{ "metadata": { "name": "Filtering_Part2" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "Introduction\n", "--------------\n", "\n", "In this section, we start designing FIR filters using the windowing design method. This is the most straightforward design method and it will illustrate the concepts we developed in the previous section.\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Windowing Method\n", "\n", "The window method of FIR filter design starts by constructing the ideal filter response, $H_d(\\omega)$. For example, consider the ideal lowpass filter,\n", "\n", "$$|H_d(\\omega)| =1 \\forall \\omega \\in (-\\omega_c,\\omega_c)$$\n", "\n", "and zero otherwise. The inverse Fourier transform is the sequence,\n", "\n", "$$h_n = \\frac{\\omega_c}{\\pi}\\frac{\\sin (\\omega_c n )}{\\omega_c n}$$\n", "\n", "if $n \\neq 0$ and \n", "\n", "$$h_{n=0} = \\frac{\\omega_c}{\\pi}$$\n", "\n", "This is obviously non-causal and infinitely long. We can shift the sequence by an arbitrary amount and then truncate to fix both problems, respectively.\n" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# omega_c = pi/4\n", "\n", "from __future__ import division\n", "from scipy import signal\n", "\n", "wc = pi/4\n", "M=20\n", "N = 512 # DFT size\n", "n = arange(-M,M)\n", "h = wc/pi * sinc(wc*(n)/pi) # see definition of np.sinc()\n", "\n", "w,Hh = signal.freqz(h,1,whole=True, worN=N) # get entire frequency domain\n", "wx = fft.fftfreq(len(w)) # shift to center for plotting\n", "\n", "fig,axs = subplots(3,1)\n", "fig.set_size_inches((8,8))\n", "subplots_adjust(hspace=0.3)\n", "\n", "ax=axs[0]\n", "ax.stem(n+M,h,basefmt='b-')\n", "ax.set_xlabel(\"n\",fontsize=16)\n", "ax.set_ylabel(\"amplitude\",fontsize=16)\n", "\n", "ax=axs[1]\n", "ax.plot(w-pi,abs(fft.fftshift(Hh)))\n", "ax.axis(xmax=pi/2,xmin=-pi/2)\n", "ax.vlines([-wc,wc],0,1.2,color='g',lw=2.,linestyle='--',)\n", "ax.hlines(1,-pi,pi,color='g',lw=2.,linestyle='--',)\n", "ax.set_xlabel(r\"$\\omega$\",fontsize=22)\n", "ax.set_ylabel(r\"$|H(\\omega)|$\",fontsize=22)\n", "ax.grid()\n", "\n", "ax=axs[2]\n", "ax.plot(w-pi,20*log10(abs(fft.fftshift(Hh))))\n", "ax.axis(ymin=-40,xmax=pi/2,xmin=-pi/2)\n", "ax.vlines([-wc,wc],10,-40,color='g',lw=2.,linestyle='--',)\n", "ax.hlines(0,-pi,pi,color='g',lw=2.,linestyle='--',)\n", "ax.grid()\n", "ax.set_xlabel(r\"$\\omega$\",fontsize=22)\n", "ax.set_ylabel(r\"$20\\log_{10}|H(\\omega)|$\",fontsize=18)\n", "#ax.axis( ymin=-40,xmax=pi/2)\n", "\n", "# fig.savefig('figure_00@.png', bbox_inches='tight', dpi=300)\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "pyout", "prompt_number": 1, "text": [ "" ] }, { "output_type": "display_data", "png": 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Vg5KTrzVb97u4uGDRokWIjIyEWq3GyJEjERgYiMWLFwMA4uLikJubiw4dOuDGjRtwcnLC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"text": [ "" ] } ], "prompt_number": 1 }, { "cell_type": "markdown", "metadata": {}, "source": [ "The figure above shows the filter sequence $h_n$ in the top plot. This has been shifted over to enforce causality. The middle plot shows $|H(\\omega)|$ as a function of frequency. The vertical green lines show $\\pm\\omega_c$ limits and the horizontal green line shows the ideal response, $|H_d(\\omega)|$. The bottom plot shows $20\\log_{10} |H(\\omega)|$ as a function of frequency. The middle plot reveals rippling in the passband that increases towards the edge of the passband. This is known as the *Gibbs phenomenon* and we need to examine it carefully because it is a serious form of distortion. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Truncating the filter coefficients is the same as multiplying the infinitely-long desired filter sequence ($h_{d}$) by a rectangular window ($w_n$); this is equivalent to a convolution in the frequency domain between the desired reponse, $H_d(\\omega)$, and $W(\\omega)$, the Fourier transform of the rectangular window. Thus, the filter output is\n", "\n", "$$Y(\\omega) = \\frac{1}{2\\pi}\\int_{-\\pi}^{\\pi} H_d(\\xi) W(\\omega-\\xi) d\\xi = \\frac{1}{2\\pi}\\int_{-\\omega_c}^{\\omega_c}W(\\omega-\\xi) d\\xi$$\n", "\n", "where \n", "\n", "$$W(\\omega)=\\sum_{n=0}^{N_s-1} \\exp \\left( -j\\omega n \\right)$$\n", "\n", "Because everything is finite, we can combine these two equations to obtain the following:\n", "\n", "$$Y(\\omega) = \\frac{1}{2\\pi}\\sum_{n=0}^{N_s-1}\\int_{-\\omega_c}^{\\omega_c} \\exp \\left( -j(\\omega-\\xi) n \\right) d\\xi =\\frac{1}{\\pi}\\sum_{n=0}^{N_s-1}\\frac{\\sin(n\\omega_c)}{n} \\hspace{1em}\\exp(j\\omega n)$$ \n", "\n", "We can expand the summation term to obtain,\n", "\n", "$$Y(\\omega) = \\frac{1}{\\pi}\\sum_{n=0}^{N_s-1}\\frac{\\cos(n\\omega)\\sin(n\\omega_c)+j\\sin(n\\omega)\\sin(n\\omega_c)}{n}$$ \n", "\n", "To understand the Gibbs phenomenon at the edges where $\\omega=\\omega_c$, we recall the following two trigonometric identities:\n", "\n", "$$2\\cos(n\\omega)\\sin(n\\omega_c)= \\sin(n\\omega+n\\omega_c)-\\sin(n\\omega-n\\omega_c)$$\n", "\n", "and likewise,\n", "\n", "$$2\\sin(n\\omega)\\sin(n\\omega_c)= \\cos(n\\omega-n\\omega_c)-\\cos(n\\omega+n\\omega_c)$$\n", "\n", "These two identities show that as $\\omega \\rightarrow \\omega_c$, the surviving terms in $Y(\\omega)$ summation oscillate at double the cut-off frequency (i.e $2\\omega_c$) which accounts for the intense rippling effect as $\\omega$ moves from $\\omega=0$ to $\\omega=\\omega_c$. Consider the real part of $Y(\\omega)$ when $\\omega \\lt \\omega_c$,\n", "\n", "$$Y_{re}(\\omega) = \\frac{1}{\\pi}\\sum_{n=0}^{N_s-1}\\frac{\\sin(n\\omega+n\\omega_c)-\\sin(n\\omega-n\\omega_c)}{2 n}$$ \n", "\n", "\n", "In this case, $\\sin(n\\omega-n\\omega_c) \\lt 0$ so it contributes positively (i.e. constructive interference) to the summation. When $\\omega \\gt \\omega_c$, the sign reverses and destructive interference reduces the real part. This is the mechanism that characterizes the transition from the passband to the stopband.