{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Investigating The Sampling Theorem" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In this section, we investigate the implications of the sampling theorem. Here is the usual statement of the theorem from wikipedia:\n", "\n", "*\"If a function $x(t)$ contains no frequencies higher than B hertz, it is completely determined by giving its ordinates at a series of points spaced 1/(2B) seconds apart.\"*\n", "\n", "Since a function $x(t)$ is a function from the real line to the real line, there are uncountably many points between any two ordinates, so sampling is a massive reduction of data since it only takes a tiny number of points to completely characterize the function. This is a powerful idea worth exploring. In fact, we have seen this idea of reducing a function to a discrete set of numbers before in Fourier series expansions where (for periodic $x(t)$) \n", "\n", "$ a_n = \\frac{1}{T} \\int^{T}_0 x(t) \\exp (-j \\omega_n t )dt $\n", " \n", "\n", "with corresponding reconstruction as:\n", "\n", "$ x(t) = \\sum_k a_n \\exp( j \\omega_n t) $\n", "\n", "\n", "But here we are generating discrete points $a_n$ by integrating over the **entire** function $x(t)$, not just evaluating it at a single point. This means we are collecting information about the entire function to compute a single discrete point $a_n$, whereas with sampling we are just taking individual points in isolation.\n", "\n", "Let's come at this the other way: suppose we are given a set of samples $[x_1,x_2,..,x_N]$ and we are then told to reconstruct the function. What would we do? This is the kind of question seldom asked because we typically sample, filter, and then do something else without trying to reconstruct the function from the samples directly.\n", "\n", "Returning to our reconstruction challenge, perhaps the most natural thing to do is draw a straight line between each of the points as in linear interpolation. The next block of code takes samples of the $sin$ over a single period and draws a line between sampled ordinates." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Populating the interactive namespace from numpy and matplotlib\n" ] } ], "source": [ "%pylab inline" ] }, { "cell_type": "code", "execution_count": 122, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 122, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig,ax = subplots()\n", "\n", "f = 2.0 # Hz, signal frequency\n", "f2 = 0.8 # Hz, signal frequency 2nd component\n", "A1 = 1\n", "A2 = 2\n", "fs = 5 # Hz, sampling rate (ie. >= 2*f) \n", "t = arange(-2,2+1/fs,1/fs) # sample interval, symmetric for convenience later\n", "x = A1*sin(2*pi*f*t)+A2*sin(2*pi*f2*t+pi/3)\n", "ax.plot(t,x,'o-')\n", "ax.set_xlabel('time',fontsize=18)\n", "ax.set_ylabel('amplitude',fontsize=18)\n", "\n", "tc = arange(-2,2+1/fs,0.01/fs) # sample interval, symmetric for convenience later\n", "xc = A1*sin(2*pi*f*tc)+A2*sin(2*pi*f2*tc+pi/3)\n", "ax.plot(tc,xc,'k')\n", "\n", "# fig.savefig('figure_00@.png', bbox_inches='tight', dpi=300)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To drive this point home (and create some cool matplotlib plots), we can construct the piecewise linear interpolant and compare the quality of the approximation using ``numpy.piecewise``:" ] }, { "cell_type": "code", "execution_count": 123, "metadata": {}, "outputs": [], "source": [ "interval=[] # piecewise domains\n", "apprx = [] # line on domains\n", "# build up points *evenly* inside of intervals\n", "tp = hstack([ linspace(t[i],t[i+1],20,False) for i in range(len(t)-1) ])\n", "# construct arguments for piecewise2\n", "for i in range(len(t)-1):\n", " interval.append( np.logical_and(t[i] <= tp,tp < t[i+1]))\n", " apprx.append( (x[i+1]-x[i])/(t[i+1]-t[i])*(tp[interval[-1]]-t[i]) + x[i])\n", "x_hat = np.piecewise(tp,interval,apprx) # piecewise linear approximation" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now, we can examine the squared errors in the