{ "cells": [ { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
\n", "\n", "
\n", "# [Physics 411](http://jklymak.github.io/Phy411/) Time Series Analysis\n", "*Jody Klymak*\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Week 11: Non-stationary Time Series" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
\n", "\"http://paos.colorado.edu/research/wavelets/wavelet2.html\"\n", "
\n", "\n", "We saw above in the problem set about the turbulence data that the power spectrum can change a lot during a measurement time period. That data was highly non-stationary, and you were asked to deal with it by taking a spectrum during a \"quiet\" and a \"turbulent\" period. This was done subjectively, but there are techniques for proceeding more obejctively.\n", "\n", "The example on the right is of the surface temperature reflecting the El-Nino signal in the ocean. There are times when the El-Nino periodicity of about 2 years is stronger (i.e. 1880-1920 and 1960-1990) than at other times. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Motivating example 1: Chirp" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "A \"chirp\" signal changes its frequency with time, and is clearly non-stationary as power moves from low to high frequencies:" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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dG358H0uqJp49JdMsqTgmpzCG/oCSN6y2NA+jNHGPKwxtHsYQhSHVirbkNzav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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import matplotlib.pyplot as plt\n", "import numpy as np\n", "%matplotlib inline\n", "\n", "t = np.linspace(0,40.,20000)\n", "f0=0.0001\n", "k = 0.05\n", "x = np.sin(2.*np.pi*(f0*t+k*t**2))\n", "t = np.concatenate((t,t+t[-1]))\n", "x = np.concatenate((x,x))\n", "fig,ax=plt.subplots(1,1)\n", "ax.plot(t,x)\n", "plt.ylabel('y [m]')\n", "plt.xlabel('t [s]')\n", "plt.title('Chirp')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The frequency is varying in this signal, and just taking a spectrum would be a bad way of representing the changing frequency:" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "(1e-05, 1)" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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DsNzM7nP354Ep+ScwMwN+Bjzo7qmV8KT+qEUjkqyaGN7s7kuBP+ftHge87O6vuftWYAEw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\nUUo0IiKSKCUaERFJlBKNiIgk6n8A62o+tmBLCR8AAAAASUVORK5CYII=\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import matplotlib.mlab as mlab\n", "Gx,f = mlab.psd(x,2560,Fs=1/np.median(np.diff(t)))\n", "fig,ax=plt.subplots(1,1)\n", "ax.loglog(f,Gx)\n", "plt.xlabel('f [Hz]');\n", "plt.ylabel(r'$G_{xx} \\mathrm{[x^2 Hz^{-1}]}$')\n", "plt.ylim((1e-5,1))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The appropriate frequencies indeed have power, but there is no idea from this plot that the frequency content changes with time. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Spectrogram" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The spectrogram is a simple and useful way to see the spectral content in time which simply consists of computing a power spectrum over a finite-length window, and plotting the power spectrum versus frequency and time:" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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CbmslMfVK7LQKyqp8CTTPplHhS0mjJVKZBjtUNAvVCJZ+0KTAIFbj6VCLRu1F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kri6tWr/zPC0x1o80cLz/sc8Zw794TSAg0vD8VReCsD0xsjqVZepNpXJsXgRU6BM2Vl5qkRC6UG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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "N = np.shape(x)[0]\n", "n = int(np.floor(N/20))\n", "nfft=256*8\n", "Gxx = np.zeros((20*10,nfft/2+1))\n", "num=0\n", "dt = np.median(np.diff(t))\n", "tbin = np.zeros(20*10)\n", "for ind in range(0,N-n,int(np.floor(n/10))):\n", "# print ind\n", " px,f=np.squeeze(mlab.psd(x[ind+np.arange(0,n)],nfft,Fs=1/dt))\n", " Gxx[num,:]=px\n", " num=num+1\n", " tbin[num]=np.mean(t[ind+np.arange(0,n)])\n", "tbin=tbin[0:num]\n", "Gxx=Gxx[0:num,:]\n", "fig,ax=plt.subplots(1,1)\n", "ax.loglog(f,Gxx.transpose())\n", "plt.xlabel('f [Hz]');\n", "plt.ylabel(r'$G_{xx} \\mathrm{[m^2 Hz^{-1}]}$')\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Or, more usefully, we contour in frequency and time:" ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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9Ds7eB8Ogw+GNyl/n4h4+5+tiU9LQxsmeR5pXShfeOOmHTJmZlYwTt5lZybiO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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig,ax=plt.subplots(1,1)\n", "pcm=ax.pcolormesh(tbin,f,np.log10(Gxx.transpose()))\n", "plt.xlim((0,80))\n", "plt.ylim((0,10))\n", "pcm.set_clim((-3,0.3))\n", "plt.colorbar(pcm)\n", "plt.title(r'$log_{10}(G_{xx})$')\n", "plt.xlabel('t [s]')\n", "plt.ylabel('F [Hz]')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The interpretation of this is much clearer. As time moves on, the frequency of the \"chirp\" goes up in a linear fashion. \n", "\n", "The difficulty with the spectrogram is that the window of information is the same length for all frequencies. This probably does not make a lot of sense. For \"real\" signals high frequencies may vary on a short time scale, and low frequencies on a longer time scale. **Wavelets** attempt to capture this.