\n", "\n", "The following figure illustrates this effect." ] }, { "cell_type": "code", "collapsed": false, "input": [ "fig,ax = subplots()\n", "fig.set_size_inches(6,3)\n", "\n", "k=arange(M)\n", "omega = linspace(0,pi,100)\n", "\n", "ax.plot(omega,(sin(k*omega[:,None]+k*wc)-sin(k*omega[:,None]-k*wc)).sum(axis=1))\n", "ax.set_ylabel(r\"$Y_{re}(\\omega)$\",fontsize=18)\n", "ax.grid()\n", "ax.set_title(r\"$\\omega_c = \\pi/4$\",fontsize=22)\n", "ax.set_xlabel(r\" $\\omega$\",fontsize=22)\n", "ax.set_xticks([0, pi/4,pi/2.,3*pi/4, pi,])\n", "ax.set_xticklabels(['$0$',r'$\\frac{\\pi}{4}$',r'$\\frac{\\pi}{2}$',r'$\\frac{3\\pi}{4}$', r'$\\pi$'],fontsize=18)\n", "ax.set_xlim(xmax=pi)\n", "ax.annotate(\"Gibbs phenomenon\",xy=(pi/4,10),fontsize=14,\n", " xytext=(20,0),\n", " textcoords='offset points',\n", " arrowprops={'facecolor':'b','arrowstyle':'->'})\n", "\n", "# fig.savefig('figure_00@.png', bbox_inches='tight', dpi=300)\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "pyout", "prompt_number": 2, "text": [ "" ] }, { "output_type": "display_data", "png": 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FmJgAK1ao53x79gCLFvGEIc98XUuXAqdPA3v3qnbeb7/lCWDSJNWOU5yCAl7D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\nP3UQdhG0H1fvAAAAAElFTkSuQmCC\n", "text": [ "" ] } ], "prompt_number": 2 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now that we have a grip on the the Gibbs phenomenon, we need to control this form of distortion. Fortunately, we already have all of the tools in place from our prior discussion of window functions." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Using Windows for FIR Filter Design\n", "\n", "The root of the Gibbs phenomenon is the sudden truncation of the filter sequence by the rectangular window. We can mitigate this effect by smoothly guiding the filter coefficients to zero using a window function. The following figure is the same as before but now we use a Hamming window to terminate the ideal filter sequence." ] }, { "cell_type": "code", "collapsed": false, "input": [ "wc = pi/4\n", "\n", "M=20\n", "\n", "N = 512 # DFT size\n", "n = arange(-M,M)\n", "win = signal.hamming(len(n))\n", "h = wc/pi * sinc(wc*(n)/pi)*win # see definition of np.sinc()\n", "\n", "w,Hh = signal.freqz(h,1,whole=True, worN=N) # get entire frequency domain\n", "wx = fft.fftfreq(len(w)) # shift to center for plotting\n", "\n", "fig,axs = subplots(3,1)\n", "fig.set_size_inches((8,8))\n", "subplots_adjust(hspace=0.3)\n", "\n", "ax=axs[0]\n", "ax.stem(n+M,h,basefmt='b-')\n", "ax.set_xlabel(\"n\",fontsize=16)\n", "ax.set_ylabel(\"amplitude\",fontsize=16)\n", "\n", "ax=axs[1]\n", "ax.plot(w-pi,abs(fft.fftshift(Hh)))\n", "ax.axis(xmax=pi/2,xmin=-pi/2)\n", "ax.vlines([-wc,wc],0,1.2,color='g',lw=2.,linestyle='--',)\n", "ax.hlines(1,-pi,pi,color='g',lw=2.,linestyle='--',)\n", "ax.set_xlabel(r\"$\\omega$\",fontsize=22)\n", "ax.set_ylabel(r\"$|H(\\omega)|$\",fontsize=22)\n", "ax.grid()\n", "\n", "ax=axs[2]\n", "ax.plot(w-pi,20*log10(abs(fft.fftshift(Hh))))\n", "ax.axis(ymin=-80,xmax=pi/2,xmin=-pi/2)\n", "ax.vlines([-wc,wc],10,-80,color='g',lw=2.,linestyle='--',)\n", "ax.hlines(0,-pi,pi,color='g',lw=2.,linestyle='--',)\n", "ax.grid()\n", "ax.set_xlabel(r\"$\\omega$\",fontsize=22)\n", "ax.set_ylabel(r\"$20\\log_{10}|H(\\omega)|$\",fontsize=18)\n", "#ax.axis( ymin=-40,xmax=pi/2)\n", "\n", "# fig.savefig('figure_00@.png', bbox_inches='tight', dpi=300)\n", "\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "pyout", "prompt_number": 3, "text": [ "" ] }, { "output_type": "display_data", "png": 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fPtyOkRMRETUesumQmJiYiI8//hgA8PHHH+ORRx6p1yYmJgaFhYUoLi5GVVUV\nVq9ejcTERADA6dOnDe3Wrl2L7t27OydwIiIiNyOb4ZPPnz+Pv/3tbzh58iSCgoLw2Wefwc/PD6dO\nnUJycjJyc3MBABs3bsT06dOh0+kwYcIEzJgxAwAwevRo7N+/HwqFAp06dUJWVpahDwMRERFZwKpu\njC5o48aNQlhYmBASEiIsXLhQ6nDsrmPHjkL37t2F6OhoITY2VupwbDZu3Dihbdu2Qrdu3QzPnTt3\nThg0aJAQGhoqxMfHCxcuXJAwQuuZ+myzZ88WlEqlEB0dLURHRwsbN26UMELbnDx5UlCr1ULXrl2F\ne+65R0hPTxcEwX32n9jnc5d9eOPGDaFnz55CVFSUEBERIbzyyiuCILjH/hP7bO6y7+rU1NQI0dHR\nwl/+8hdBEKzbd7I5c+BIOp0OYWFh2LJlC5RKJWJjY5GdnY2IiAipQ7ObTp06Ye/evWjVqpXUodjF\nd999h+bNm2P06NE4ePAgAOCll15CmzZt8NJLLyEtLQ0XLlwwOR6G3Jn6bHPmzEGLFi3w/PPPSxyd\n7c6cOYMzZ84gOjoaV69exX333Yd169bho48+cov9J/b5PvvsM7fZh9evX0ezZs1QU1ODBx54AG+9\n9RbWr1/vFvvP1Gf75ptv3GbfAcA777yDvXv34sqVK1i/fr1Vvztl0+fAkfLz8xESEoKgoCB4e3sj\nKSkJOTk5Uodld+5U5/Xt2xctW7Y0em79+vUYM2YMAGDMmDFYt26dFKHZzNRnA9xn/919992Ijo4G\nADRv3hwREREoKytzm/0n9vkA99mHzZo1AwBUVVVBp9OhZcuWbrP/TH02wH32XWlpKTZs2ICJEyca\nPpM1+65RFAemxkeo+2F2FwqFAoMGDUJMTAyWLVsmdTgOYc5YGK4sIyMDUVFRmDBhgujw4a6muLgY\n+/btQ1xcnFvuv7rPd//99wNwn31YW1uL6OhoBAQEYMCAAbjnnnvcZv+Z+myA++y75557DosWLYKH\nxx+Hd2v2XaMoDhoaH8FdbN++Hfv27cPGjRvx3nvv4bvvvpM6JIcSGwvDVbnjOB1Xr17FyJEjkZ6e\njhYtWhi95g777+rVq3jssceQnp6O5s2bu9U+9PDwwP79+1FaWoq8vDxs27bN6HVX3n+3fzatVus2\n++6rr75C27Zt0aNHD9EzIebuu0ZRHDQ0PoK7aNeuHQDA398fjz76KPLz8yWOyP7qxsIAIDoWhqtq\n27at4YeYqIbQAAAgAElEQVR24sSJLr//qqurMXLkSDz99NOG25Ldaf/Vfb6nnnrK8PncbR8CgK+v\nL4YNG4a9e/e61f4D/vhsP/zwg9vsux07dmD9+vXo1KkTRo0aha1bt+Lpp5+2at81iuKgofER3MH1\n69dx5coVAMC1a9ewefNmtxznwZyxMFyVO43TIQgCJkyYgK5du2L69OmG591l/4l9PnfZhxUVFYbT\n6jdu3MDXX3+NHj16uMX+E/tsdQdOwLX33fz581FSUoLjx4/jv//9Lx588EF88skn1u07x9xIIT8b\nNmwQunTpIgQHBwvz58+XOhy7OnbsmBAVFSVERUUJ99xzj1t8vqSkJKFdu3aCt7e3oFKphA8//FA4\nd+6cMHDgQJe+lUoQ6n+25cuXC08//bTQvXt3ITIyUnj44YcNk5C5ou+++05QKBRCVFSU0a1h7rL/\nTH2+DRs2uM0+LCgoEHr06CFERUUJ3bt3F/75z38KgiC4xf4T+2zusu9updVqheHDhwuCYN2+axS3\nMhIREZH5GsVlBSIiIjIfiwMiIiIywuKAiIiIjLA4ICIiIiMsDojIIVJTU+Hh4YGjR49i2LBhaNGi\nBYKCgjB37ly3GaqWyF2xOCAih3r00UcxaNAg5OTk4JFHHsHs2bMN91wTkTx5SR0AEbm3F1980TDp\ny4MPPoitW7ciOzsbY8eOlTYwIhLFMwdE5FDDhg0zWr7nnntw8uRJiaIhInOwOCAih2rVqpXRctOm\nTXHz5k2JoiEic7A4ICIiIiMsDojI6Vx1ul+ixoLFARE5HW9lJJI3FgdE5BAKhcLkGQKx