interpolant. The following snippet plots the $sin$ and with the filled-in error of the linear interpolant." ] }, { "cell_type": "code", "execution_count": 124, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0.5, 1.0, 'Errors with Piecewise Linear Interpolant')" ] }, "execution_count": 124, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "ax1 = figure().add_subplot(111)\n", "ax1.fill_between(tp,x_hat,A1*sin(2*pi*f*tp)+A2*sin(2*pi*f2*tp+pi/3),facecolor='red')\n", "ax1.plot(tp, x_hat,'k')\n", "ax1.set_xlabel('time',fontsize=18)\n", "ax1.set_ylabel('Amplitude',fontsize=18)\n", "ax2 = ax1.twinx()\n", "sqe = ( x_hat - sin(2*pi*f*tp))**2\n", "ax2.plot(tp, sqe,'b')\n", "ax2.axis(xmin=-1,ymax= sqe.max() )\n", "ax2.set_ylabel('squared error', color='b',fontsize=18)\n", "ax1.set_title('Errors with Piecewise Linear Interpolant')\n", "\n", "# ax1.figure.savefig('figure_00@.png', bbox_inches='tight', dpi=300)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Note: I urge you to change the $fs$ sampling rate in the code above then rerun this notebook to see how these errors change with more/less sampling points." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now, we could pursue this line of reasoning with higher-order polynomials instead of just straight lines, but this would all eventually take us to the same conclusion; namely, that all of these approximations improve as the density of sample points increases, which is the *exact* opposite of what the sampling theorem says --- there is *sparse* set of samples points that will retrieve the original function. Furthermore, we observed that the quality of the piecewise linear interpolation is sensitive to *where* the sample points are taken and the sampling theorem is so powerful that it *has no such requirement*. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Reconstruction" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's look at this another way by examing the Fourier Transform of a signal that is bandlimited and thus certainly satisfies the hypothesis of the sampling theorem:\n", "\n", "$ X(f) = 0$ where $ |f|> W $\n", "\n", "Now, the inverse Fourier transform of this is the following:\n", " \n", "$ x(t) = \\int_{-W}^W X(f) e^{j 2 \\pi f t} df $\n", "\n", "We can take the $X(f)$ and expand it into a Fourier series by pretending that it is periodic with period $2 W$. Thus, we can formally write the following:\n", " \n", "$$ X(f) = \\sum_k a_k e^{ - j 2 \\pi k f/(2 W) } $$\n", "\n", "we can compute the coefficients $a_k$ as \n", "\n", "$$ a_k = \\frac{1}{2 W} \\int_{-W}^W X(f) e^{ j 2 \\pi k f/(2 W) } df $$\n", "\n", "These coefficients bear a striking similarity to the $x(t)$ integral we just computed above. In fact, by lining up terms, we can write:\n", "\n", "$$ a_k = \\frac{1}{2 W} x \\left( t = \\frac{k}{2 W} \\right) $$\n", "\n", "Now, we can write out $X(f)$ in terms of this series and these $a_k$ and then invert the Fourier transform to obtain the following:\n", "\n", "$$ x(t) = \\int_{-W}^W \\sum_k a_k e^{ - j 2 \\pi k f/(2 W) } e^{j 2 \\pi f t} df $$\n", "\n", "substitute for $a_k$\n", " \n", "$$ x(t) = \\int_{-W}^W \\sum_k ( \\frac{1}{2 W} x( t = \\frac{k}{2 W} ) ) e^{ - j 2 \\pi k f/(2 W) } e^{j 2 \\pi f t} df $$\n", "\n", "switch summation and integration (usually dangerous, but OK here)\n", "\n", "$$ x(t) = \\sum_k x(t = \\frac{k}{2 W}) \\frac{1}{2 W} \\int_{-W}^W e^{ - j 2 \\pi k f/(2 W) +j 2 \\pi f t} df $$\n", "\n", "which gives finally:\n", "\n", "$$ x(t) = \\sum_k x(t = \\frac{k}{2 W}) \\frac{sin(\\pi (k-2 t W))} {\\pi (k- 2 t W)} $$\n", "\n", "And this what we have been seeking! A formula that reconstructs the function from its samples. Let's try it!" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Note that since our samples are spaced at $t= k/f_s $, we'll use $ W= f_s /2 $ to line things up." ] }, { "cell_type": "code", "execution_count": 125, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0.5, 1.0, 'sampling rate=5.00 Hz')" ] }, "execution_count": 125, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "ax = figure().add_subplot(111)\n", "t = linspace(-2,2,100) # redefine this here for convenience\n", "ts = arange(-2,2+1/fs,1/fs) # sample points\n", "num_coeffs=len(ts) \n", "sm=0\n", "for k in range(-num_coeffs,num_coeffs): # since function is real, need both sides\n", "# sm+=(sin(2*pi*(k/fs)))*sinc( k - fs * t)\n", " sm+=(A1*sin(2*pi*f*(k/fs))+A2*sin(2*pi*f2*(k/fs)+pi/3))*sinc( k - fs * t)\n", "\n", "ax.plot( t,sm,'--',t,(A1*sin(2*pi*f*t)+A2*sin(2*pi*f2*t+pi/3)),ts, (A1*sin(2*pi*f*ts)+A2*sin(2*pi*f2*ts+pi/3)),'o')\n", "ax.set_title('sampling rate=%3.2f Hz' % fs )\n", "\n", "# ax.figure.savefig('figure_00@.png', bbox_inches='tight', dpi=300)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can do the same check as we did for the linear interpolant above as" ] }, { "cell_type": "code", "execution_count": 130, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([-2. , -1.95959596, -1.91919192, -1.87878788, -1.83838384,\n", " -1.7979798 , -1.75757576, -1.71717172, -1.67676768, -1.63636364,\n", " -1.5959596 , -1.55555556, -1.51515152, -1.47474747, -1.43434343,\n", " -1.39393939, -1.35353535, -1.31313131, -1.27272727, -1.23232323,\n", " -1.19191919, -1.15151515, -1.11111111, -1.07070707, -1.03030303,\n", " -0.98989899, -0.94949495, -0.90909091, -0.86868687, -0.82828283,\n", " -0.78787879, -0.74747475, -0.70707071, -0.66666667, -0.62626263,\n", " -0.58585859, -0.54545455, -0.50505051, -0.46464646, -0.42424242,\n", " -0.38383838, -0.34343434, -0.3030303 , -0.26262626, -0.22222222,\n", " -0.18181818, -0.14141414, -0.1010101 , -0.06060606, -0.02020202,\n", " 0.02020202, 0.06060606, 0.1010101 , 0.14141414, 0.18181818,\n", " 0.22222222, 0.26262626, 0.3030303 , 0.34343434, 0.38383838,\n", " 0.42424242, 0.46464646, 0.50505051, 0.54545455, 0.58585859,\n", " 0.62626263, 0.66666667, 0.70707071, 0.74747475, 0.78787879,\n", " 0.82828283, 0.86868687, 0.90909091, 0.94949495, 0.98989899,\n", " 1.03030303, 1.07070707, 1.11111111, 1.15151515, 1.19191919,\n", " 1.23232323, 1.27272727, 1.31313131, 1.35353535, 1.39393939,\n", " 1.43434343, 1.47474747, 1.51515152, 1.55555556, 1.5959596 ,\n", " 1.63636364, 1.67676768, 1.71717172, 1.75757576, 1.7979798 ,\n", " 1.83838384, 1.87878788, 1.91919192, 1.95959596, 2. ])" ] }, "execution_count": 130, "metadata": {}, "output_type": "execute_result" } ], "source": [ "t" ] }, { "cell_type": "code", "execution_count": 132, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0.5, 1.0, 'Errors with sinc Interpolant')" ] }, "execution_count": 132, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "ax1 = figure().add_subplot(111)\n", "ax1.fill_between(t,sm,(A1*sin(2*pi*f*t)+A2*sin(2*pi*f2*t+pi/3)),facecolor='red')\n", "ax1.set_ylabel('Amplitude',fontsize=18)\n", "ax2 = ax1.twinx()\n", "sqe = (sm - (A1*sin(2*pi*f*t)+A2*sin(2*pi*f2*t+pi/3)))**2\n", "ax2.plot(t, sqe,'b')\n", "ax2.axis(xmin=-2,ymax = 0.01)\n", "ax2.set_ylabel('squared error', color='b',fontsize=18)\n", "ax1.set_title('Errors with sinc Interpolant')\n", "\n", "# ax1.figure.savefig('figure_00@.png', bbox_inches='tight', dpi=300)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "These interpolating functions are called the \"Whittaker\" interpolating functions. Let's examine these functions more closely with the following code" ] }, { "cell_type": "code", "execution_count": 128, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(-0.9, 0.5, 'no interference here')" ] }, "execution_count": 128, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig = figure()\n", "ax = fig.add_subplot(111) # create axis handle\n", "k=0\n", "fs=2 # makes this plot easier to read\n", "ax.plot (t,sinc( k - fs * t), \n", " t,sinc( k+1 - fs * t),'--',k/fs,1,'o',(k)/fs,0,'o',\n", " t,sinc( k-1 - fs * t),'--',k/fs,1,'o',(-k)/fs,0,'o'\n", ")\n", "ax.hlines(0,-1,1)\n", "ax.vlines(0,-.2,1)\n", "ax.annotate('sample value goes here',\n", " xy=(0,1),\n", " xytext=(-1+.1,1.1),\n", " arrowprops={'facecolor':'red','shrink':0.05},\n", " )\n", "ax.annotate('no