"text/plain": [
"<matplotlib.figure.Figure at 0x7387198>"
"<matplotlib.figure.Figure at 0x714f4a8>"
]
},
"metadata": {},
@@ -794,7 +794,7 @@
"data": {
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truncated
"text/plain": [
"<matplotlib.figure.Figure at 0x6be4cc0>"
"<matplotlib.figure.Figure at 0x70cf4e0>"
]
},
"metadata": {},
@@ -871,7 +871,7 @@
"data": {
"image/png": 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truncated
"text/plain": [
"<matplotlib.figure.Figure at 0x720ccc0>"
"<matplotlib.figure.Figure at 0x711c518>"
]
},
"metadata": {},
@@ -913,7 +913,7 @@
"data": {
"image/png": 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truncated
"text/plain": [
"<matplotlib.figure.Figure at 0x8596550>"
"<matplotlib.figure.Figure at 0x8481048>"
]
},
"metadata": {},
@@ -954,7 +954,7 @@
"book_plots.plot_track([0, n], [160, 160+n], c='k', label='Actual weight')\n",
"book_plots.plot_track(range(1, n+1), predictions, c='r', label='Predictions')\n",
"book_plots.show_legend()\n",
"book_plots.set_labels(x='day', y='weight (lbs)')"
"book_plots.set_labels(x='day', y='weight (lbs)');"
]
},
{
@@ -1015,7 +1015,7 @@
"data": {
"image/png": 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truncated
"text/plain": [
"<matplotlib.figure.Figure at 0x726bba8>"
"<matplotlib.figure.Figure at 0x711c9b0>"
]
},
"metadata": {},
@@ -1078,9 +1078,7 @@
"\n",
"$$\\mathbf{x} = \\begin{bmatrix}62 \\\\ 0.3\\end{bmatrix}$$\n",
"\n",
"Finally, a hat '$\\hat{}$' indicates an *estimate*. So the output of the predict step time $k$ at is the *estimate* of our state, which we denote as $\\mathbf{\\hat{x}_k}$. \n",
"\n",
"So, the algorithm is simple. The state is initialized with $\\mathbf{x_0}$. We then enter a loop, predicting the state for time $k$ from the values from time $k-1$. We then get the measurement $z_k$ and choose some intermediate point between the measurements and prediction, creating the estimate $\\mathbf{\\hat{x}_k}$."
"So, the algorithm is simple. The state is initialized with $\\mathbf{x_0}$. We then enter a loop, predicting the state for time $k$ from the values from time $k-1$. We then get the measurement $z_k$ and choose some intermediate point between the measurements and prediction, creating the estimate $\\mathbf{x}_k$."
]
},
{
@@ -1423,7 +1421,7 @@
"data": {
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truncated
"text/plain": [
"<matplotlib.figure.Figure at 0x718f208>"
"<matplotlib.figure.Figure at 0x8498278>"
]
},
"metadata": {},
@@ -1484,7 +1482,9 @@
"cell_type": "markdown",
"metadata": {},
"source": [
"Now let's write a function that generates noisy data for us. Recall from chapter 0 (**author's note**: I have not yet written chapter 0!) that we model a noisy signal as the signal plus white noise generated by `numpy.random.randn()`. We want a function that we call with the starting value, the amount of change per step, the number of steps, and the amount of noise we want to add. It should return a list of the data. Test it by creating 30 points, filtering it with `g_h_filter()`, and plot the results with `plot_g_h_results()`."
"Now let's write a function that generates noisy data for us. In this book I model a noisy signal as the signal plus [white noise](https://en.wikipedia.org/wiki/White_noise). We've not yet covered the statistics to fully understand the definition of white noise. In essence, think of it as data that randomly varies higher and lower than the signal with no pattern. We say that it is a serially uncorrelated random variable with zero mean and finite variance. If you don't follow that, you will by the end of the *Gaussians* chapter. You may not be successful at this exercise if you have no knowledge of statistics. If so, just read the solution and discussion.\n",
"\n",
"White noise can be generated by `numpy.random.randn()`. We want a function that we call with the starting value, the amount of change per step, the number of steps, and the amount of noise we want to add. It should return a list of the data. Test it by creating 30 points, filtering it with `g_h_filter()`, and plot the results with `plot_g_h_results()`."