\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Example #2" ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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HjBC1+ZYWUZjX1endc5uaRJzTKUQnXDyMlodRXJqadCvF2GNLxst2lbw8IR6T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\nI0wztBfT6nNlqpeYzzwC4QBGnxpF/LE4ll6/FMmDScsRqUy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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# lets make an x\n", "N=10240\n", "pi = np.pi\n", "x1 = 1.*np.random.randn(N)\n", "t = np.arange(0.,N/10.,1./10.)\n", "f=1./10.\n", "b = 60\n", "x3=5.*np.cos(2*pi*f*t)*np.exp(-(t-100)**2/2/b**2)\n", "x2 = 3.*np.cos(2*pi*f/6.*t)*np.exp(-(t-800)**2/2/(b/1.)**2)\n", "x4=5.*np.cos(2*pi*f*t)*np.exp(-(t-500)**2/2/b**2) +3.*np.cos(2*pi*f/6.*t)*np.exp(-(t-500)**2/2/(b/2.)**2)\n", "x=x1+x2+x3+x4\n", "\n", "fig,ax=plt.subplots(1,1)\n", "ax.plot(t,x1+10,t,x2+20,t,x3+30,t,x4+40,t,x)\n", "\n", "plt.xlabel('t [s]')\n", "plt.ylabel('Signal')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "First, lets take the spectrogram of this:" ] }, { "cell_type": "code", "execution_count": 44, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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L6fQ7SMVRzf2e7br4wGlQqpQoDIZUR+VCl43xnrWXdLD5elrAqkN6mbrXPQj3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Wm6qngE78L6tp9FUpa13z9HynX85NdkeXS99PJ+td7H8qrXkBR+zbv+1Efh7g/Aw0uqsfZDQ93s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\ntNPJR6fNA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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "N = np.shape(x)[0]\n", "n = int(np.floor(N/20)) # length of each spectrogram...\n", "nfft=220*10\n", "Gxx = np.zeros((20*10,nfft/2+1))\n", "num=0\n", "dt =np.median(np.diff(t))\n", "tbin = np.zeros(20*10)\n", "for ind in range(0,N-n,int(np.floor(n/10))):\n", " Gxx[num,:],f=mlab.psd(x[ind+np.arange(0,n)],nfft,Fs=1/dt)\n", " num=num+1\n", " tbin[num]=np.mean(t[ind+np.arange(0,n)])\n", "tbin=tbin[:num]\n", "Gxx=Gxx[:num,:]\n", "fig,ax=plt.subplots()\n", "pcm=ax.pcolormesh(tbin,f,np.log10(Gxx.transpose()))\n", "plt.xlim((0,1000))\n", "plt.ylim((0.02,0.5))\n", "pcm.set_clim(-5,3)\n", "fig.colorbar(pcm,ax=ax)\n", "plt.title(r'$log_{10}(G_{xx})$')\n", "plt.xlabel('t [s]')\n", "plt.ylabel('F [Hz]')\n", "ax.set_yscale('log')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This isn't unreasonable as a representation. However, it requires a bit of tuning to get the correct length of FFTs. Too short, and the low frequencies are lost, and too long there are not enough spectra to capture the envelope shape. Wavelets offer and alternative method to accomplish the same thing" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Wavelets: Continuous wavelets" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "[Wavelets](http://en.wikipedia.org/wiki/Wavelet) are basically localized sine wave packets, where the amplitude of the sine wave is enveloped, so that it tapers to zero at a finite distance from the center of the \"wavelet\". This serves to confine the region of analysis to the envelope, allowing localization in time. Wavelets are then constructed from a **Mother Wavelet** by expanding or contracting the mother wavelet so it picks up lower or higher frequencies. \n", "\n", "A simple mother wavelet is a Gaussian envelope modulating a sine wave:" ] }, { "cell_type": "code", "execution_count": 49, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 49, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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6/esYUzeGMXVjOOewc3h+w9/7J4L5BZCdqqV+AeR05Sicx0mTAiMG+xPitS8h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\nbA0/MAsXLux9Pn/+fObPn59vl4OOkyC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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def motherwave(t,tau,s,c):\n", " # t is time\n", " # tau is center of the wavelett\n", " # s is the half width of wavelett, \n", " # c is number of oscillations per half wavelett (apprx)\n", " g = 1/np.sqrt(s)*np.exp(-0.5*((t-tau)/s/2)**2)*np.sin(c*(t-tau)/s)\n", " return g\n", "tau = 200. # offset in space\n", "s = 50. # half-width\n", "c = 4. # number of oscillations\n", "g = motherwave(t,tau,s,c)\n", "fig,ax=plt.subplots()\n", "ax.plot(t,g)\n", "ax.text(tau,0.3,'s=%1.1f' % a)\n", "tau = 550 # offset in space\n", "s = 25 \n", "g = motherwave(t,tau,s,c)\n", "ax.plot(t,g)\n", "ax.text(tau,0.3,'s=%1.1f' % a)\n", "tau = 700\n", "s = 12.5\n", "g = motherwave(t,tau,s,c)\n", "ax.plot(t,g)\n", "ax.text(tau,0.3,'s=%1.1f' % a)\n", "tau = 900\n", "s = 6.25\n", "g = motherwave(t,tau,s,c)\n", "ax.plot(t,g)\n", "ax.text(tau,0.3,'s=%1.2f' % a)\n", "ax.set_title('c = %d'%c)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here the wavelet envelope has a half-width of $s$, and we specify $c=4$ oscillations per envelope. As the wavelet gets smaller, it analyzes shorter wavelengths or higher freqeuncies. Thus, the tradeoff we are used to between long-time observations needed for low frequencies, and only short-time observervations needed for high-frequency is met in this design. \n", "\n", "The idea of the wavelett transform is the same as that for the Fourier transform. We define a \"scale\" $s$ for our envelope, and an offset $\\tau$ in time, and convolve our signal with the wavelet $\\psi(s,\\tau)$:\n", "\n", "$$\\gamma(s,\\tau) = \\int_{-\\infty}^{\\infty}x(t) \\psi(s,t-\\tau) \\ \\mathrm{d}t$$\n", "\n", "Above our wavelet was \n", "\n", "$$\\psi(s,t-\\tau) =\\frac{1}{\\sqrt{a}} \\mathrm{e}^{-(t-\\tau)^2/2s^2}\\sin\\left(\\frac{c(t-\\tau)}{s}\\right)$$\n", "\n", "The \"scale\" $s$ sets how wide the wavelet is and how many oscilations it has. The \"offset\" says where the wavelet is centered in time. The resulting co-efficient $\\gamma(s,\\tau)$ gives us the amplitude of the wavelet present in the signal $x(t)$ centered around $\\tau$ at the scale $s$. \n", "\n", "We can discretely approximate to get the amplitude at various scales $s$ and offsets $\\tau$:" ] }, { "cell_type": "code", "execution_count": 51, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "(98, 102)" ] }, "execution_count": 51, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# lets do 100 lateral translations, and 100 different scales. We'll chose scales to go from 1/2 the domain width to c*2*dt:\n", "I = 12\n", "M = 6\n", "at = np.zeros(I*M)\n", "for i in range(I*M):\n", " at[i]= 2.**(-(i*1.)/(M*1.))\n", "at = at*t[-1]\n", "#print at\n", "taut = np.linspace(0,t[-1],100)\n", "dt = np.median(np.diff(t))\n", "g = motherwave(t,100,at[-1],c)\n", "fig,ax=plt.subplots()\n", "ax.plot(t,g) \n", "ax.set_xlim((98,102))" ] }, { "cell_type": "code", "execution_count": 52, "metadata": { "collapsed": false }, "outputs": [], "source": [ "Amp = np.zeros((I*M,100))\n", "nj = 0\n", "for tau in taut:\n", " ni=0\n", " for a in at:\n", " g = motherwave(t,tau,a,c)\n", " Amp[ni,nj] = np.sum(x*g)\n", " ni=ni+1\n", " nj=nj+1" ] }, { "cell_type": "code", "execution_count": 84, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 84, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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v5T0LEnIuDr9dO/tyk+vEC5UePez1ql0bqFs3sWcQdC0dHTsG10tuvz358mTR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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import matplotlib.colors as colors\n", "fig,axs=plt.subplots(2,1,figsize=(6,6),sharex=True)\n", "fig.subplots_adjust(hspace=0.4)\n", "ax=axs[0]\n", "ax.plot(t,x)\n", "ax.set_xlabel('t [s]');ax.set_ylabel('Signal')\n", "cb=fig.colorbar(pcm,ax=ax)\n", "fig.delaxes(cb.ax) # this trick makes a colorbar and then deletes it so the size of axes are same\n", "\n", "ax=axs[1]\n", "pcm=ax.pcolormesh(taut,at/c,np.abs(Amp),norm = colors.LogNorm())\n", "ax.set_ylim((0.04,40)); ax.set_xlim(0,1030)\n", "pcm.set_clim((0.04,1000))\n", "ax.set_xlabel('t [s]');ax.set_ylabel('scale [s]');ax.set_title('Sin packets, c=%1.0f' % c)\n", "ax.set_yscale('log')\n", "\n", "fig.colorbar(pcm,ax=ax)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "So we see that scales of around 10 s light up in two locations: centered at 500 s and 800 s. Scales of around 2 s light up centered near 100 s and 500 s. Therefore the wavelet picks up the signals we created at the frequencies and times. \n", "\n", "Note the striping in the amplitude plot above makes things hard to interpret. Thats becayse the phase between the wiggles in the wavelet and the wiggles in the signal don't line up, producing interference patterns. It is possible to ameliorate this problem using \"Gabor Waveletts\". In these wavelets the sine-wave is allowed to have arbitrary phase and the wavelet amplitudes are now complex instead of real:\n", "\n", "$$\\psi(s,\\tau) =\\frac{1}{\\sqrt{a}} \\mathrm{e}^{-(t-\\tau)^2/2s^2}\\mathrm{e}^{jc(t-\\tau)/s}$$" ] }, { "cell_type": "code", "execution_count": 87, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def motherwave(t,tau,a,c):\n", " g = 1/np.sqrt(a)*np.exp(-np.pi*((t-tau)/2/a)**2)*np.exp(np.complex(0.,1.)*c*(t-tau)/a)\n", " return g\n", "\n", "I = 12\n", "M = 6\n", "at = np.zeros(I*M)\n", "for i in range(I*M):\n", " at[i]= 2.