interference here',\n", " xy=(0,0),\n", " xytext=(-1+.1,0.5),\n", " arrowprops={'facecolor':'green','shrink':0.05},\n", " )\n", "\n", "# fig.savefig('figure_00@.png', bbox_inches='tight', dpi=300)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The vertical line in the previous plot shows that where one function has a peak, the other function has a zero. This is why when you put samples at each of the peaks, they match the sampled function exactly at those points. In between those points, the crown shape of the functions fills in the missing values. Furthermore, as the figure above shows, there is no interference between the functions sitting on each of the interpolating functions because the peak of one is perfectly aligned with the zero of the others (dotted lines). Thus, the sampling theorem says that the filled-in values are drawn from the curvature of the sinc functions, not straight lines as we investigated earlier. \n", "\n", "As an illustration, the following code shows how the individual Whittaker functions (dashed lines) are assembled into the final approximation (black-line) using the given samples (blue-dots). I urge you to play with the sampling rate to see what happens. Note the heavy use of `numpy` broadcasting in this code instead of the multiple loops we used earlier." ] }, { "cell_type": "code", "execution_count": 129, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fs=5.0 # sampling rate\n", "k=array(sorted(set((t*fs).astype(int)))) # sorted coefficient list\n", "fig,ax = subplots()\n", "\n", "ax.plot(t,(sin(2*pi*(k[:,None]/fs))*sinc(k[:,None]-fs*t)).T,'--', # individual whittaker functions\n", " t,(sin(2*pi*(k[:,None]/fs))*sinc(k[:,None]-fs*t)).sum(axis=0),'k-', # whittaker interpolant\n", " k/fs,sin(2*pi*k/fs),'ob')# samples\n", "ax.set_xlabel('time',fontsize=14)\n", "ax.axis((-1.1,1.1,-1.1,1.1));\n", "\n", "# fig.savefig('figure_00@.png', bbox_inches='tight', dpi=300)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "However, if you've been following carefully, you should be somewhat uncomfortable with the second to the last plot that shows the errors in the Whittaker interpolation. Namely, *why are there any errors*? Does not the sampling theorem guarantee exact-ness which should mean no error at all? It turns out that answering this question takes us further into the implications of the sampling theorem, but that is the topic of our next post.\n", "\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Summary" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In this section, we started our investigation of the famous sampling theorem that is the bedrock of the entire field of signal processing and we asked if we could reverse-engineer the consquences of the sampling theorem by reconstructing a sampled function from its discrete samples. This led us to consider the famous *Whittaker interpolator*, whose proof we sketched here. However, after all this work, we came to a disturbing conclusion regarding the exact-ness of the sampling theorem that we will investigate in a subsequent posting. In the meantime, I urge you to start at the top of notebook and play with the sampling frequency, and maybe even the sampled function and see what else you can discover about the sampling theorem." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## References" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "* This is in the [IPython Notebook format](http://ipython.org/) and was converted to HTML using [nbconvert](https://github.com/ipython/nbconvert).\n", "\n", "* See [Signal analysis](http://books.google.com/books?id=Re5SAAAAMAAJ) for more detailed mathematical development.\n", "\n", "* The IPython Notebook corresponding to this post can be found [here](https://github.com/unpingco/Python-for-Signal-Processing/blob/master/Sampling_Theorem.ipynb)." ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.7.6" } }, "nbformat": 4, "nbformat_minor": 1 }