]
},
{
@@ -1509,14 +1509,15 @@
"cell_type": "code",
"execution_count": 30,
"metadata": {
"collapsed": false
"collapsed": false,
"scrolled": false
},
"outputs": [
{
"data": {
"image/png": 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truncated
"image/png": 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truncated
"text/plain": [
"<matplotlib.figure.Figure at 0x857dac8>"
"<matplotlib.figure.Figure at 0x847da58>"
]
},
"metadata": {},
@@ -1533,6 +1534,47 @@
"plot_g_h_results(measurements, data)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Discussion\n",
"\n",
"`randn()` returns random numbers centered around 0 - it is just as likely to be greater than zero as under zero. It varies by *one standard deviation* - don't worry if you don't know what that means. I've plotted 3000 calls to `randn()` - you can see that the values are centered around zero and mostly range from a bit under -1 to a bit more than +1, though occasionally that get much larger."
]
},
{
"cell_type": "code",
"execution_count": 31,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x72ca940>]"
]
},
"execution_count": 31,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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truncated
"text/plain": [
"<matplotlib.figure.Figure at 0x71918d0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.plot([random.randn() for _ in range(3000)], lw=1)"
]
},
{
"cell_type": "markdown",
"metadata": {},
@@ -1549,7 +1591,7 @@
},
{
"cell_type": "code",
"execution_count": 31,
"execution_count": 32,
"metadata": {
"collapsed": false
},
@@ -1567,16 +1609,16 @@
},
{
"cell_type": "code",
"execution_count": 32,
"execution_count": 33,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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truncated
"image/png": "iVBORw0KGgoAAAANSUhEUgAAA5kAAAEPCAYAAADI9gBRAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
"text/plain": [
"<matplotlib.figure.Figure at 0x8580cf8>"
"<matplotlib.figure.Figure at 0x709a748>"
]
},
"metadata": {},
@@ -1612,7 +1654,7 @@
},
{
"cell_type": "code",
"execution_count": 33,
"execution_count": 34,
"metadata": {
"collapsed": false
},
@@ -1630,16 +1672,16 @@
},
{
"cell_type": "code",
"execution_count": 34,
"execution_count": 35,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAA6UAAAEPCAYAAAC6OWLnAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
"image/png": 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truncated
"text/plain": [
"<matplotlib.figure.Figure at 0x734a208>"
"<matplotlib.figure.Figure at 0x7313eb8>"
]
},
"metadata": {},
@@ -1677,7 +1719,7 @@
},
{
"cell_type": "code",
"execution_count": 35,
"execution_count": 36,
"metadata": {
"collapsed": false
},
@@ -1695,7 +1737,7 @@
},
{
"cell_type": "code",
"execution_count": 36,
"execution_count": 37,
"metadata": {
"collapsed": false
},
@@ -1704,7 +1746,7 @@
"data": {
"image/png": 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truncated
"text/plain": [
"<matplotlib.figure.Figure at 0x74401d0>"
"<matplotlib.figure.Figure at 0x85fc9b0>"
]
},
"metadata": {},
@@ -1754,7 +1796,7 @@
},
{
"cell_type": "code",
"execution_count": 37,
"execution_count": 38,
"metadata": {
"collapsed": false
},
@@ -1772,7 +1814,7 @@
},
{
"cell_type": "code",
"execution_count": 38,
"execution_count": 39,
"metadata": {
"collapsed": false,
"scrolled": true
@@ -1782,7 +1824,7 @@
"data": {
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truncated
"text/plain": [
"<matplotlib.figure.Figure at 0x86fb0b8>"
"<matplotlib.figure.Figure at 0x8664d68>"
]
},
"metadata": {},
@@ -1814,7 +1856,7 @@
},
{
"cell_type": "code",
"execution_count": 39,
"execution_count": 40,
"metadata": {
"collapsed": false
},
@@ -1823,7 +1865,7 @@
"data": {
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truncated
"text/plain": [
"<matplotlib.figure.Figure at 0x87706d8>"
"<matplotlib.figure.Figure at 0x86ab080>"
]
},
"metadata": {},
@@ -1859,7 +1901,7 @@
},
{
"cell_type": "code",
"execution_count": 40,
"execution_count": 41,
"metadata": {
"collapsed": false
},
@@ -1868,7 +1910,7 @@
"data": {
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truncated
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},
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@@ -1906,7 +1948,7 @@
},
{
"cell_type": "code",
"execution_count": 41,
"execution_count": 42,
"metadata": {
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},
@@ -1915,7 +1957,7 @@
"data": {
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"text/plain": [
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@@ -1955,7 +1997,7 @@
},