**(-(i*1.)/(M*1.))\n", "at = at*t[-1]\n", "Amp = np.zeros((I*M,100))*np.complex(0.,1.)\n", "nj = 0\n", "for tau in taut:\n", " ni=0\n", " for a in at:\n", " g = motherwave(t,tau,a,c)\n", " Amp[ni,nj] = np.sum(x*g)\n", " ni=ni+1\n", " nj=nj+1" ] }, { "cell_type": "code", "execution_count": 97, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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j26QKlVmzdHsNGAAMGpTeM3C1pWHKFHc55/LLM6/P5B0WlHiFk0mx4WMXLsLG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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import matplotlib.colors as colors\n", "fig,axs=plt.subplots(2,1,figsize=(6,6),sharex=True)\n", "fig.subplots_adjust(hspace=0.4)\n", "ax=axs[0]\n", "ax.plot(t,x)\n", "ax.set_xlabel('t [s]');ax.set_ylabel('Signal')\n", "cb=fig.colorbar(pcm,ax=ax)\n", "fig.delaxes(cb.ax) # this trick makes a colorbar and then deletes it so the size of axes are same\n", "\n", "ax=axs[1]\n", "pcm=ax.pcolormesh(taut,at/c,np.abs(Amp),norm = colors.LogNorm())\n", "ax.set_ylim((0.04,40)); ax.set_xlim(0,1030)\n", "pcm.set_clim((0.04,1000))\n", "ax.set_xlabel('t [s]');ax.set_ylabel('scale [s]');ax.set_title('Gabor Wavelets c=%1.0f' % c)\n", "ax.set_yscale('log')\n", "cb=fig.colorbar(pcm,ax=ax)\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Above we have plotted the absolute value of the amplitude of the complex wavelet co-efficients. There is also a phase component that we could have plotted if we wanted. The result is is similar to the basic wavelet above, but now the amplitude is more continuous across the features in the signal.\n", "\n", "Note that we can change $c$, the number of oscillations in each wavelet:" ] }, { "cell_type": "code", "execution_count": 127, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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zntBZpug3Fl68pt2Quq9zPfoNtJEwJaFfu+sfmoqgjTPUREhbx488IvE4Utpj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\nRyeph45QmKZ+zhAeAvjYwFKWmTT1CE4SJ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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "num=0\n", "fig,axs=plt.subplots(2,2)\n", "axs=axs.flatten()\n", "\n", "\n", "for num,c in enumerate([2., 4., 12., 20.]):\n", " I = 12\n", " M = 6\n", " at = np.zeros(I*M)\n", " for i in range(I*M):\n", " at[i]= 2.**(-(i*1.)/(M*1.))\n", " at = at*t[-1]\n", " Amp = np.zeros((I*M,100))*np.complex(0.,1.)\n", " nj = 0\n", " for tau in taut:\n", " ni=0\n", " for a in at:\n", " g = motherwave(t,tau,a,c)\n", " Amp[ni,nj] = np.sum(x*g)\n", " ni=ni+1\n", " nj=nj+1\n", " ax=axs[num]\n", "\n", " pcm=ax.pcolormesh(taut,at/c,abs(Amp),norm = colors.LogNorm())\n", " ax.set_ylim((0.05,300/10.))\n", " pcm.set_clim((0.01,200))\n", " ax.set_xlabel('t [s]')\n", " ax.set_ylabel('time scale [s]')\n", " ax.set_title('Gabor packets, c=%1.0f' % c)\n", " ax.set_yscale('log')\n", "fig.tight_layout()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We see that more oscillations in each wavelet does a better job of localizing in \"scale\", but a poorer job of localizing in time. So there is still the tradeoff between resolution in time and in frequency." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Conditions for a well-formed wavelet" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "There are many forms possible for wavelets, and there is a whole field of wavelet carpentry. Such wavelets need to have some relatively obvious properties:\n", " \n", " 1. The spectral response of the wavelet should be finite, which we can write as \n", " \n", " $$\\int \\frac{\\left| \\psi(\\omega) \\right|^2}{\\left|\\omega \\right|}\\ \\mathrm{d}\\omega < \\infty$$\n", " \n", " 2. The momments vanish \n", " \n", " $$ \\int_{-\\infty}^{\\infty} \\psi(t) t\\ \\mathrm{d}t =0$$\n", " \n", " $$ \\int_{-\\infty}^{\\infty} \\psi(t) t^2 \\mathrm{d}t =0$$\n", " \n", " etc.." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Discrete Wavelets: Desaubies Wavelet" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The wavelets above were digital approximation of *continuous* wavelets. They don't conserve information, and are not necessarily orthonormal, and therefore, from an information point of view are not ideal. \n", "\n", "The **Desaubies Wavelett** is a very compact and discrete wavelet that allows us to decompose our signals uniquely into wavelet co-efficients, the same way we can decompose into Fourier co-efficients. There are other discrete wavelets, but this is one fo the most popular.\n", "\n", "Desaubies wavelets consist of the \"smoothing\" operation and its opposite, the \"detail\" operation. If we have $N$ data points, then \n", "\n", "$$C = \\begin{pmatrix}\n", "c_0 & c_1 & c_2 & c_3 & 0 & 0& 0 & 0& \\cdots & 0 & 0\\\\\n", " c_3 & -c_2 & c_1 & -c_0 & 0 & 0& 0 & 0 & \\cdots & 0 &0 \\\\\n", "0 & 0 & 0& 0 & c_0 & c_1 & c_2 & c_3 & \\cdots & 0 & 0 \\\\\n", "0 & 0 & 0& 0 & c_3 & -c_2 & c_1 & -c_0 & \\cdots & 0 & 0 \\\\\n", "&&&&&& & \\ddots\\\\\n", "c_2 & c_3 & 0& 0 & 0& 0 &\\cdots & 0& 0 & c_0 & c_1 \\\\\n", "c_1 & -c_0 & 0& 0 & 0& 0 &\\cdots & 0& 0 & c_3 & -c_2 \n", "\\end{pmatrix}$$\n", "\n", "Where \n", "\n", "\\begin{align} \n", "c_o & = \\frac{1+\\sqrt{3}}{4\\sqrt{2}}\\\\\n", "c_1 & = \\frac{3+\\sqrt{3}}{4\\sqrt{2}}\\\\\n", "c_2 & = \\frac{3-\\sqrt{3}}{4\\sqrt{2}}\\\\\n", "c_3 & = \\frac{1-\\sqrt{3}}{4\\sqrt{2}}\\\\\n", "\\end{align}\n", "\n", "These wavelets have the desired properties:\n", " \n", " 1. normal: $c_o^2+c_1^2+c_2^2+c_3^2 = 1$\n", " 2. orthogonal: $c_2c_0 + c_3c_1 = 0$\n", " 3. \"detail\" filter returns zero if convolved with a steady signal: $ c_3-c_2+c_1-c_0 = 0$\n", " 4. \"smoothing\" filter returns zero if convolved with an oscilation: $ 0c_3 - 1 c_2 +2 c_1 -3 c_0 = 0$\n", " \n", "To compute wavelet co-efficients, we dot $C$ with our data $x$ to get $N$ co-efficients:\n", "\n", "$$ Cx = \\begin{pmatrix}\n", "s_1\\\\d_1\\\\s_2\\\\d_2 \\\\ \\vdots \\\\ s_{N/2}\\\\d_{N/2}\n", "\\end{pmatrix}$$\n", "\n", "where the $N/2$, $s_n$ co-efficients are the signal smoothed at the highest-frequency scale, and the $N/2$ $d_n$ co-efficients are the detail at the highest freqeuncy scale. We save the \"detail\" co-efficients as the output from our wavelet transform and pass the \"smooth\" co-efficients to a $N/2\\times N/2$ version of $C$. This returns $N/4$ \"detail\" co-efficients at the bigger scale, which we keep, and $N/4$ \"smooth\" co-efficients which we pass to a $N/4\\times N/4$ version of $C$. We keep doing this until we have $N$ co-efficients in total. " ] }, { "cell_type": "code", "execution_count": 130, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 130, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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56cCTomKTCYFQgNLaUlZUrmB5xXI21G2gurWamrYaWgOt0XN6nB4Kswrpk93H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\nk1UAYhn646HR9f7n9Y86OnRG4dcKk+7f9uC2pM4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IHQlbCVOK/WmB9snvnHD6yOkiHIJQ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\ncIyIhyAIguCY/wMrNSH5vyOZIgAAAABJRU5ErkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# make the signal:\n", "N=1024\n", "x1 = np.random.randn(N)/1.2\n", "t = np.arange(0.,N,1.)\n", "f=1./30.\n", "b = 60\n", "\n", "x3=5.*np.cos(2*pi*f/2*t)*np.exp(-(t-400)**2/2/b**2)\n", "x2 = 1.5*np.cos(2*pi*f/4.*t)*np.exp(-(t-700)**2/2/(2*b)**2)\n", "x4=3.*np.cos(2*pi*f*3*t)*np.exp(-(t-100)**2/2/b**2)\n", "x=x1+x2+x3+x4\n", "\n", "fig,ax=plt.subplots()\n", "ax.plot(t,x1+10,t,x2+20,t,x3+30,t,x4+40,t,x)\n", "ax.set_xlabel('t [s]')\n", "ax.set_ylabel('Signal')" ] }, { "cell_type": "code", "execution_count": 134, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 134, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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GSNYQb+QQBrAlTphvAejhhzD5Tl1dXSAjmSBfn+EXVnmsMgvdyRGSVcR7CG6Lql4e6wPg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\n5EmmvqVzC3SyC/j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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "c0=(1.+np.sqrt(3.))/4./np.sqrt(2.)\n", "c1=(3.+np.sqrt(3.))/4./np.sqrt(2.)\n", "c2=(3.-np.sqrt(3.))/4./np.sqrt(2.)\n", "c3=(1.-np.sqrt(3.))/4./np.sqrt(2.)\n", "xn=x\n", "D=[] # this is list of arrays containing the wavelet co-efficients\n", "T=[] # this is a list of arrays containing the times that the co-efficients apply to\n", "num=0\n", "tn=t\n", "\n", "while np.shape(xn)[0]>2:\n", " num=num+1\n", " N = np.shape(xn)[0]\n", " # Make the matrix M\n", " C = np.zeros((N,N))\n", " for i in range(0,N/2-2):\n", " C[2*i, 2*i+np.array(range(0,4))]= [c0, c1, c2, c3]\n", " C[2*i+1, 2*i+np.array(range(0,4))]= [c3, -c2, c1, -c0]\n", " C[N-2,[0,1]]=[c2,c3]\n", " C[N-1,[0,1]]=[c1,-c0]\n", " C[N-2,[N-2,N-1]]=[c0,c1]\n", " C[N-1,[N-2,N-1]]=[c3,-c2]\n", "\n", " # get the wavelet co-efficients at this scale\n", " S = np.dot(C,xn)\n", " # save the \"detail\" co-efficients\n", " D.append(S[range(1,N,2)])\n", " # figure out what time the \"details\" each apply to.\n", " T.append(tn[range(1,N,2)])\n", " # take every second time for the next iteration\n", " tn = tn[range(0,N,2)]\n", " # make xn the \"smooth\" part of the previous. so it is N/2 long\n", " xn=S[range(0,N,2)]\n", "D.append(xn)\n", "\n", "# plot the co-efficients\n", "num=0\n", "fig,ax=plt.subplots()\n", "for d in D[0:-1]:\n", " ax.step(T[num],abs(d)+num*3)\n", " ax.text(1026,num*3,'dt=%d s'% (np.median(np.diff(T[num]))))\n", " num=num+1\n", "ax.set_xlabel('t [s]')\n", "ax.set_ylabel('d [m]')\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here we have plotted the wavelet co-efficients versus time. The time series is 1024 s long, asmpled at 1 Hz. There are $1024/2 = 512$ co-effcients in the blue line, $256$ co-efficients in the green line, etc. There are two co-efficients at $dt = 512$\n", "\n", "So, we see that this picked up peaks in the magenta and yellow lines, which correspond to dt=32 s and dt=64 s, or frequencies near .032 and 0.0156 Hz. The red line at 8 s and the cyan line at 16-s scale picks up the early high-frequency signal. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Compression with wavelets" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The signal $x(t)$ is exactly recoverable using the inverse of the procedure above using the wavelet co-effcients in the same way that the inverse of the Fourier transform can recover the signal from the Fourier co-efficients. " ] }, { "cell_type": "code", "execution_count": 135, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "(512,)\n" ] } ], "source": [ "print np.shape(D[0])" ] }, { "cell_type": "code", "execution_count": 140, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 140, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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BBwD77ZfsulEvgGhUdIDp/nxT1I1qmcuHghT6UCjZotezV8rtpNDrrpuyMvG/\nyUc/bRpQWZlq2dldoE4W4KuvAvcoSZ2nTbMiLaZMEb/ZWdGqaL/5pv0+VKG389E/9ZTzDe1m0cdi\nwP/7f96Hw6swlvyw+fHHYPOiyHMYi6VeRw0NyUJv5zdWl/mx6E2uG79C73efXnETelnPzZu9lVdX\nJ0ZIA2K+BD2IQBd61aJXScdHv22bqCcJvTM5EXppAavWmy708bi48fSQODsfvRRs9fXczaKX26n+\nfN1107ZtskW/cSPwyCNWnUzRAnYXmdMN9cgjwmqXqGGmct925aqC4cUKamiwF3rAeTCQm9AvWpRa\nJz/obxVBCptq0ev104U+kRCD0kxTNAblo/d6jD74IHXfs2dndmzWrbMeom7lyMyubha9vD7V47J1\nq+XKlNh1xkqhV5MJuqHfE7kYeFcM5ETo1Se3qYOsrEyc/EjEXejlw0Kuq97MJoverjNWdd3I79Ki\nV4X+ySfFgCWJdJuo/nGvQs858N575nVVEXAT+okTgauvFt+dLnR5LEtLzTeRXOZ0g7l1xq5bl7ye\nX7LZIWty3UhMQr/XXubzk47Qm1w3Xrc3PfgGDLDSaKfDkCHAz3/urR6TJ4tPPTLJDrV9psR+6v7U\nqB69fD9C/9NP4lzpAzAJMzkXen2w08iR1hyeeuij6o/XXTeRSLJFr7tr7Hz0MgWx7rqxE/pPPklu\ni1wuBc4J0w2lzBQGQNTxhRdS324A+wt/t91EZ7LTOoB1LO0GJcltnV573UIDZdRRuha9mozOiRkz\nUuuwc6dzTn7ddTN0qJiYu337VB/9sGHOdVQ/3Xj33eRQWr8WvYp6XZhyDXlFjQ7L9K1JPx7q6HPT\nGA87d6xu0fuxzseOFfeSLMvrSPPWSk6EXn1y6xa9jHvX/bXqOoB3142dRa9vp7tu1M5Y9WLU3Rrx\nuHCD6GkUVGSuc5NFb2L27OQy3G7okhJ/ueDthN6LALlZ9Mce614GINIim3KZRKMiTfSGDc7b69Eh\ngBiIdPTR9tvoFn379sBpp4m2NDR4z9Lo1yL/73/N26cj9KbRvX5Ytkxc16ZoMD+YjDU9GaB8O9ax\ne0vXhX7WLPE2YbpPZNZLue4XXyTvO1u5poqFnAi9mtlRt+ilz04KsxcfvRRmvz569a1BlqGPjJUW\nfSxmzhIZj6emW9Uv7iFDzMvlxamjuxbcBmhFIt6EXh5Lk39eLd/pweLmo5861TlV8erV1nlwevvo\n3Nn5zcJ8yFBEAAAgAElEQVSts+2HH4R7Q0VeG59/nrx/KfReh/r7dd3o7UwkxCjws8923k7Nqqrv\n28/+VfbaC7jhhsyFvkuX1O29Cr2d8WZyDV1/vYhu27jR6v8BRESW3H7tWmE0SA0AyKJ3IydCr+aZ\n1i36SESc8HA4dWYn1YWih1faCb1fH72T66aqKrUtsZgQNjlxuCzbhH7RS7+6TjRq9tHb3ZDhsD+h\nt/O1ehnx62VUp1MsvTxvW7a4v32Y9rF6tThuN99s3q9k9mzxpyLb/cknllEBiGtEd9044dd1Ywqd\nffVV9+1Mbxi6KzMdtm0zGxJ+UJOsOVn0ctkzz1jre3XdSBoagHPPFVF6Os8/b2VR7dCBXDdeyYnQ\ny158wN51I4VZ+vnat3f20XuNuonFkjtd7aJudIs+Hk+2YvbeWwxgiceBgQOT22cnyF4tJzuLXt9e\nndNWCr2XDqy1a83LvVj0bq4bwFno5fbbtrnX1ST0L78sxhXY7VdiEkHZrm7dki36cDg9ofd6PvV2\nSGPCjpEjxaeb0Kfbaa2fH6+drHbY+ehVi/6556z17Sx6u+suHvc2CYlqCEqhV0OqCYucW/Qm140q\n9LrFLkXb5KOXUTfhsPjdzqJXBd0UdaP66OWgrXhcDMSQSOs/FkvNHpmp0KsWvXoj6NvLqAlAxPMD\n3jpj7QjCdSN/s2urWnY6oXBe09qa2ioFbcUK4C9/SbbovbpunM6HHbrQ33mneGDZIc+rSegzdbkA\nyaNRGxvN/R06XiKxnFw3dg8o09gY04NR0rWriHwzoe5PtejTDQwoZgxjNoPHj0Uv/efy4ozFhI/Z\nFF4pf2/bVpxou6gbVdD1kbHS2pKv86pFr/q2S0osQdZvSLsLy+urthrnrUbT6OW2aWOVufvu4jOT\nOGIvrht5vtJ13ahCn45Fb2rfF1+Ia8rNopdCIt8I5KhbP0KvT1fpBVM7Fi60X9+pLyUI143qy77h\nhtRIMhNODxUvnbG6uKvlerHoZQz/2rVimkC7OuquXX1/hCDnrhvdoleTkKmhj7rQO4VXlpc7W/Ry\nxK1T1I18nZc3WzSaKvRqfVROP93c7nRcN3IouXpzmvAi9Lmy6J2E3s/gLq9CP2qUCJU0DUo6+2xL\nVPV2SWH347o55ZTMXTdeyabrRm4bRP4aXeBNrhs7oV++3N1H/+yzwFdfWf87XVsmNycJfSp574w1\n+ejVAVFehF5a9NKKj0btLXo9jl5dHo2KZfKtQBV0WR/d0geSowMkpkE6duidsYC7KMpsn0G4brx0\nxqYr9Nmw6E1x17KeTz4p0vAC5oe1Wg8v4ZWvvBKMRe+EOrDN7jc/+9cJOh20LOvAA8Wnye1oV9cr\nr3SOugFSR9Y69f+YHixBtrVYyLlFr0/tZ+ejVy360tLUqBu1M7a83BJ6k0UvBX3lShFJoz4sHn1U\nXFjqdlL0TRa9SehN6CkedFSRMj0UvIji6af7n21Kxe0VWl0nCNdNUBa9k9ADIuQTEOdQHUOgC73X\nzthMffQqhx5q/5upPula9F99ZSW8k8dJr9cxx3gvz65OgD/XDQAcfrj4lNeGPgOXfi1Nm2auR329\nFbpNQu9Mzi16GZaoiq3sULUTeumjV33q6u+qRS8F22TRL1wo4nHVDl85o5D0icsynFw3XizB+nrn\nC04t25SLxZTxUqdPH2/W+OjR5t+DdN146YwNwqK/+25z6gZdTL74Apgzx9miz0bUzbp15nbI81ld\nbV++qT7pCtg11wDnnCO+26W68DuNYzQqsmmqx7quDrjrLvHdrjNWR52m024/XpkyRXyS0DuTc6FX\nEyHpFr10q6idplJwVaFXHxChkFiud8aq36UvPhazOlvVyB3Aqofq/tFFQo7g9SIQbkKv3nQmofcS\nNumWC15mtpS5S3TkA8tLlIJb1E2ufPRXX50cJinRheWww0Sno0no5Xby/7/+1bleflw3VVXWLFYq\nUuhND11ZrunhLu8HIPl6+vZb5/wu6rFUo41U/Ar9Sy+J+qvH4eOPLYvbzqK3Y/ly83I/Qi+PNQm9\nMzl33UhUsVVj4HUfvOqj14U+HreE14tFr/r+ZRmqxermuolGxTZeIl3mzXO+4NSb2iT0XlLEymNg\nh0zfYCfSF10kUiM7WfRSMHIRdWNXto40HJyEXmYZVR/K8rt8wDk9sJ94IrVsP53rdlxwAfDww+bf\n3IRePcb77ON99idV6NXj5MUFqaK6XSXq6HGvrhu9Xjp+hN6UppuEPpWMhZ4xNpox9g1j7FvG2HWm\ndfz66AGz60YVaSkuutDrFr0UeruoG3lR6K4b3UUjhV4+CNw47jgxTZsd6nB3U2esnIzBCXnsvKxn\noqRE+EudHhZeUshm00dv2u/Wrcnrq2IoGTxYfJqsaznYzEno1WkhvVqpTuvV1wMTJiSHyMo8Qeo1\nr2Mn9ECqb1tFPZbyAdLQALz1lrXczqL/n/8xLze5ZdQ6DxiQvM5rrznnMLJ7I8k0aoaEPpWM4ugZ\nY2EA9wEYAWA1gM8YYy9yzpPiUFTXzdKl4tPORy/FW1r3dj56PxZ9aakl4lLopXtIom4nv+vWoLTo\nM53koLw8WUhMnbEyqgYAwBJYtTqOumgMcR5HPBFHnMdRF4pjayKGVdusZfFEHLGEWA9d4kAojvmb\nY9i6Mp60bSwRQzwRx+vL4qidEMfjPa1l6nrfd4oBh8UxdU4cLGSVra63vFcMD34fx5tvpdZh+Yo4\ncGIcYHFc8GIMCZ68Ds4SdQSLo74kDvAYhvw7Ds45Tul7Cjo2nAGgu/E4qiMz9ePXs6f4VHOqy3Wk\nJWvXSQmY/f9uAiQtUXVuAZV99zWXFwqJ5Gymeqijw3Wh93od2j1gVYu+osIyyG6/Hfi//zPXRf0E\nkq3vrVut4IBEQjzIrrzSvl52aQt8CX24AWizDWhoD4QbgWg5Zq/5FMftMchHIcVPpgOmjgCwlHO+\nHAAYY08BOAlAktDXJ3YCEO94EyaIZXY++mY3ToijIRpHItwIlEWxPR5FqH0jdkai2BCPor5dI3Y2\nRsG7RrG9QxSL6hqxqyqKHyui2BhtRKxdFFuro5jLG7Fpzyi2VcQQCsfxfkMcS/eIAYPjWNAxhu39\n4kBdDF/vHkdiWAyvxeJoqInh285xvBSPA8fHABbHFz1i2DEyjlA4jrtWxoExcSAUaxYphJr+Z3HX\nZXXhGHrdGwf+IJZ90CYOFo4B11nrPRmJAX9u+h/Ang+GEQlFEA6FEWZhhENhNDaEgbIIXnjIWhZm\n1no4JQwkwvjfOWFULkreVq6Hw8Ko52H856vkbeV6m8vDQFUEizeFURIxrxNiEbRhZejYNrV8tj4M\nrAoDPIyRvVO3fWFSGEhEAB5GOBJGoiGMW24Koz5Wj2nzpuGlb24BruwAbNwXWL8/sHVPYFsPYHs3\nbGjoCoSqEI2mmub66Et5zQHeXG8moR85UoyytUPuy276P92CTiREptNf/EKMizC569QQQr1NTm9Z\n+iTsJlSLurraSq0st73gguRJd0xvLLpVrlv9Tta1EHoOVGwAdv8G6LAcWHwCOO9ov5GEJYB9/wuM\n+BPQbg1Q2mRNPvIujp8xHPxgCqZXyVTouwNYqfy/CsAAfaX63/UGNuwHlDa9a4biqO2wC6EQR0kJ\nQ+yyKL5tW4/rt9SjcY8GxCc0Yl44isGvhYHxJfiAlSCEEiR6l+KncAm+jpagsW8pYo0liB9Ygm92\nK8XqaAl+6luCaEUp6tuUYEdFCbZ1K8FyVoqdHUvQyCMIszA2JiKoKw2DVUQQDYeRCEUAhBFmpUBj\nW1SGIgjvDKN0ZxhdSyLAWiFSXX4ewYplYbQpC+OIkWHMWiDECYmw9Znwtqy8PIJ3vgzjlZfDGPf7\nMHr1CWPJouT1TjstAiTCeObpMMBDiBmu27vvFsJzjyHhF2DdsDO+tUbcpqxzrvj87xPm3894Avj+\nZeC+GfYC+cWdwOlVwHG/TP1txhrggTni+/mHpP6OxdZXqclDe4rPUXuPwjPTYzjj0mXA7ouAPRaJ\nz95vAe3WYNKqNcDE9eh5fyeURbsCv+kGbO8K7KjCV2VVOObqLujWrgqP/L9KIBHBusZKbNrVHqGS\n3QA496ibhF5NZGfCzbesC/0RR1guJgDo2FGkXlZTYHMO/Oc/4nssJuaRlfHrXoXezn2iZpXdbbfk\neq5aJR48JqFXLW59MhT9YbB1K8DBhYh3+g6oWA90+B7o+D0ein0LjF8gRHtDX3Gv9PsX6pY9DGAv\n+8Z1WA78+lwgUg+89nfg+6PFtn+oBtoZpggjMhZ6b4/N+08Hyn4CouVAm0OB0sNxyIByVJQz9N6L\nY+p/StGnTxnO/00ZFnxdiqceL8WB+5Xg7rtCGDUKGD5cWDPffy/yghx1FPDJfOEG+uEH4OjjhZC9\nPkvcBEuXis9PPwdGjAC+WiZC7UpLgd8cAzz+LfDjh8DhPYAfPwXqNgL9egFffgCMOBX46Eug897A\niGHA9M9FE/Y7BPh4DlDeGfhlB+AehyHtbpR0AHp3BLqVA9gGrFoEQEvixJo6j52OsFvUjbqeHTU1\nInLCDi8+eqeoGy99CAccIATMSCICbNpH/C0+KemnzQDA4nj3+/V45tUf8ZfP1gCVPwKVa7E5vBiN\nXd7Dt41rgRN3AqEYplfswAv/2Iotg7YBh5Whx10dgMs64J8NHYCzOwD1HYC6jkB9B9z3RQegn1h2\nwrgOQNeOQEM7LNss3kbKImVoW9IW5SXl4s3IQ1ul0Euh/N//TV1HP46cA5dcYv2mzs3rtXPb1Gk7\naRJw+eXi2F93nVW38nJxn3TvntoHIP37qtD/7nfJ68TiCaDL13hn50xg1Ao8yr4Efv2luPc3/QLY\n0QXY0hNYfQQG9D0LPzywv1gGBoSiwC8nY9EvjwC6HgWsGgisHAz82A+INvX6tlsNXHgUMPv3wKw/\nAlw5CD8eKt4MACR4AiGWk1iTwKitrUVtbW1Wys5U6FcDUCODqyGs+mTq/gFI66Hp4infCVSGgKow\ngM1AWRRoFwHCMSDMgXDI8onL3CSy89Tko9dTIOjZK1W/vNrpqseJSxeSyUcvf8+0s0iP4zZl6jN1\nMOp4FXonQbj1VuCPf3QvI92oG7f6jR0rHsqXXWb+3fTqnzRvAQ9j9zZd8fOSrsCS/s3rHNETGHag\niDy6ssnfPOpUYPp04IQTOV5+Ywc+Xr8FP99nC3511RZM/XwLULYFaLsZKNuCH3euBn6+ACjbgoVl\nW4ATtwBttmHEownEEjHUx+pRF6vDruguhFgIbSNtURYuB65sK0SpsVL5E/8/tLISH86sxPxtFcDh\nlXh0XiUqS8VfRUkFKksrsS5aCVRUYsqtlRj/h7bgipCdcgrwzjvJx4Zz87lx89+feqpwF40fL4Re\ndlA7uXzkm4XRHdN1DnDEfdi87wygrhPw3THA5l7A0tHA2n7Azs4pmyxqQLMeiIJLgPdvRN+GSzF/\n5ztAj0+A0VcBeywU7ro1hwFtfwIWngZ8ND61Dj/8Eth3BgBgW8M2dCjrkLpOAVNTU4Oamprm/282\n5eZOk0yF/nMAfRhjPQGsAXAGgLO8bKj66IHUzlhV3NV4eDU0Uq4biaRG3ZjCK/VoHXX+SnVQidqJ\nK5GinMlIVIkMSXPLU+MWPRCE0JeXe0sJm2493KzcBx4Qnyah79pVCJEbXbtana+SeFzUSz3G8tyV\nRBjQ2A7V7dsB66vRKwxAc0Hc+Rbwd0Pk0zLt4cs5RzQRRV20Dku+34UjBtcBJTuFm7JUfoq/rhU7\nEWI70BDeAHT+Hm8t24GdjTuxo3FH89+a7TuBsTtww5YdwJ/r8EqiHNjHemCMm1cJnFMJxEtx85p1\n+MdNO7Dbz+pQF61DNCF8RwwM2/sz4AAGcKnc8rv4HPEqQ8lbTb9dFcaHbSNAnzB2IYKDp0YQCUUQ\nb4wAF0UU96P4ftaLEeCMiOWODEWB6lnAp1ei9KH5aNzUzf2kwf4tLtKwBzD/TPEHAKEofvaLJdjU\n5jOgam6zyPfrp2XiXDAGGCkC/7bUb2lxQp9NMhJ6znmMMfZ7AG8ACAP4lx5xI+ncOfm1007oEwkr\nOkYXers4elXopRvBlAJBj9tXLXo11liWoVr0MkStZ8/0o24uvFBMNC79oW55arxY9F5CydyE3jTO\nQeJlhK4XofdzzK69FrjjDpG5cOXK1N9Nx0UffKOeY0Ac99NOs+qrYppJLBwWkTCqBW0iFmOo7lGK\ndetK0bGkfZM/yczF+wtXSXwI8M0IYP/9U9f56Scxh3BjI3Dp2ARGHL8Lb8y0HhYX/WMHrrl/p/BP\n7+yCngfshmefKMPnn7TFkCNLUFIiHj5nnc3xzjtNB4o1+QCVz2c/4Oi5p/Cf79kzjmEnxvHyqzGU\nVcTx6MQYYokYflgVwylTYk1BB7Hm4IJFK2PAhpgSaBATvvLt3RH1eW/svz9w001WYsCJE8X8wEkk\nSnBIt/3xzjv7A7hAOfbaelt6AQDalbRH93bmSK3WSsZpijnnrwF4zW09U85pKdhAqkVfUiI6i6Tr\nRh8wpVrmukXvlNRMHQHr5LrRhV5+Nw1h1+nUKXlGHsnDDycLfaYWvVMeeH09O9q2tbfoZVSIfGW3\nw4vQ+0mnfOed1mhe6VLwi27R9+xp5fBX67JggUgl8fvfJ2/PGDBunL3Qn3oq0KOHyHMvDRi7zlh5\nnuQgrnDYLPKAuHYuvBB46CEAPIRwvBLYUdn8+zVjktev7C36e/Y6VszqNKbp9zYxAA4P8J+3B6qb\n6oMtQN8uwMsbgXA9cHDTzGq7R5EcatHE9lWwXLEaft2a+ltXJAKsWZO6nuk6t9tXabQKJWGP+S1a\nCTnrreisuehMFr0aXllSInr9Kyrsfe2JhPgtHE4ezGSX1Mw0ElcXers4ellPdcCLzgUXiE/TQJyT\nlH5E+bBwEj81rM4Or0LvtB+n0bUffSSietw6/eQYAxOybC9vBipyVG+6g1+k0Jvy2qh12W8/8/li\nzDwgScblP/+8yJSpGjCmY1BZCVx8sfjewYcnQdbRbdJru3NjmrpQdXPo23UzeFvsyq6zEfl0kPep\nhHNzmKnp2Nrdh5t+oimmdHIm9PooUV3oVQs8FBIX+saNwgrSffTxeLLrRgq9m4/ei0UfComQsC1b\nkgVBfSDZIXOmmERNDk5ZsgR48EH3sry4bpyiXfT17HBy/8iy3YSec+shp5OORQ9Yg47SnfZu3bpk\na9FO6J0wjartqIR4qwKVSJjrKg0TwHqj8IKs97vvOq+n1sHNPaYOkDLNa6sv93PO9trLe5I4FdW9\nBiS/Xd5zj/W9d+/UbW3vjxAJvU7OhL601Hp1Bby5bjZtEtuEQiLtaiQCzJolLC052lUXejuLXn2w\nqNa/PogmHBY+640bk28M1bVjd0M5ZUWUv/Xp491H76UzNpEQbXSaNcgtNNJtP24CYvKjS9IV+jPO\nEJ+6eJomjDbx0Uf2Fr3XujglDQOSj10sZi/0sg/ETz+F1zr6EXonITaJpt/cRH7PsdxG3Y88nt27\nizxMALBsmXiQ6Mg6D9BH7oQynBS3CMmZ0MsJPSRunbGq0MvtZs0Snz/+aFnp0kevC71q3cuHiXwT\n0NMiA8kWvaS01LLgvFj0cluTxWjaLigf/UsvAYMcRnynK/ReYujdkELv13UjJ3PRxbOqynsZ6Vr0\n0mVz8cViJis71OsnHjcLfSzm/sAwkU2hHzIkeeJ7wLoGvIyotcOPf17G3+tCr+a21yPh7Pant4Us\n+lQKSuilK0K16HfbzdpOWkbhsBBhmTY4HLbi6E1JzWQUj1yup0UGzEJveo2NRESemusM6du8WPQq\nskyZFkJFfeW3IxQSiaPc3BtuDycvD5R0kTduOtYeIEaKSjp18leOFx+9CRmF07atc2I69dhJoe+u\nBXt4GTBmQq1jnz7266Uj9E89lXqNBmHR+xH6W2+19qHWWxV63a1rt7+U/YbJotfJqevGi0UvrfFI\nRAh7mzapF1xjo5XoTBV6tTNW9/mrLhvVdWOKupGo+1V/r6xMjdJQ17Hr3NOR+7rqqtTfvFr0W7YI\nsXdbz+k3N4veTUCcbnApdD//uXMZe+zh/Lvcj1+hz8RHD5gnmfn6a/GZSFiJuWIx8de3r/eynVDb\n2a6d/Xp2homkf3+RakEtU7pEVIIQej8d56rL1uS68WLRS1LqHoqm/YAtVnIq9PoJla4UwDqZqutm\n1y5ztsjGRjFkOxq174w1WfSmtMi6j97NojetJ5HLTFEJTuu7ZS20w2l7t32rv9l16Hp13Qwfbv9b\nLCZe099+27kMmdnRjXQtelXc//QnMQG1F0w52w86SHz++KP1AJMWvdt0gF5R2+nkWze5WtTrprpa\n5K4HrLaY2mTqjPUb2upH6GX73n/fqvekScnzz7q5S025dwAAoZhtZszWSk6FXj1hUujV1AJ6Z2x9\nfbLLZ7/9gD33tCx6wL4zVrfoVYvcyaI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ORK5CYII=\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def invertWavelet(D):\n", "# return the signal using the co-effcients in D\n", " n = 0\n", " s = D.pop()\n", " while np.shape(D)[0]>0:\n", " d=D.pop()\n", " sn = np.concatenate([s,d])\n", " s=1.*sn\n", " N = np.shape(sn)[0]\n", " s[range(0,N,2)]=sn[range(0,N/2)]\n", " s[range(1,N,2)]=sn[range(N/2,N)]\n", " C = np.zeros((N,N))\n", "\n", " for i in range(0,N/2-2):\n", " C[2*i, 2*i+np.array(range(0,4))]= [c0, c1, c2, c3]\n", " C[2*i+1, 2*i+np.array(range(0,4))]= [c3, -c2, c1, -c0]\n", " C[N-2,[0,1]]=[c2,c3]\n", " C[N-1,[0,1]]=[c1,-c0]\n", " C[N-2,[N-2,N-1]]=[c0,c1]\n", " C[N-1,[N-2,N-1]]=[c3,-c2]\n", " s = np.dot(C.transpose(),s)\n", " return s\n", "D0=list(D)\n", "xn=invertWavelet(D0)\n", "fig,ax=plt.subplots()\n", "ax.plot(x,label='Signal')\n", "ax.plot(x-xn,label='Sig minus Reconstruction')\n", "ax.legend(fontsize='small')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "So, aside from some small edge effects, the signal is well-recovered. \n", "\n", "However, we might expect from the amplitudes above that a lot of the signal is just in a few of the wavelet co-efficients. So we can trim most of the 1024 co-efficients, and invert to recover the signal." ] }, { "cell_type": "code", "execution_count": 145, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 145, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "Dnew =[]\n", "thresh=3.\n", "num=0\n", "for d in D:\n", " dd=1.*d\n", " dd[(abs(d))0)+ngood\n", " ax.step(T[num],abs(d)+num*3)\n", " num=num+1\n", "ax.set_title('%d coefficients retained out of %d' % (ngood,np.shape(x)[0]))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "So here we have thrown out all signals weaker than an arbitrary threshold. Note that sometimes a certain scale is zeroed out, and other times its active. This gives the wavelett more flexibility than just a Fourier-domain filter: If the high frequencies become important (i.e. 0-150 s above) then they are retained during that time period, and ignored other times.\n", "\n", "Reconstituting the signal:" ] }, { "cell_type": "code", "execution_count": 147, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 147, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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nLeIt8R4FwLOA9hXvw/zh8/G3TX9DtaMaybZkVNmr0Cu1F7blb8Pcj+aie3J3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\nE9UBP1EB8IeHu1m47/vgQSZctIXTjh5lDwgX9jy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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "D0=list(Dnew)\n", "xn=invertWavelet(D0)\n", "fig,ax=plt.subplots()\n", "ax.plot(x,label='Signal')\n", "ax.plot(xn+10,label='31-co-eficient reconstruction')\n", "ax.legend(fontsize='small')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "So we have recovered a decent representation of the signal with only 35 co-efficients (out of 1024) for a factor of 33 compression. Wavelets are used extensively in audio, image, and video compression. " ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 2", "language": "python", "name": "python2" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 2 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython2", "version": "2.7.10" } }, "nbformat": 4, "nbformat_minor": 0 }