{
"cell_type": "code",
"execution_count": 42,
"execution_count": 43,
"metadata": {
"collapsed": false
},
@@ -1964,7 +2006,7 @@
"data": {
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truncated
"text/plain": [
"<matplotlib.figure.Figure at 0x6c7ff60>"
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]
},
"metadata": {},
@@ -2001,7 +2043,7 @@
},
{
"cell_type": "code",
"execution_count": 43,
"execution_count": 44,
"metadata": {
"collapsed": false
},
@@ -2010,7 +2052,7 @@
"data": {
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truncated
"text/plain": [
"<matplotlib.figure.Figure at 0x87abfd0>"
"<matplotlib.figure.Figure at 0x8663a20>"
]
},
"metadata": {},
@@ -2037,7 +2079,7 @@
},
{
"cell_type": "code",
"execution_count": 44,
"execution_count": 45,
"metadata": {
"collapsed": false
},
@@ -2046,7 +2088,7 @@
"data": {
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truncated
"text/plain": [
"<matplotlib.figure.Figure at 0x71e0e10>"
"<matplotlib.figure.Figure at 0x6b7d0f0>"
]
},
"metadata": {},
@@ -2100,7 +2142,7 @@
},
{
"cell_type": "code",
"execution_count": 45,
"execution_count": 46,
"metadata": {
"collapsed": false
},
@@ -2109,7 +2151,7 @@
"data": {
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truncated
"text/plain": [
"<matplotlib.figure.Figure at 0x87b8908>"
"<matplotlib.figure.Figure at 0x7352eb8>"
]
},
"metadata": {},
@@ -2151,7 +2193,7 @@
},
{
"cell_type": "code",
"execution_count": 46,
"execution_count": 47,
"metadata": {
"collapsed": false
},
@@ -2160,7 +2202,7 @@
"data": {
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truncated
"text/plain": [
"<matplotlib.figure.Figure at 0x8719d30>"
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]
},
"metadata": {},
@@ -2182,7 +2224,7 @@
},
{
"cell_type": "code",
"execution_count": 47,
"execution_count": 48,
"metadata": {
"collapsed": false
},
@@ -2191,7 +2233,7 @@
"data": {
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truncated
"text/plain": [
"<matplotlib.figure.Figure at 0x747cd30>"
"<matplotlib.figure.Figure at 0x73868d0>"
]
},
"metadata": {},
@@ -2215,7 +2257,7 @@
},
{
"cell_type": "code",
"execution_count": 48,
"execution_count": 49,
"metadata": {
"collapsed": false
},
@@ -2224,7 +2266,7 @@
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truncated
"text/plain": [
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@@ -2248,7 +2290,7 @@
},
{
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"execution_count": 50,
"metadata": {
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},
@@ -2265,7 +2307,7 @@
},
{
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"execution_count": 50,
"execution_count": 51,
"metadata": {
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},
@@ -2274,7 +2316,7 @@
"data": {
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@@ -2296,7 +2338,7 @@
},
{
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"execution_count": 52,
"metadata": {
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@@ -2305,7 +2347,7 @@
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truncated
"text/plain": [
"<matplotlib.figure.Figure at 0x8564c50>"
"<matplotlib.figure.Figure at 0x711cf98>"
]
},
"metadata": {},
@@ -2351,7 +2393,7 @@
},
{
"cell_type": "code",
"execution_count": 52,
"execution_count": 53,
"metadata": {
"collapsed": true
},
@@ -2372,7 +2414,7 @@
},
{
"cell_type": "code",
"execution_count": 53,
"execution_count": 54,
"metadata": {
"collapsed": false
},
@@ -2383,7 +2425,7 @@
"(0.96, 0.24)"
]
},
"execution_count": 53,
"execution_count": 54,
"metadata": {},
"output_type": "execute_result"
}
@@ -2401,7 +2443,7 @@
},
{
"cell_type": "code",
"execution_count": 54,
"execution_count": 55,
"metadata": {
"collapsed": false
},
@@ -2427,7 +2469,7 @@
},
{
"cell_type": "code",
"execution_count": 55,
"execution_count": 56,
"metadata": {
"collapsed": false
},
@@ -2438,7 +2480,7 @@
"(1.965, 0.375)"
]
},
"execution_count": 55,
"execution_count": 56,
"metadata": {},
"output_type": "execute_result"
}
@@ -2456,7 +2498,7 @@
},
{
"cell_type": "code",
"execution_count": 56,
"execution_count": 57,
"metadata": {
"collapsed": false
},
@@ -2470,7 +2512,7 @@
" [ 4.9014, 0.7306]])"
]
},
"execution_count": 56,
"execution_count": 57,
"metadata": {},
"output_type": "execute_result"
}
@@ -2488,7 +2530,7 @@
},
{
"cell_type": "code",
"execution_count": 57,
"execution_count": 58,
"metadata": {
"collapsed": false
},
@@ -2499,7 +2541,7 @@
"(array([ 3.8 , 13.2 , 101.64]), array([ 8.2 , 9.8 , 0.56]))"
]
},
"execution_count": 57,
"execution_count": 58,
"metadata": {},
"output_type": "execute_result"
}