54lIPjgr\nIxERERnhmQMiIiIywuKAiIiIjLA4ICIiIiMsDoiIiMgIiwMiIiIywuKAiIiIjLhEcTB+/HgEBASg\ne/fuDbbbs2cPvLy8sGbNGidFRkRE5H5cojgYN24cNBpNg210Oh1efvllDBkyhKOvERER2cAlioO+\nffuiZcuWDbbJyMjAY489Bn9/fydFRURE5J68pA7AHsrKypCTk4OtW7diz549okOzcshWIiJqbKw5\nm+4SZw7uZPr06Vi4cCEUCgUEQWgwEXWvN/SYPXu2We0a44O5YW6YG+aGuZH+YW5urOUWZw727t2L\npKQkAEBFRQU2btwIb29vJCYmShwZERGR63GL4uDYsWOG/48bNw7Dhw+3qTAoLi62Q1TuibkRx9yI\nY27EMTfimBtxjs6NSxQHo0aNwrfffouKigoEBgZizpw5qK6uBgCkpKTYfXvR0dF2f093wdyIY27E\nMTfimBtxzI04R+emUU3ZXNcngYiIqDGw9rjnFh0SiYiIyH5YHJig1WqlDkG2mBtxzI045kYccyOO\nuRHn6NywOCAiIiIj7HNARETkptjngIiIiOyCxYEJvM4ljrkRx9yIY27EMTfimBtx7HNARERETsU+\nB0RERG6KfQ6IiIjILlymOBg/fjwCAgLQvXt3k6+vWrUKUVFRiIyMRJ8+fVBQUGD1tnidSxxzI465\nEcfciGNuxDE34tjn4Hfjxo2DRqMRfb1z587Iy8tDQUEBZs2ahb///e9OjI6IiMh9uMTESwDQt2/f\nBmeh6tWrl+H/cXFxKC0tNdlu7NixCAoKAgD4+fkhOjoaarUawB+VGJcbXq4jl3jkslz3nFzikdOy\nWq2WVTxcdp3lOnKJRy7Ldc+ZypdWq7V51kaX6pBYXFyM4cOH4+DBgw22e+utt/Drr79i6dKlRs+z\nQyIRETUm7JD4u23btuHDDz9EWlqa1e9xe8VKf2BuxDE34pgbccyNOOZGnKNz4zKXFcxRUFCA5ORk\naDQatGzZUupwiIiIXJLbXFY4efIkHnzwQaxcuRL333+/yfV5WYGIiBoTa497LlMcjBo1Ct9++y0q\nKioQEBCAOXPmoLq6GgCQkpKCiRMnYu3atejQoQMAwNvbG/n5+UbvweLAdR0sP4idpTvRrW039A7s\nLXU4RI3GmatnsP7IegT8KQAPhz8sdThkIbcvDuzB3CTd2gOUjEmVm/Rd6Zi+aTqmxk1F+pB0p2/f\nHPzeiGNuxMk9N9+f/B59P+qLPoF98P347526bbnnRkrm5oYdEomIiMguWByYwEpVHHMjjrkRx9yI\nY27EMTfiHJ0bFgdERERkhMWBCby3VhxzI465EcfciGNuxDE34jjOARGAbm27IfneZPRS9bpzYyKy\nm4A/BSD53mSEtAqROhRyIt6tQERE5KZ4twIRERHZBYsDE3idSxxzI465EcfciGNuxDE34hydG5co\nDsaPH4+AgAB0795dtM3UqVMRGhqKqKgo7Nu3z4nRERERuReX6HPw3XffoXnz5hg9erTJeRU2bNiA\nzMxMbNiwAbt378a0adOwa9eueu3Y54CIiBoTa497Zt+tsHjxYly6dMniDTTE19cX06dPv2O7vn37\nori4WPT19evXY8yYMQCAuLg4XLx4EeXl5QgICLBXqCQxzq1AJA3OrdA4mV0cdOjQAVeuXLHrxlu0\naGGX9ykrK0NgYKBhWaVSobS01GRxMHbsWAQFBQEA/Pz84NXOCy8UvgAAqD1ea2j3QL8HMLvjbAB/\njESl1WrxU/lP9dp7dPJA78DejaK9cFqAZ29Pp8ez9fhWTM+ajv4d+2On105Z5ef5Q68CV5TQ7aiB\n4s/+ULRRIfTPkRjW4gFUVQGdOqkhCEBhoRanr5zG/87uBwAI50sAQQFFq47o6BuEgX5dIAh/tD9+\nXIszV8uhqTgMCAoIF4oBAAq/zlD9uQP6+3aEpyfQpYsa3t5AcbEWv904hS8r8gDPagjnSqDw0EHR\nriUiAkLwdLsh8PQEYmLU8PICDhzQ4vilo3i39H0oPGpQe+oSoBDgoWyO6LaxSAkYC50OiI5Wo6YG\n2LNHi6MVx/FByReAzhvCqYsQaj2haB2IEL8IDPONQ00NEBSkRnU18OuvWpRdLMfms8UQzp8ABA/A\nQwdFy44IbNkOD7b6I34vL/3nLb9+Cl+e+xbwqIZwrhQKz+rf4w/FWOVD8PQEevbUf159/L/inyWL\n9fvr5E1A8ICinR+i2t6HCW1HQacDIiP18e/dq0XRuWIsL/kK0Hmj9sw5oNYTitYdEOwbhoQ/32sU\nf2GhFqcv/4Yt54sACBAuHQMgwKNlEAJ9VVD7dYJCAXTurIZCoY//t2tnsOHcQUAh6D+zQoCiVSCC\nWnbE4JZdoVDoP6+Pj35/ld88if/8vBQKZXMIl4qAZmfhEXYDfTrI4+cdABRBClTXVqPbtW7wHerr\n1HjWbluLD7w/kNXPu1zaL168WPT4pTqvQn/f/rCF2cXBiBEjbNqQo91+2kShUJhst2LFCqPl709+\nj6pfqvQLHX5/shio1lXXG55SrVbD66RX/fa6RtS+FtDpdJLEgyDAv6s/qg5Jl5+TJ4HVq4E9e4A9\ne9Q4cLAPqi8nAy1OA95fAb4hQMkNnPVtjvP31B0E9G/TtKkaTarLoLt8ClAIgLc/AAG4JqDSoxla\nddbHc+UKoFAAAQFqVN1VAt3pQn27P3fS/1tbi1pBh06d9Ae9CxcA/QSlalTePA3dyRtArTeg89b/\ne8obpU3a4uu7e6GmBli3DqipAWpq1Lh0PQY1FT2BWi/DQ+dRg5+aeCO9TSd4eeGWhxrXdNGoOaMC\nPKsAz2r9v+eqcaFFS1zuqkaTJsCJE4C3tz7+2hYnUXuhAGh6HmitAmo9IdReQS38oVTq4//tN308\ntbW/x3/iBqBr8sdnKG2Ckib+yG17P6qqgOxs/eetrlbj0vWeqD4/UJ9PhQ7wqAE8avBLUx98FBAG\nLy/9/vLyAry91bhScx41p1rqY/eo1v97tQaX/twatd3UaNoUqKjQt+/YUQ2vaydQe/EgAAXgpwSg\ngK62FjodoFLpi7gbNwBBAPz91bjZpAS6khP69k1a6v+9rMCN2lZoere+/dGjQGUlcOOGGiXnKqA7\ndAoojAOu3q0vMms9kR9wGv+JD0HPnsCf/wxER0v4++H3Y45vuK/ROs6I52D5QXn/PpSwfXR0NLw6\nm2gPQNlHiRXjVwAAPv74Y1jDJfocAEBxcTGGDx9uss/BP/7xD6jVaiQlJQEAwsPD8e2339Y7c2Dq\n2kutUItqXXW991QoFGji2aTe82wvTfu6WRmn9JyCRfGLnBrP6dPAyv944ovPvVBWBvTpA8TGAj17\nAt2618KvVTU8buvaK/d8sr1821++DBwt9MD+H72xZw+wc6e+AHzkEWDsuFpE31uN2//2cWQ820u2\nY+B/BpqcldEV8tnY2zu8z4GcJSYmIjMzE0lJSdi1axf8/PzM7m/gofBAU6+mZm+L7aVtr1AonBbP\nL78A8+YBX30F/PWvwJIl+sLA09NoDQDyyQ/bu357/1aAfxzQKw6YNEn/3NGjwGefAU8+4YFWrZpi\n5kwgMRH1ilJHxGPqoGTP92d757W3hEvcyjhq1Cj07t0bR44cQWBgID788ENkZWUhKysLADB06FB0\n7twZISEhSElJwb/+9S+btsd7a8U1htxcuAA8+yzQrx8QEaG/LLB0qX7ZuDAw1hhyYy3mRpw5uQkJ\nAV59FSgs1P87Zw7wwAPAjz86Pj4p8XsjzmXmVqisrMTPP/+M8vJyXLp0CR4eHvD19UXHjh0RGhoK\nz4Z+q95Bdnb2HdtkZmZa/f4kf86aW2HjRmDiRODhh/VnDlq1cujmiCzi4QE8+qj++/nRR8DQoUBy\nMvD66/p+Ho7AuRUaJ5v6HBw5cgTZ2dnIycnBTz/9BJ1OZ7LdXXfdhV69emHkyJF44okn4Ovra3XA\ntuA4ByRGpwNefhn4/HPg448BTiNPruDMGWDcOP3ZrjVrgPbtpY6I5Mba455VxcHRo0cxc+ZMbN68\nGb169ULfvn0RFxeHgIAAtGrVCq1bt0ZVVRXOnTuH8+fPo7i4GHl5ecjLy0NRURGeeeYZzJo1C3fd\ndZfFAduCxQGZcuUKkJSk70H+2Wc8W0CuRRCA+fOBDz7Q34ly331SR0RyYvVxT7DQ0qVLhbCwMOHt\nt98Wrly5Yunqwq+//ipMnDhRCAsLE/bt22fx+rYw9+Nu27bNsYG4MHfLzblzgtCzpyAkJwtCVZVt\n7+VuubEn5kacvXLzxReC4O8vCHl5dnk7WeD3Rpy5ubHiMC8IgiBY1Odg3rx5OHXqFA4ePAhvKy9w\nhYaGYtmyZTh27BhGjx6NBQsWoG/fvla9F5EtLlwAHnwQGDgQeOst1Ls9jMiVjBypHxNhxAj95TFe\nGiNbmH1Z4aeffsKPP/6I0aNH223jN27cwNy5czF//ny7vWdDeFmB6ly/DsTHA3FxwNtvszAg97F1\nq/4y2aZNQI8eUkdDUnNqnwNXxeLAddlzbgWdTj+gTMuWwIoVd75XnMjVrFkDTJ4M7NgB/D5avNU4\nt4Jrs/a4Z5dfi5WVlfjxxx/xyy+/oLa29s4ryBzvrRUnVW62Ht+KlK9SsPrn1Ta/18yZwNWrwPLl\n9i0M+L0Rx9yIc0RuRowAXnpJf8vj1au2vdfR80eR8lUKFu2oPzKpo/F7I84lxjkIDw/HiRMn0KxZ\nM0RHR6NDhw7o27cvnnrqKbtNrkRkD6tX6+9IyM933H3hRHIwbRpQUKC/1fGzz3jpjCxjl7+bRowY\ngeHDh6OwsBDff/89Vq1ahY4dO2LAgAEuOThRvQl/yMCVc1NYqD/VumYN0KaN/d/flXPjaMyNOEfl\nRqEA3n8fOHYMsHHQWMnweyPO0bmxS3Hw9ttvIycnB+3atQOgv8YxdOhQfPPNN1ixYgVGjx5t87V+\njUaD8PBwhIaGIi0trd7rFRUVGDJkCKKjo9GtW7d6sy9S41ZZqe+klZqqn+GOqDFo2hT473/13/v9\n+6WOhlyJQ7ti+fr64tNPP8Wnn36KxYsXW/0+Op0OkydPhkajwaFDh5CdnY3Dhw8btcnMzESPHj2w\nf/9+aLVavPDCC6ipqbFqe7zOJc5VczN7NhAYCDzzjOO24aq5cQbmRpyjcxMaCrz7LvDkk8DNmw7d\nlN3xeyPO0blxeD/tLl264L777sP7779v9Xvk5+cjJCQEQUFB8Pb2RlJSEnJycozatGvXDpcvXwYA\nXL58Ga1bt4aXl1tMOkmwbW6FXbv0dyUsXcrrrtQ4PfkkEB6uP4Ngqbq5FRLDEu0eF8mX3Y+e33zz\nDTw9PfHAAw/Ay8sLtbW1uHjxIsrLy61+z7KyMgQGBhqWVSoVdu/ebdQmOTkZDz74INq3b48rV67g\ns88+M/leY8eORdDv9/b4+fkhOjracO2mrhLjcsPLdZy5/YGdB8LzpCdQYdn2q6uBKVPUyMgADh3S\n4tAhx8Vb95zU+0eOy2q1WlbxNLZlhQJ46iktJkwARoxQo2dPy9ZfOnwptFqtJN/vOnLKpxyW654z\nlS+tVovi4mLYwu7jHLz66qtIT0+Hj48PHnvsMezfvx979uzB66+/jlRrylYAX375JTQaDZYtWwYA\nWLlyJXbv3o2MjAxDmzfffBMVFRVYvHgxioqKEB8fjwMHDhjdLcFxDhqfefOAPXv0Y84TNXarVgHv\nvKO/W8eGiXLJhUg6zsGt5s+fj3PnzmHdunW455578PPPP+ONN96wujAAAKVSiZKSEsNySUkJVCqV\nUZsdO3bgr3/9KwAgODgYnTp1wpEjR6za3u0VK/3BlXJTXKy/1mpDdxeLuFJunI25EefM3DzxBNC8\nuf4Smyvg90aco3PjkD4HPj4+6Nu3L6ZOnYpPP/0Us2fPRm5urtXvFxMTg8LCQhQXF6OqqgqrV69G\nYqLx9a/w8HBs2bIFAFBeXo4jR46gc+fONn0Ocm3PPad/2DpCHJG7UCiA997Td9A9e1bqaEjO7HJZ\nQafTwbOBc1TdunWDp6cnDhw4YPU2Nm7ciOnTp0On02HChAmYMWMGsrKyAAApKSmoqKjAuHHjcPLk\nSdTW1mLGjBl44oknjN6DlxUajw0b9IPA/PST/nYuIvrD888Dly7pRwkl9ybp3AoTJkxA7969MWHC\nBJOv9+jRA8eOHcOlS5ds3ZRNWBy4LkvmVrh5E+jWDcjMBIYMcVKARC7k8mUgIgL44gug1x1uAOLc\nCq5N0j4Hy5cvR9u2bTFu3DgsWbIEhYWFqKqqwunTp/Haa6/hwIEDGDZsmD025RS8ziVOqtxYMrfC\nO+8A3bs7vzDg90YccyNOitz8+c/AokX6EUPvNB0O51aQJ0fnxm63Mg4fPhzDhw/HTz/9hP/973/Y\nv38/zp49i+bNmyMjIwMTJ06016aIRFVU6IuDXbukjoRI3kaN0nfW/ewz/eihRLcyuzg4d+4c7rrr\nLjRr1qzBdt26dUO3bt3MDuDEiRPo2LGj2e2d4db7SMmY3HMzfz7w+ONASIjzty333EiJuREnVW4U\nCmDhQiA5WT+LY5MmkoTRIH5vxDk6N2ZfVqipqcG4ceNsGszodp9//jkWLFhgt/ejxu3ECeDjj4FZ\ns6SOhMg1PPigfnjl34eQITIwuzgICAjA/PnzMXLkSHz88cc2dewrLS3FpEmTsH79elnO2sjrXOLk\nnJvZs/VzJ9x9tzTbl3NupMbciJM6NwsWAG++CVy9KmkYJkmdGzmT1TgHwcHByM3NRV5eHrp06YL5\n8+dj//79ZhUKV69excaNGzFu3Djce++9iIyMxCeffML5D8gsd5pb4eBBYONG4P/+z8mBEbm4Hj2A\nAQP0A4aZwrkVGierb2X88ccfsWjRIuTk5MDT0xOxsbFQqVTw8/ODr68vqqqqcP78eZw/fx7Hjx9H\nQUEB/P39MWHCBEybNg3+/v72/ix3xFsZ3dfw4cDAgcD06VJHQuR6jh0DevYEDh8GJPjVTA4k2TgH\nly9fxpYtW7Bjxw4cPnwYZWVluHbtGjw9PeHn54egoCBERkaib9++6NOnDzw8HD4RpCgWB+4pPx8Y\nORI4epQDHhFZ69lngT/9CfjnP6WOhOzJacXB119/jfj4eIs3JAfmJunWma7ImBxz8/DDQHy8/p5t\nKckxN3LB3IiTS25KS4GoKOCXX+Rz9kAuuZEjc3PjtEGQXnzxRYs3Yg8ajQbh4eEIDQ1FWlqayTZa\nrRY9evRAt27d+IVqJA4c0M+6KDI4JxGZSaXS3wb81ltSR0JyYPGZA39/f5SXlzv18oBOp0NYWBi2\nbNkCpVKJ2NhYZGdnIyIiwtDm4sWL6NOnDzZt2gSVSoWKigq0adPG6H14WcH9/O1vQFwc8MILUkdC\n5PpOngSio4FffwVu+/VJLsra457FtwqcO3cOnTt3xqBBg6BWqzFgwAAolUqLN2yJ/Px8hISEIOj3\n6fWSkpKQk5NjVBx8+umnGDlypGEq59sLgzpjx441vI+fnx+io6MNZxnqbg3hsvyWD5YfxIqcFejk\n1wmT/6a/fvDxx1p8/TXw4YfSx8dlLrvL8uOPq/H220BCgn45PCYc64+sx9mfz6JPhz6Sx8flhpfr\n/l9cXAybCBZSKBRGDw8PDyEkJESYOHGisGrVKqGsrMzkeuPGjbN0Uwaff/65MHHiRMPyJ598Ikye\nPNmozfTp04Vnn31WUKvVwn333Sf85z//qfc+5n7cbdu2WR2ru5MqN4t3LhaQCmHqxqmG5556ShDm\nzZMkHJP4vRHH3IiTW25OnBCEVq0E4exZ/fJ3J74TkAqhz/I+To9FbrmRE3NzY8VhXhAEQbD4zEGn\nTp2Ql5eHTZs2YePGjdiyZQuKiopQVFSE5cuXQ6FQIDg4GAMGDIBarYZarUa7du2wc+dOqwsYhUJx\nxzbV1dX48ccf8c033+D69evo1asX7r//foSGhlq9XZKvoiL9uAYyHEOLyKV16AA89ph+jpL586WO\nhqRicXHQtm1bKJVKjB8/HuPHj4dOp8POnTsxatQoBAcHY8+ePTh69CiOHj2KZcuWQaFQoFOnTjhx\n4oTVQSqVSpSUlBiWS0pKDJcP6gQGBqJNmza46667cNddd6Ffv344cOCAVcVB3Wkaqk8uuVm4UD8a\noq+v1JH8QS65kSPmRpwcc/Pqq8C99wIS9T83kGNu5MLRubG4V+Gt1zUAwNPTEw888ABUKhW0Wi0u\nXbqEPXv2ID09HY8//jhUKhWOHTuG2jvNC9qAmJgYFBYWori4GFVVVVi9ejUSE41H63r44Yfx/fff\nQ6fT4fr169i9eze6du1q9TZJvk6eBNasAaZNkzoSIvfUsSPwyCPAkiVSR0JSsbg4aHqHUWa8vLxw\n3333YcqUKcjOzsaJEydw5MgR+Pj4WB2kl5cXMjMzkZCQgK5du+Lxxx9HREQEsrKykJWVBQAIDw/H\nkCFDEBkZibi4OCQnJ1tdHNxeANEf5JCbf/4TmDgRaN1a6kiMySE3csXciJNrbmbMAN57D7h2xVOy\nGOSaGzlwdG4svqzwxBNP4NNPP7VondDQUHTq1MnSTRl56KGH8NBDDxk9l5KSYrT84osvSjYOAzlW\n3dwK4U0HYOan+oFaiMhxQkKAhARgc3YokuOSEdJKgnnQSTIWj3MQERGBw4cP13u+V69eDXY6/Oc/\n/4mXXnrJ8gjtiOMcuL4XXgB0OmDxYqkjIXJ/hw4BajVw/Lh+aGVyPU4bIfH48eNYs2YNbty4YdF6\nUhcG5PrOngU++ogzLxI5S9euQP/+wAcfSB0JOZvFxUFVVRUee+wxtGrVCoMHD8Y777yDQ4cO3XG9\n/fv3WxWgFHidS5yUuXn3Xf3wrg4ec8tq/N6IY27EyT03r70GvP02YOHfg3Yh99xIydG5sbg48PHx\nwZgxY6BUKrFlyxa8+OKL6NatG/bt24cnnngCGRkZ2Lt3L3Q6ndF648ePt1vQ1PhcuABkZQEvvyx1\nJESNS1QUEBsLLF8udSTkTBb3OYiMjERBQQEAoLS0FFqtFlqtFtu2bcPx48cN7Zo1a4aYmBj07t0b\nsbGxSElJwW+//Wbf6C3EPgeua84coLhYf1mBiJxrzx5gxAhOi+6KnDZlc2ZmJiaLzI1bUlJiVCzc\nOrazQqGodzbB2VgcuKbLl4GgzjV4bumXGBgbiN6BvaUOiajROHP1DNYfWY8Ppj+MSaMDkJwsdURk\nCad1SBQrDAD9KIVPP/00li9fjmPHjqG4uBgrVqzA448/7lIHZV7nEidFbt5/H+h071G8fjAJq39e\n7fTtm4vfG3HMjTi55+bo+aNI+SoFNQ+kYsECoLraeduWe26kJLs+B5bo0KEDRo8ejezsbHTo0MGR\nmyI3de2aviNi/Ng9UodC1Kj9OfQgOnYELBzmhlyUQ4uDW7W2cTg7jUaD8PBwhIaGIi0tTbTdnj17\n4OXlhTVr1li9LY7nLc7ZuVm2DOjTB2jX+bxTt2sNfm/EMTfiXCk3s2bpJ2Ny1hViV8qNs8lubgVr\nbdiwwep1dTodJk+eDI1Gg0OHDiE7O9vkQEw6nQ4vv/wyhgwZ4lKXMci0mzeBRYuAmTOljoSIAGDA\nAP2w5Z9/LnUk5GhOKw4CAgKsXjc/Px8hISEICgqCt7c3kpKSkJOTU69dRkYGHnvsMfj7+9sSKq9z\nNcCZufnwQyA6Wj87nCvg90YccyPOlXKjUOjPHrz5JmDDXHpmc6XcOJvs5laQQllZGQIDAw3LKpUK\nu3fvrtcmJycHW7duxZ49e6BQKEy+19ixYxEUFAQA8PPzQ3R0tOH0zO3Jrlu+/fXGvLx//36nbK+y\nEkhN1WLOHABQo1vbbhjmPQy+p/+Yo1kO+bh1uW6gL7nEw2XXWK4jl3huX1Z2VyL53mQoTiig1Wox\nZIgas2YB8+Zp0beve/y+ccVlsd83df+/9W5Ba5h9K+PixYtx6dIlmzZ2O19fX0yfPv2O7b788kto\nNBosW7YMALBy5Urs3r0bGRkZhjZ//etf8eKLLyIuLg5jx47F8OHDMXLkSKP34a2MruP994H//Q+w\n4WoUETnIunXAG28Ae/fqzyaQfFl73DP7zEGHDh1w5coVizfQkBYtWpjVTqlUoqSkxLBcUlIClUpl\n1IiG9xwAACAASURBVGbv3r1ISkoCAFRUVGDjxo3w9vZGYmKi/QImp6isBBYs4HVNIrlKTARefx3Y\nuBEYOlTqaMghBBdQXV0tdO7cWTh+/LhQWVkpREVFCYcOHRJtP3bsWOHLL7+s97y5H3fbtm3Whur2\nnJGb998XhIcecvhm7I7fG3HMjThXzc1//ysI998vCLW1jtuGq+bGGczNjbWHead1SLSFl5cXMjMz\nkZCQgK5du+Lxxx9HREQEsrKykJWVJXV4ZEeVlfpbpWbPljoSImrIY4/p5zz55hupIyFHsHj4ZFfG\nPgfy98EHwPr17GtA5Ao++UQ/IRNvKpAvp82t4MpYHMjbzZtAly76vgZxccavHSw/iJ2lO9GtbTfO\nrUDkRHVzKwT8KQAPhz9s9FpNDRAWpi8QOF6RPDltboXG4PZbjOgPjsxNZqZ+TIPbCwMA2Hp8K1K+\nSuHcCi6KuREn99zUza2waMeieq95eenvWnjlFcARf3fJPTdScnRuWByQLFy4AKSl6e9SICLXMWqU\n/qzf2rVSR0L2xOLABDXPj4lyVG7S0oBHHgEiIhzy9k7B74045kacq+fGw0P/8ztjhv1nbHT13DiS\no3PD4oAkV1Kin2ApNVXqSIjIGoMHAyqVfshzcg8sDkzgdS5xjshNairw978DSqXd39qp+L0Rx9yI\nc4fcKBT6swdz5uinWbcXd8iNozg6Ny4xtwK5r59/1g+T/OuvDbfr1rYbku9NRi9VL+cERkQAgIA/\nBSD53mSEtAppsF1MDNCvH/Duu8BrrzkpOHIY3spIkhEEYNAg/VCs06ZJHQ0R2aqoSH+30b59wC1z\n5ZGEeCsjuZzVq4GKCuDZZ6WOhIjsIThY//P83HNSR0K2cpniQKPRIDw8HKGhoUhLS6v3+qpVqxAV\nFYXIyEj06dMHBQUFVm+L17nE2Ss3ly8DL76on33Ry00ubvF7I465EeduuXnlFf2Zg02bbH8vd8uN\nPXGcAwA6nQ6TJ0+GRqPBoUOHkJ2djcOHDxu16dy5M/Ly8lBQUIBZs2bh73//u0TRkjlSU/U9nHtz\nsEMit3LXXUBGBjB5sn78A3JNLtHnYOfOnZgzZw40Gg0AYOHChQCAV155xWT7CxcuoHv37igtLTV6\nnn0O5KGgQN/X4OefAX9/qaMhIkd49FH9iKezZkkdSeNm7XHPJU7olpWVIfCW3i0qlQq7d+8Wbb98\n+XIMFZlkfOzYsQgKCgIA+Pn5ITo62jCYRN1pGi47brm2Fnj9dTXmzgV+/tn89Q+WH8SKnBXo5NcJ\nk/82WTafh8tcdvfl8JhwrD+yHmd/Pos+HfqYvX5SkhbJycCoUWqEhMjn87j7ct3/i4uLYROrJnp2\nsi+++EKYOHGiYfmTTz4RJk+ebLLt1q1bhYiICOH8+fP1XjP343IOcXG25uaddwShb19BqKmxbL3F\nOxcLSIUwdeNUm7bvSPzeiGNuxMk9N9+d+E5AKoQ+y/tYvO477wjCAw9Y/vNeR+65kZK5ubH2MO8S\nfQ6USiVKSkoMyyUlJVCpVPXaFRQUIDk5GevXr0fLli2dGSKZ4fBhYN484KOPAE9PqaMhIkebNk0/\nvPLixVJHQpZyieIgJiYGhYWFKC4uRlVVFVavXo3ExESjNidPnsSIESOwcuVKhIQ0PFjHndSdpqH6\nrM1NZSXw1FPA3Ln6253cEb834pgbce6cGw8P/R8DCxcC+/dbvr4758ZWjs6NS/Q58PLyQmZmJhIS\nEqDT6TBhwgREREQgKysLAJCSkoI33ngDFy5cwKRJkwAA3t7eyM/PlzJsusVLLwEdOwL/+IfUkRCR\nM3XurD9z8PjjwA8/AC1aSB0RmcMlzhwAwEMPPYQjR47g6NGjmDFjBgB9UZCSkgIA+Pe//41z585h\n37592Ldvn02Fwa0dO8iYNbn58ktg/Xpg+XL9GOzuit8bccyNuMaQmyefBPr2BVJS9COjmqsx5MZa\njs6NyxQH5JoOHNCfLfj8c8CWbiCcW4FIGnVzKySGJd65cQOWLNHPobJokZ0CI4dyiXEO7IXjHDhX\neTlw//3AggVAUpLU0RCR1EpL9XMvvP++fk4VcjzOrUCycvEikJAAjBvHwoCI9FQqYO1aYOJE4Pvv\npY6GGsLiwARe5xJnTm6uXAGGD9dfY2xMo6PxeyOOuRHX2HLTsyewahUwcqS+g2JDGltuLME+B+RS\nLl7Uz5kQEQGkp7t3B0Qisk58PLB0KTB0KLB9u9TRkCnsc0B2U1ysP2MwcCDw7rssDIioYZs26cc/\nycoCRoyQOhr3xD4HJCmtFujVC5gwwTGFwcHyg1i6dyl2lOyw7xsTUYPOXD2DpXuXIueXHLu/d0IC\nsHEjMHWqfoA0nc7umyArsTgwgde5xN2em8pKYOZM4IkngBUrgOnTHXPGYOvxrUj5KgWrf15t/ze3\nE35vxDE34uSem6PnjyLlqxQs2uGYexBjYoDdu4FvvtHP1nry5B+vyT03UmKfAwnst2acz0bi1tx8\n/TUQGQn89BOwb5/+r4DGjN8bccyNOOYGUCr1xcHgwfppntPS9H94MDfiHJ0blykONBoNwsPDERoa\nirS0NJNtpk6ditDQUERFRWHfvn1Wb+vixYtWr+vuLl68iC1bgAEDgGee0Q9okpMDBARIHZn0+L0R\nx9yIY270PD2BGTP0ZxG2bwdCQoCvv76Iq1eljkyeHP29cYniQKfTYfLkydBoNDh06BCys7Nx+PBh\nozYbNmzA0aNHUVhYiKVLlxrmWCDbCQJw5Agwfz6QmQk8/zwwZox+lkUOZEJE9hQcrB9u/csvgaIi\n/ZwskyYBW7cC1dVSR9d4uMTES/n5+QgJCUFQUBAAICkpCTk5OYiIiDC0Wb9+PcaMGQMAiIuLw8WL\nF1FeXo4AK/6kLS4utkfYkhGEP8Yvr/t/Q8sA0LSpfga1ykrg1Cng55+BQ4eAgweBvDygpgZ49FGg\nZ89i5ObyTgRTXP1740jMjTjmxrSePYH77y/G3Ln6cRFeekn/R8p99+k7P8fFAV26AB06AH/6k/53\nkk4H3LwJ3Lihf9TU6H+veXrq/731UfecQvHHc7f+v2657iE3Dv/eCC7g888/FyZOnGhY/uSTT4TJ\nkycbtfnLX/4ibN++3bA8cOBA4YcffjBqA4APPvjggw8+GtXDGi5x5kBhZtkm3HYv5+3r3f46ERER\n/X97dx4XVfX+AfwzLMriggqMCCoGIgIKKImmGCqIWJDb13ApTbTFLc3c+LaYGW70U8mMXCpMc0lN\nMZdwATW/KiBSCuYWKJAoixKiss35/XEFGZgLs98Z5nm/Xrzszpy59+HpMPPMveeeU59ejDmwt7dH\ndnZ2zXZ2djYcHBwabJOTkwN7e3utxUgIIYQ0FXpRHPj4+ODGjRvIyspCeXk5du3ahdA6I+FCQ0Ox\ndetWAMD58+dhZWWl1HgDQgghxNDpxWUFExMTrF+/HkFBQaiqqkJ4eDi6d++Ob7/9FgDwzjvvYPjw\n4Th8+DCcnZ1haWmJ77//XuCoCSGEED2l1EiFJmb37t3Mzc2NGRkZsYsXL/K269y5M+vRowfz8vJi\nL774ohYjFI68uTly5Ajr1q0bc3Z2ZitWrNBihMIpLCxkAQEBrGvXriwwMJA9ePBAZjtD6jfy9INZ\ns2YxZ2dn1rNnT5aamqrlCIXTWG4SEhJYq1atmJeXF/Py8mKff/65AFEK46233mK2trbMw8ODt42h\n9pvGcqOpfkPFAWPs6tWr7Nq1a8zf37/BD0BHR0dWWFioxciEJ09uKisrmZOTE8vMzGTl5eXM09OT\nZWRkaDlS7Zs/fz5buXIlY4yxFStWsIULF8psZyj9Rp5+cOjQIRYcHMwYY+z8+fPM19dXiFC1Tp7c\nJCQksJCQEIEiFNbp06dZamoq7wegofYbxhrPjab6jV6MOdA0V1dXuLi4yNWWGdgdD/LkpvY8FKam\npjXzUDR1tefWmDRpEvbv38/b1hD6jTz9gG8+kqZO3r8RQ+gnsvj5+aFNmza8zxtqvwEazw2gmX5D\nxYECRCIRAgIC4OPjg02bNgkdjs7Izc1Fx44da7YdHByQm5srYETaUXuSLbFYzPtmZSj9Rp5+IKtN\nTk6O1mIUijy5EYlE+N///gdPT08MHz4cGRkZ2g5TZxlqv5GHpvqNXgxIVIfAwEDk5eXVezwyMhIh\nISFy7ePs2bOws7NDfn4+AgMD4erqCj8/P3WHqnWq5kbeeSj0EV9uvvjiC6ltkUjEm4em2m/qUtd8\nJE2RPL9jr169kJ2dDQsLCxw5cgQjRozA9evXtRCdfjDEfiMPTfUbgykOjh07pvI+7OzsAAA2NjYY\nOXIkkpKSmsSbvKq5kWceCn3VUG7EYjHy8vLQvn173L17F7a2tjLbNdV+UxfNR8JPnty0bNmy5r+D\ng4Mxffp0FBUVoW3btlqLU1cZar+Rh6b6DV1WqIPv2s3jx49RUlICACgtLUV8fDx69OihzdAEx5cb\neeahaIpCQ0MRGxsLAIiNjcWIESPqtTGkfkPzkfCTJzf37t2r+RtLSkoCY4wKg2cMtd/IQ2P9Ru1D\nHPXQvn37mIODAzMzM2NisZgNGzaMMcZYbm4uGz58OGOMsVu3bjFPT0/m6enJ3N3dWWRkpJAha408\nuWGMscOHDzMXFxfm5ORkMLkpLCxkQ4YMqXcroyH3G1n9ICYmhsXExNS0mTFjBnNycmI9e/Zs8O6g\npqax3Kxfv565u7szT09P1q9fP3bu3Dkhw9WqsLAwZmdnx0xNTZmDgwPbsmUL9ZtnGsuNpvqNiDED\nHR5LCCGEEJnosgIhhBBCpFBxQAghhBApVBwQQgghRAoVB4QQQgiRQsUBIYQQQqRQcUAIIYQQKVQc\nEELULjw8HFVVVQ22mTdvHrp06YKysjItRUUIkRcVB4QQtTp48CBeeuklGBsbN9ju5s2buH37NtLT\n07UUGSFEXlQcEELUat++fQgPD2+0XUxMDCwsLGBhYaGFqAghiqDigBCiNleuXIG3t3e9xyMiInDi\nxAmpx+zs7ODl5QUXFxdthUcIkRMVB4QQtYmPj0dwcLDUY0+fPsW6devqXWZgjKFTp04wMqK3IUJ0\nDf1VEkLUJi0tDZ07d5Z6LDk5GWZmZhgwYIDU40eOHGmSS1cT0hSYCB0AIaTpyM/PR2FhIezs7Goe\nu3TpEsaMGQMTk+dvN8XFxfjkk0+QkJAgRJiEkEbQmQNCiNq0aNECX3/9dc12XFwcIiIikJaWBolE\nAgC4fv06hgwZgsmTJ6Nly5ZChUoIaQAVB4QQtfH390dkZCS8vb3h4eGBkSNHYtGiRUhOTkb37t3h\n6+sLNzc3uLm5YebMmUKHSwjhQZcVCCFqM3XqVJw9exaHDh2Co6Mj4uLi8Morr6CyshJr1qwBYwyr\nV6/GnDlzhA6VENIAEWOMCR0EIYQQQnQHXVYghBBCiBQqDgghhBAihYoDQgghhEjRu+IgOzsbgwYN\ngru7Ozw8PBAdHQ0AKCoqQmBgIFxcXDB06FA8fPhQ4EgJIYQQ/aR3AxLz8vKQl5cHLy8vPHr0CL17\n98b+/fvx/fffw9raGgsWLMDKlSvx4MEDrFixQuhwCSGEEL2jd2cO2rdvDy8vLwDchCvdu3dHbm4u\n4uLiMGnSJADApEmTsH//fiHDJIQQQvSW3p05qC0rKwsvv/wyrly5gk6dOuHBgwcAuAVd2rZtW7Nd\nTSQSCREmIYQQIhhlPub17sxBtUePHmH06NFYt25dvSlYRSIRbyHAGGv059NPP5WrnSH+UG4oN5Qb\nyg3lRvgfeXOjLL0sDioqKjB69Gi88cYbGDFiBABALBYjLy8PAHD37l3Y2toKGSIhhBCit/SuOGCM\nITw8HG5ublJTsIaGhiI2NhYAEBsbW1M0KCMrK0vVMJssyg0/yg0/yg0/yg0/yg0/TedG79ZWOHv2\nLLZt24aePXvC29sbALB8+XIsWrQIY8eOxZYtW+Do6Ijdu3crfYzqAY+kPsoNP8oNP8oNP8oNP8oN\nP03nRq8HJCpKJBKpdA2GEEII0SfKfu7p3WUFQgghhGgWFQcyJCYmCh2CzqLc8KPc8KPc8KPc8KPc\n8NN0bqg4IIQQQogUGnNACCGENFE05oAQQgghakHFgQx0nYsf5YYf5YYf5YYf5YYf5YYfjTkghBBC\niFbRmAOiF3Zc3oGoc1EIcw/D/P7zhQ6HEINx6e4lTD04FV7tvbAldIvQ4RAFKfu5J9cMiWPGjEFh\nYaHCO6/N1NQU+/btQ4sWLVTaDzFM90vvI/VuKgZ0GiB0KIQYlNKKUqTeTYW5ibnQoRAtkqs42LNn\nj6bj0CmJiYnw9/cXOgydRLnhR7nhR7nhR7nhR7nhp+nc0JgDQgghhEih4kAGqlT5UW74UW74UW74\nUW74UW74aTo3Kq3KKJFIkJmZiaKiIohEIojFYojFYjRr1kxd8RFCCCFEyxQ+c/Dw4UOsXbsWAwcO\nhKWlJVxdXfHKK68gJCQEzs7OsLCwQK9evbB06VLk5uZqImaNo3tr+QmVmzCPMKRMS8GH/T4U5Pjy\noH7Dj3LDT9dz49XeCynTUrA5dLPWj63ruRGSzsxzwBjD6tWr4efnh3v37iEiIgK5ubkoLy/H/fv3\ncffuXZSVlaGwsBBRUVGoqqrC8OHDMW/ePDx58kSTvwMxAOIWYvTu0BsdW3cUOhRCDEqLZi3Qu0Nv\nuFq7Ch0K0SK55jl48uQJpkyZgoCAALz55pswNTWVa+cSiQR79uzB9u3bERMTAzs7O5UDVgXNc0AI\nIcSQaHRthaioKERGRiI8PFzuwgAAjIyMMHbsWGzevBkrV65UODhFHT16FK6urujatatWjkcIIYQ0\nRXIVBx9//DG6dOmi9EFsbGywdu1apV8vj6qqKsycORNHjx5FRkYGduzYgatXryq1L7rOxY9yw49y\nw49yw49yw49yw0/TuVHpboWJEyciNTUVjo6OGDBgAEaPHo1u3bqpKzaFJCUlwdnZGY6OjgCAsLAw\nHDhwAN27d2/wdXmP8hB3LU7qsWvXr6G4fTFec31NrvYAILYUG0T7a9ev4XrL6zoTjy61r86NrsSj\nS+1r50YX4tGl9gevH5TKjdDx6FL7oidF2Hhxo87Eo+/tFaFScVBZWYmQkBB89NFHqKioQExMDP78\n809ERUXBwcFBpcAUlZubi44dnw9Wc3BwwIULF+q1mzx5ck0BYWVlBWM7Y8z+azb3ZNazRo7Ahf9d\nQOu81gCe30+amJiIy/cuy2zfv2N/w2l/V/vx7Li8A5/+8Cm623RHXFmc2vdfWQn88ksizl+7hf+7\n/BvwpB3wz79AeQvArBesjSywyjgRlZWApaU/ysqAgoJEPHr6FP+UvgwwY64tAJj0Q3NjM1iZJIIx\noHlzfzAGlJUloryqAsUVrwAQAZX/e9b+JZgaNUNL40QAXHuAa18pqcC/Va9y7Wra90MzY/72xZWv\nPGt/DhCxmvatZLSvkFSguHL48/YAYNIXzYybobWJjPZVFXhYGSzd3rQvmhk3R+tn+zcz49o/fZqI\nCkk5HlYOAzBMav/NTfjbP6gIerb/88/274vmxs1hZSK7fVHFUOn2Jr5obtIcbWS0L68qR1FFoMz9\nV7c3N+faP3nyrH1lANeu4nl7MxMznvZlKKwY8qz9s/efZn1gZmKGtjztCyreq9WeAWbesDQ3QecW\niTA1BWxt/dG8OVBSkohy4yKce1oMmD0EStOBZo+AF6rQq5sYzb1bw8xMM3+PlqaWGMgGYkH/BVp9\n/8n9Nxezk3T8/VCg9gDw86Gf67cH0LGoI35p8wtUofaFl06dOoU333wTJ06cgLOzszp33aC9e/fi\n6NGj2LRpEwBg27ZtuHDhAr766quaNrIGZtwovIHV/1tdb3/ObZ2xoP+Ceo9Te2Harzu/DnN+m4M3\nPd9Ec+PmSu2fMeDR/XYoyrKHcaEHbJ/449o1IDsbuH8fsLYGrNs/xb/Nr8Ks1SM0t3yMZpaP0czy\nCTratkJYr1fRrBnQvPnzn7uPb2NbxhaIjKoAACIRABGDo1VnvOPzDkQiSP1kPshEzMVvuHZ43he7\ntHHE9Bdn1Iv/7wd/45vkb55tiWoed7RyxPQXp9drn/ngb3yTElPz+9bs38oR78lsn4lvUr55/gAT\n1ez/vRffk9k+5tn+a8fU2aoz3vOR3f7bi98+3z17Hv+7Pu822r46ns5WnXnb1/5mWf0rO7Z2xDs+\n78hun1rrm2j1/lt3ltk+60EmNqZukhnP273fltE+C5tqta/+feVuLzGCpMoYHcy7IKz7JJSVAeXl\nQFkZ8OQJcCP3Hg7+eQblpRYoK7VA+SMLlBZZofyBDUoL28DSEnBwAJycgO7dgTYd83CubCPadLoL\nI5OqmuMo8vdYfXajf8f++H3K7422V3T/1F6z7ZUdkKiRVRnff/99XL9+HUeOHFH3rnmdP38eS5Ys\nwdGjRwEAy5cvh5GRERYuXFjTRt4k0Xze/ITKTXVxMNt3NtYNWyfXa8rLgQsXgIQE7t/kZMDYGPD2\n5t44u3cHunUDOncG7OwABcbaykT9hh/lhp+6csMYUFDAFbs3bgBXr3I/ly8Dt28Dnp7Aiy8CAwcC\ngwYBbdvKt9/f7/wOv+/9ZBYHmkb9hp+8udHoqoyNkUgkkEgkMDHhdufi4oLvvvtOHbuWm4+PD27c\nuIGsrCx06NABu3btwo4dO7QaAxFebi7wyy/A4cPA778DLi7A4MHA1KnAt98C9vbPvt0T0sSIRICN\nDffTq5f0cyUlwMWLQFISsGUL8NZb3N/G0KHAqFFA7970d0GkqaU4OHz4MCZOnAh/f3/4+/tjzZo1\nGDx4sDp2LTcTExOsX78eQUFBqKqqQnh4eKODEflQpcpPF3OTnw9s3w78/DP3TenVV4EpU4Bt2+T/\ndqQOupgbXUG54aeN3LRsCfj7cz8LFjw/q3b4MDB+PLc9ejQwcSJ3Zk1XUL/hp9NrK1R79dVX8c8/\n/yApKQmxsbFo06aNIN/ag4ODERwcrPXjEu2TSIDjx4FNm4Bjx4DXXgM++ggYMgSgpT0IaVizZoCf\nH/cTGQlcuQLs3s39HdnaAtOmAePGAa1aCR0pEYraxxwwxhASEgInJyesWyfftWFtoTEHqhMqN/ce\n3UPOvzmwMrXF6V87YuVKwMwMePtt7puPlZXWQ6qH+g0/yg0/XcpNVRUQH88V3adOcZfj3p5Riocm\nf8GymaXWp1DWpdzoGk2POVBpyeatW7dCIpHUCyQ4OBixsbGq7JoQKa1NxPj9597w79URO3YAGzYA\nly4B06frRmFASFNgbAwEBwP79nFjFB4/Bl70ssSmpb1h8ZjWVjAkKp05uHbtGmJjY+Hl5YWQkBCY\nm5ujuLgYo0aNQn5+Pv788091xqoyWltB/0gkwK5dQEQE0KMH8MkngI+P0FERYjju3wfWruUG9L79\nNrBoEdC6tdBREXkJeivj1atX8euvvyInJweZmZlwdHTEBx98UDPZkK6g4kC/nD8PzJ7N3aIVFQW8\n/LLQERFiuHJzgY8/Bg4dApYsAd55BzBS6dwz0QadmudAV9GYA9VpIzePHnGDC3ftAlav5sYU6MOb\nEPUbfpQbfvqWmz/+AGbM4Ir2zZu5+UI0Rd9yo006MeYgMjIS9+7dU3jn1QoKCjBnzhylX08Mx7Fj\n3OWDBw+4EdQTJ+pHYUCIofD0BE6f5op2Pz9g2TKgokLoqIi6yXXmoKSkBO+88w6GDRuGCRMmwNjY\nWK6dM8awd+9ebNu2DTExMWjfvr3KAauCLivorooKblzBrl3cSOmgIOnnd1zegahzUQhzD8P8/vOF\nCZIQA3Tp7iVMPTgVXu29sCV0i9Rzd+5wtz2WlHB/u7WWtyE6QqNnDlq2bImtW7eiqKgIvXr1wief\nfIL4+HgUFxfXa1taWopTp07hs88+g7e3N86fP48dO3YIXhgQ3XXnDjeeICODuwOhbmEAAPdL7yP1\nbipySnK0HyAhBqy0ohSpd1NxreBavec6dQKOHOHmR/DxAX79VYAAiUbIfcLWxMQEc+bMwalTp9Cm\nTRusXr0aYrEY5ubmaN++Pezs7GBmZgYrKyt89NFHaN68OX799VdERUXB3Nxck7+D2tEa4vzUnZv4\neG6+95EjgYMHgXbt1Lp7raJ+w49yw0/fc2NkBCxcyN3+OH06sHgxd5eROuh7bjRJ07lReIZEKysr\nzJ07F3PnzkV5eTny8vJw//59SCQS2NjYoH379npXDBBhbNzI3Zr488/cYjCEEP3Vvz+Qmsqt1TB2\nLPDjjwB9FOgvhYZ6LV68WGq7WbNm6NSpE3x8fNCnTx906dKlSRQGNDqWnzpyI5Fw3y5WrwbOnGk6\nhQH1G36UG35NKTfW1tyg4ubNuQXP8vNV219Tyo26aTo3ChUHaWlpmoqDGIiKCu4OhNOngXPngK5d\nhY6IEKJOzZtzi54FBAD9+gG3bgkdEVGGQsXBsWPHMHToUKxcuRLJyclNduQ/Xefip0puKiq4xVz+\n/Rc4cYL7liGvMI8wpExLwYf9PlT6+JpG/YYf5YafrufGq70XUqalYHPoZrlfIxIBn38OfPghdwZB\n2QJB13MjJJ0ac2BhYYG///4bx48fBwC0bt0aAwcOxKBBgzB48GD07Nmzpu3s2bMRHR2t3miJ3qou\nDJ4+Bfbu5b5dKELcQgxxC7FmgiOE8GrRrAV6d+it1GvffZf7d/Bg4ORJwMlJjYERjVJohsSxY8di\n9+7duHnzJuLj4xEfH4/ffvsNZWVlAABra2v4+/tj0KBB+O6775CcnKyxwJVB8xwIQ9XCgBCi32Ji\ngOXLqUAQglamTz5//jz69u0r9dikSZMwe/ZsJCYm4tSpUzhz5gyKi4shEolQVVWlcECaRMWB9jEG\nvPUWt3jLL79QYUCIoYqJAVat4sYaiekkoNZoZcnmuoUBABgZGaF3796YN28e4uLiUFhYiIsXSAQ3\nsgAAIABJREFUL8LZ2VnhYBozf/58dO/eHZ6enhg1apTUJEzLly9H165d4erqivj4eJWOQ9e5+Cma\nm2XLgPR07nbFpl4YUL/hR7nhZyi5efddbjDya68BT57I9xpDyY0yNJ0bhYqDBQsWNL5DIyN4e3vD\n29tb6aD4DB06FOnp6fjjjz/g4uKC5cuXAwAyMjKwa9cuZGRk4OjRo5g+fTok6pqFgyht+3ZgyxZu\nciNLS6GjIYQI7bPPAGdn4I031DdREtEMhQYkpqeny932448/VjiYxgQGBtb8t6+vL/bu3QsAOHDg\nAMaNGwdTU1M4OjrC2dkZSUlJMs90TJ48uWYpaSsrK3h5edXcL1pdidF2w9vVGmp/5gwwY0Yi1qwB\n2rdX/fg7Lu/Apz98isFdBiNmZoxO5aP2/ca1V0oTOh5d2vb399epeGhb/u3W3Vpj6sGpEOeLsaD/\nApX3t2WLPwIDgfHjE/Huu+p5vzHE7erHZOUrMTERWVlZUAlTgLGxMQsODmZr165l6enpjDHGJk+e\nrMgu1ObVV19l27dvZ4wxNnPmTLZt27aa58LDw9mePXvqvUbBX5coKTubMbGYsfh49e1z7bm1DEvA\nZh+Zrb6dEkIadeb2GYYlYP239FfbPgsKGOvalbHYWLXtkvBQ9nNPocsKlpaWuHXrFubOnQsPDw/Y\n29vj999/x5YtW3Dz5k2ptjNmzFCqWAkMDESPHj3q/Rw8eLCmzRdffIFmzZph/PjxvPsRiURKHR+g\n61wNaSw3lZXAhAnArFlArRM9BoH6DT/KDT9DzE27dtxaDPPmAZcv87czxNzIS9O5UeiyQlBQEHbv\n3o2cnBycPHkSJ0+eREJCAqZNmwYAsLOzg5+fH/z8/HDhwgWlAjp27FiDz//www84fPgwTpw4UfOY\nvb09srOza7ZzcnJgb2+v1PGJapYtA0xNgUWLhI6EEKLLPDyA//s/YMwY4OJFoEULoSMitSl0K2NK\nSgp8fHzqPX7r1i2pYuH+/fsauZXx6NGjmDdvHk6dOgXrWtPrZWRkYPz48UhKSkJubi4CAgJw8+bN\nemcP6FZGzUpMBMaP5xZfUfcK3evOr8Oc3+Zgtu9srBu2Tr07J4Tw+v3O7/D73g/9O/bH71N+V/v+\n33oLMDEBNm1S+64JlP/cU+jMgazCAACcnJzg5ORUcwYhPT0do0aNUjiYxsyaNQvl5eU1AxP79euH\nDRs2wM3NDWPHjoWbmxtMTEywYcMGlS4rEMXl53O3Kf3wg/oLA0JI0xUdDXh7c5cZNPCxQZSk0JkD\nRYSFhWHnzp2a2LXS5K2gao8AJdL4cvP660CnTtxKi5pw79E95PybA1tLW3Rs3VEzB1ER9Rt+lBt+\nup6bR+WPcK3gGiybWcLV2lUjxzh3jisMLl+WXnNF13MjJHlzo5UzB4pYsmSJpnZNdMz+/cClS9xZ\nA02htRUIEYYqayvIq18/bor1uXOBH3/U6KGInDR25kAX0ZgD9SsuBtzdgZ9+AgYOFDoaQoi+Ki0F\nevQAvv4aCA4WOpqmQytrK+g7Kg7Ub+5coKQE2Cz/aq6EECLT0aPAzJnAlSuAmZnQ0TQNGi0OxowZ\ng8LCQqUCq2Zqaop9+/ahhYD3q9CYA9XVzk16OuDvD2RkADY2goalE6jf8KPc8KPcSBsxAujTB4iI\noNw0RCfGHOzZs0fhHZOmjTFg9mzg00+pMCCEqM+aNYCPD/Dmm0JHYtjosgJRytGjwJw53Ok/E40N\na31ux+UdiDoXhTD3MMzvP1/zBySEAAAu3b2EqQenwqu9F7aEbtHKMRcv5m6PpsuVqtOJuxX279+P\nAwcO4OrVqygpKUG7du3g4OCAUaNGYcyYMeo8FBGQRML98UZGaqcwAID7pfeRejcVAzoN0M4BCSEA\ngNKKUqTeTYW5ibnWjrlgAeDiAnz4IeCqmbsnSSMUWluhIR999BFOnjyJoKAgfPrpp4iOjsaCBQsQ\nFBSEo0ePYpEezadL83nzS0xMxO7dQLNmwMiRQkejW6jf8KPc8KPc1NemDTB/PvD224lCh6KzdGpt\nhYZ06tQJb7/9tsznJk2ahJiYGHUdighIIgGWLgXWrQNoEkpCiKbMmgWsXMlNjNSjh9DRGB61nTnI\nzs6GRCKR+VxZWRlu376trkNpHI2O5Vdc7I8WLYCAAKEj0T3Ub/hRbvhRbmQzNwcWLPDHihVCR6Kb\nNN1v1Hbm4OWXX0aPHj3wwgsvwMrKCmZmZmCMoaCgAFeuXMGqVavUdSgiEMa4cQYREXTWgBCiee+9\nB7zwAnDrFuDkJHQ0hkWtdys8fvwYp06dwp07d1BUVIRWrVqha9euGDhwIMx0YEYLmudANSdOAFOm\nJCIz0x9GajvnJB9aW0G/UW746XputLG2Ap/ExEScOOGPggLgm2+0emidpxPzHMjLwsICwTTvZZO1\nfj239rq2CwOA1lYgRCjaWFuhITNmAN27AytWAK1bCxaGwdHaPAfXr1+Hi4uLNg7Fi+Y5UF5ODtCz\nJ3DnDiDgJJeEEAP0+uuAnx83tTJRjLKfe1r7Drh161ZtHYpowMaNwIQJVBgQQrRv+nRgwwZu3BPR\nDrWdOZgyZQoyMzN5n798+TIKCgrUcSil0ZgD5VRUAJ06AcePA/n5lBs+1G/4UW74UW74VeeGMcDD\ngysQXn5Z6Kh0g96MOfjvf/+LZcuWYfLkyTIDiYqKUteh8OWXX2L+/PkoKChA27ZtAQDLly/Hd999\nB2NjY0RHR2Po0KFqO56hO3YMcHTklmam+VoIIdomEgFTpgBbt1JxoDVMjb766ive5zZu3KiWY9y5\nc4cFBQUxR0dHVlhYyBhjLD09nXl6erLy8nKWmZnJnJycWFVVVb3XqvnXNRhvvMHYunXCxvDTnz+x\nXt/2Yqt+XyVsIIQYmNR/Ulmvb3uxKQemCBpHdjZjbdsy9vSpoGHoHWU/99R6t8LMBkaLTJs2TS3H\n+OCDD7Bq1Sq89tprNY8dOHAA48aNg6mpKRwdHeHs7IykpCT07du33usnT54MR0dHAICVlRW8vLxq\nTs1UT0dJ28+3y8qAgwf9sWqVsPHcL72P1HOpcHzoCPSHYPmgbdo2tG2TF0yQejcV5TfLkdgqUbB4\nbt5MhIMDEB/vj5AQ3cmPrm1X/3dWVhZUokpFMnfuXHb8+HGZz1VVVbGtW7ey3bt3q3IIKfv372dz\n5sxhjDGpMwczZ85k27Ztq2kXHh7O9uzZU+/18v66CQkJqgfbROzZw9jgwc+3hcrN2nNrGZaAzT4y\nW5Djy4P6DT/KDT9dz82Z22cYloD139Jf68eum5sNGxgbN07rYegkefuNsh/zKp05KC0tRQ+eSa8X\nLVqEY8eOoUuXLjAyMsLo0aPl2mdgYCDy8vLqPf7FF19g+fLliI+Pr3mMNTDIQkRT+KnFzp3AuHFC\nR0EIIdw8K4sXA6WlgKWl0NE0bSrdytihQwdER0fD09MTS5culXruxx9/RExMDPbs2YPffvtN7n0e\nO3YMly9frvfzwgsvIDMzE56enujSpQtycnLQu3dv3Lt3D/b29sjOzq7ZR05ODuzt7ZX+vapP0xi6\nigogPh6odQWHctMAyg0/yg0/yg2/urmxsQG8vYFTp4SJR5dout+oVByUlJTg77//RnBwMBISEvDT\nTz8BACoqKnDv3j14eHjAyMgInTp1UjlQDw8P3Lt3D5mZmcjMzISDgwNSU1MhFosRGhqKnTt3ory8\nHJmZmbhx4wb69Omj8jEN3fnz3HzmNjZCR0IIIZzAQO5LC9EslYoDMzMz/PTTT1ixYgVOnDiB9PR0\nAMDDhw8BAJbPzvsYGal/rqXalw3c3NwwduxYuLm5ITg4GBs2bFDpskLtgR2G7Ngx7g+xNqFyE+YR\nhpRpKfiw34eCHF8e1G/4UW746XpuvNp7IWVaCjaHbtb6sWXlJjCQe28ydJruNyqNOaj9AWxkZITm\nzZsDAKqqqqTaNTQ2QFl///231HZERAQiIiLUfhxDduwY8PnnQkfBobUVCBGG0Gsr1NWrF5CXB+Tm\nAipcPSaNUOkrfXFxMd544w0sXrwYAwcOROvWrfHkyRNs3boVxsbGuH37NhhjDc6cqIvoGiDw8CFw\n5QowYID045QbfpQbfpQbfpQbfrJyY2wMDB7MzdhqyHR6zMGKFStgbm6Oo0ePIjQ0FF26dMHChQvx\n5MkTpKenIzw8HP/5z38wePBgdcVLtCQhAXjpJUAHVtomhBApdGlB8zS6KuOFCxdw8+ZNTJgwQVOH\nUAitrSC/998HOnQAFi6Ufpxyw49yw49yw49yw48vN7ducdMo5+RoPyZdIW+/EXRthVu3buG3335D\nRUUFBg0ahJ49ewIAfH194evrq45DEC374w8gJEToKAghpL4XXgBKSoCCAsDaWuhomiaVzxwsXrwY\nq1atkqpM3nvvPXz99dcqB6duylZQhoYxoF074K+/AFtboaPh7Li8A1HnohDmHob5/ecLHQ4hBuPS\n3UuYenAqvNp7YUvoFqHDqeHnB3z2GTf+gPBT9nNPpTEH3377LQoKCpCSkoK7d+/i1q1biI+PR0FB\ngU4WB0Q+OTlA8+a6UxgA4NZWuJuKnBIDPo9IiABKK0qRejcV1wquCR2KFE9P4M8/hY6i6VKpOLhy\n5Qo2bdoEb29viMVidOnSBQEBAdi1axfS0tLUFaPW6fp9x5r255/AsytD9Rh6bhpCueFHueFHueHX\nUG569jTs4kDT/Ual4qChKYrbtm2ryq6JgBoqDgghRBcYenGgaSoVB7m5ubzPFRcXq7JrQTW1kcOV\nlUBsLDBiBODgAPTrB3z6KVBnrqoaDRUHTS036kS54Ue54Ue54ddQbjw8gIwM7v1NlkOHgKAgoHNn\n7j3vs8+A/HzNxCkEnZ7noFu3bggPD0dqairy8/ORlZWF06dP480334SHh4e6YiQqOHuWW6jku++A\nsWOB06eBVau4x0eN4lY3q+vPP7nreYQQoqtatOBmSLxxo/5zGzYA06ZxPydPAsuWcbMqdu8OrF0L\nSCTaj1fvKLXQcy0ffPABMzIyYiKRqObnnXfeUXW3GiHvr6vr66vLQyJh7MsvGbO1ZWzPHm67trIy\nxv7zH8Zmz5Z+/MkTxszNuedlESo3eSV5LCU3hd15eEeQ48ujKfQbTaHc8NP13JSUlbCU3BR2Nf+q\n1o/dWG5GjWJs507px06fZqxjR8Zu3arf/q+/GOvXj7GQEMYePFBfnEKQt98o+zGv8opIX375JdLT\n07FmzRpERUUhJSUFMTEx+Oabb1SvXIhSJBLgvfeA7duBCxeA0aOBuutQNWsGfPkl8OOP3P3C1TIy\nAGdn7nldIm4hRu8OvdGxdUehQyHEoFSvreBq7Sp0KPX07MnNyVLbV18BCxZwcyHU1a0bkJgIODoC\n/fsD//yjjSj1k9zzHBQVFeHKlSty7VQikWDWrFm4fPmySsGpmyHMc1BZCbz1FnDnDvDrr0DLlg23\nHzMGGDQImDGD296+HTh4ENi5U/OxEkKIKvbs4d6zfvmF287J4QqGrCygVauGX7t8ObBlC7dGg6Oj\npiMVjsZnSExLS0NAQIBCARHtKi8Hxo3jxhEcOQJYWDT+mlmzgHffBaZP584u3LrFnTkghBBd5+TE\nvWdV+/ZbYMKExgsDAFi8mPvyNHAgEB8PuOreiRFByX1ZoW3btggLC0NlZSUkEkmDP1VVVRg4cKAm\n49Yofbzv+MkT7m4ExoADB+QrDADuDwMAkpO5f2/d4v7g+OhjbrSFcsOPcsOPcsOvsdxUFwfVX4xj\nY7kvO/KaORNYupSbZbHu5QldpzPzHDg5OWHevHkwMmr8JSKRCJ988olKgfH56quv0L17d3h4eGBh\nrVWBli9fjq5du8LV1RXx8fEaObauKikBhg8H2rYFdu/mZjeUl0gE9O37/H7hmzcbLg4IIURXtGrF\nfRHKywOKiril5t3cFNvH5MnAunXcbY8pKRoJUy8pvbZCYWEhMjMzUVhYiMrKSlhZWcHFxQU2Njbq\njrFGQkICIiMjcfjwYZiamiI/Px82NjbIyMjA+PHjkZycjNzcXAQEBOD69ev1Cpm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"text": [ "" ] } ], "prompt_number": 3 }, { "cell_type": "markdown", "metadata": {}, "source": [ "The figure above shows the frequency response using a Hamming window to gently terminate the filter sequence. Note that the Gibbs effect is significantly reduced, producing a much flatter mainlobe at the cost of a wider mainlobe. The mainlobe widens because the mainlobe of the Hamming window is wider than that of the rectangular window. The much lower sidelobes of the Hamming window flattens the Gibbs phenomenon at the edge of the passband.\n", "\n", "I invite you to download the IPython notebook corresponding to this post and try the above for different values of $M$. Note that drop from the passband to the sidelobes steepens with increasing $M$. As we have seen before with window functions, this is because the window's mainlobe narrows with increasing sequence length. Naturally, you can use other window functions besides Hamming and change the sidelobe level and mainlobe width. The most popular window used for this method of filter design is the Kaiser-Bessel window because it provides extra parameters for tuning the frequency response.\n", "\n", "Let's consider a design example using Kaiser-Bessel and the filter design tools in the signal.fir_filter_design module." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The signal.fir_filter_design module provides functions for filter design using the Kaiser-Bessel window ( among other windows). For example, to design a lowpass filter using the Kaiser-Bessel window, we need the a subset of the following parameters: maximum passband ripple ($\\delta$), width of the transition region, Kaiser-Bessel parameter $\\beta$, and the number of filter taps. The fir_filter_design provides tools to solve for some of these parameters given others. For example, the fir_filter_design.kaiserord() function can determine the number of taps given the maximum allowable passband ripple and the width of the transition region. \n", "\n", "Consider the following low pass filter specification." ] }, { "cell_type": "code", "collapsed": false, "input": [ "Ns =300 # number of samples \n", "N = 1024 # DFT size\n", "\n", "fs = 1e3 # sample rate in Hz\n", "fpass = 100 # in Hz\n", "fstop = 150 # in Hz\n", "delta = 60 # in dB, desired attenuation in stopband" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 4 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now, we need to determine the number of tabs and the Kaiser-Bessel $\\beta$ parameter using the fir_filter_design.kaiserord() function as shown below. For the FIR window design method, the $\\delta$ parameter is simultaneously the maximum allowable passband ripple and the desired attenuation in the stopband." ] }, { "cell_type": "code", "collapsed": false, "input": [ "from matplotlib.patches import Rectangle\n", "\n", "M,beta= signal.fir_filter_design.kaiserord(delta, (fstop-fpass)/(fs/2.))\n", "\n", "hn = signal.firwin(M,(fstop+fpass)/2.,window=('kaiser',beta),nyq=fs/2.)\n", "w,H = signal.freqz(hn) # frequency response\n", "\n", "fig,ax = subplots()\n", "fig.set_size_inches((8,3))\n", "\n", "ax.plot(w/pi*fs/2.,20*log10(abs(H)))\n", "ax.set_xlabel(\"frequency( Hz )\",fontsize=16)\n", "ax.set_ylabel(r\"$20\\log_{10} |H(f)|$\",fontsize=22)\n", "ymin,ymax = -80,5\n", "ax.axis(ymin = ymin,ymax=ymax)\n", "ax.add_patch(Rectangle((0,ymin),width=fpass,height=ymax-ymin,color='g',alpha=0.3))\n", "ax.add_patch(Rectangle((fpass,ymin),width=fstop-fpass,height=ymax-ymin,color='r',alpha=0.3))\n", "ax.add_patch(Rectangle((fstop,ymin),width=fs/2-fstop,height=ymax-ymin,color='y',alpha=0.3))\n", "ax.set_title(\"Number of taps=%d\"%M)\n", "ax.text(10,-15,'passband',fontsize=14,bbox=dict(color='white'))\n", "ax.text(200,-15,'stopband',fontsize=16,bbox=dict(color='white'))\n", "ax.grid()\n", "\n", "# fig.savefig('figure_00@.png', bbox_inches='tight', dpi=300)\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "display_data", "png": 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0dOT9998nJSUFhUJBu3bt2LBhAzY2Njg7O7Njxw7+97//cenSJXx8fJg2bZpm\nAppCocDPz4/hw4czaNAgcnJyeOCBB1i6dKnm+suXL+fpp5+mffv2KJVK3n777bvugq1Xrx7r1q3j\nueeeo127dgQGBjJ37lwefPDBmmnEWvBg6Fme/zSYnMtWuDkWVn6CiWvUqBGNGzdm/vz5ZGRkYGNj\nQ+vWrVm3bh0hISGAeiGwzz//nCVLlqBSqUhLS8PHx4dffvmFqVOnMmfOHC5cuICfnx8ffvhhhU/K\nLFy4kLi4OIYNG0ZJSQmRkZF89NFH5Y4bPXo0dnZ2jB8/npycHEJDQ/nmm29wdnYG1ENkP/74I+PH\nj2fUqFG4uroSHR2Nt7c3Tz/9tNa1dO1xiI6OJj8/n/nz57N69WqCg4OJjY1l5MiRRrXypBCmTOeV\nHvPz81mwYAFr167l0KFDmqzd0dGRVq1aERwcrPVV9uFgjHRd6bFHjx4EBwdX+KF4r6nKSo+OMavp\nFl47KycOf78dXVte4Ln+/+h8Tl1d6bG6tm3bRs+ePdm6davW45OmqCorPQpRVxhspUd7e3veeOMN\nDhw4QG5uLlu3bqVhw4Y89NBD3Lhxgy+//JLx48fTrVs3XFxc8Pb2ZsCAAUyfPp0dO3aYZG+ESqXS\n24RAoV8jumWy6k9Z4VMIIWpKlaYlOzk50bNnT5RKJTExMezdu5f8/HyOHj3K2rVrmTZtGh07duTY\nsWPMmDGDLl264Orqyrhx4zSPHJqCil5cI3RXW3MYAB4IOceRdHtOn7et/GBRqXv5/4GMrRuGtLPx\nq9aqJk888YTmezMzMwICAggICGDIkCGa7VeuXOHgwYPs37+fXbt20blzZ5YsWULfvn2rU7VB/P77\n77UdgqgiK0sVAzueI263BxMGnqrtcExa9+7dTbKHUAhRs6r1sPrzzz9f6TEODg507tyZ8ePHM2PG\nDP766y/Nm+OMUVFJUW2HYHSq2ia1sQ7DrR687yxxu+vm45WlpfJ7ereq2mayPoBhSDsbv+qvm3oX\nwsPDMTc3L/cYljHZmHr7hW6EaYloe55RC0K4lG+Bs31x5SeYkNxc+T0VQhiWQZfDGzduHK6urgwe\nPLja13r11VcJDAykTZs2DB48WOvNdbNnz8bf358WLVqwefPmatclqqY25zAA2NuW0K3lBTbsq7tv\nsJRxX/2TNjYMaWfjZ9CEYdq0aRw8eLBGEoY+ffpw+PBhDhw4QEBAgOYNd8nJyaxZs4bk5GQ2btzI\nuHHjtJZ+N5p+AAAgAElEQVRBFveWujwsIYQQhmSyC+5HRERo1p6/7777NEsox8XFMXz4cCwtLTXv\nv0hISKjNUO9ZtT2HAWBQaDab9rlTXFI3Z/nLuK/+SRsbhrSz8at0DsOFCxewtbXVepthTfjnn39o\n3LhxjVxr+fLlDB+uXnAnKytL622LXl5e5d6mB7BgygI8lOo/aHYOdjQJbEJwqPoXNilB3TUm5eqV\nO6O2LUld7h4cbPByw/oFuDhs4bONaTw/wPeOx/v7qeMt6xot+wCTspSlLGVTLMfHJxEb+ysA3t7V\nv4GrdKXH7OxsXnjhBT766KMKX1tbFWvXruXXX3+t9PW7ERER5d6QBzBr1iwGDVKvdDdz5kz27dvH\nd999B8CECRMICwtj5MiRAIwdO5b+/ftrDYPcaaVHUXNOzljAi8Nequ0weGV5EE71inhzaModjzOl\nlR7LxMcnyZ2ZnkkbG4a0s/5Vd6XHSnsYPDw8mDVrFkOGDOGpp55i1KhRVV7EJSMjg5kzZ5Kfn88X\nX3xR6fFbtmy54/6YmBjWr1/Pr7/+qtmmVCpJT0/XqvO/r98V95aItueZuda/0oRBCCHE7ek0h6Fp\n06b88ssv/PnnnwQEBDBr1iwSExN1ylTy8/PZsGEDY8aMoV27drRu3ZoVK1Zovdq2KjZu3Mj7779P\nXFyc5vW9AJGRkcTGxlJYWEhaWhopKSmEhoZWqy5RNcYwhwHg/pa57D/pRP5189oOpcbJHZn+SRsb\nhrSz8dP5r7aTkxPLli1j3759vP/++7z77ruYm5vTsWNHvLy8cHZ2xsnJicLCQnJzc8nNzSUtLY2D\nBw/i7u7Ok08+yeHDh3F3d6+RwCdMmEBhYSEREREAdOrUicWLFxMUFERUVBRBQUFYWFiwePHie3pZ\nWwF21iV0bHaJPw65MqDjudoORwghTJLOb6v8r8uXL7N161Z27NjBkSNHyMzM5OrVq5ibm+Ps7Iyv\nry+tW7fm/vvvp3PnzponGoyBzGEwDGOZwwAwe20zsi9Zs+Cpw7c9RuYwiIpIGxuGtLP+6X0OQ5kt\nW7Zo7uZB/VrrwYMH18iaCkLoW7dWF5jweavaDkMIIUyWzrf9r7zyij7jEHWQscxhAGjfLI9jmfZ1\nbh6D3JHpn7SxYUg7Gz+dE4asrCxZMVGYLGvLUtr65bH7eP3aDkUIIUySzgnDhQsXaNKkCWPHjmXl\nypUVLoYkxK1q+10S/9U58CLxR+pWwiDr7+uftLFhSDsbv7uaiXj69GmWL1/OqFGj8PHxwd/fn6ee\neopVq1aRlZVV4TnR0dE1EqgQ1RUemMuOoy61HYYQQpgknRMGPz8/0tPTWbp0KUOGDMHR0ZETJ06w\nbNkyHnvsMby9vQkICOCZZ55h9erVnDlzBoCdO3fqLXhh3IxpDgNAeIuL7DpWn5KS2o6k5si4r/5J\nGxuGtLPx0zlhaNCgAUqlkujoaNauXUtOTg5//vknSqWSrl27YmNjQ2pqKkuWLGHkyJF4eXnRrFkz\nUlNT9Rm/EDpzdyrEw7mAw+kOtR2KEEKYHJ0Thm3btmmVzc3N6dKlC15eXmzbto28vDz27NnDwoUL\nGTp0KF5eXpw8eVImSt7DjG0OA0B4i1x2Hq078xhk3Ff/pI0NQ9rZ+Om8DoO1tfWdL2RhQfv27Wnf\nvj0TJkwAICUlhbZt21YvQiFqUPumeew74Qycru1QhBDCpOjcwzBixIi7vri/vz9+fn53fZ6oG4xt\nDgNAu6Z57DvhVNth1BgZ99U/aWPDkHY2fjonDPv3769SBaNGjarSeULoQxu/yySn21NULO8XEUKI\nu6FzwpCWlsb333/P9evX76qCyZMn33VQunjzzTdp06YNbdu2pVevXlqvtJ49ezb+/v60aNGCzZs3\n66V+UTljnMNQz6YEH/frHMmwr+1QaoSM++qftLFhSDsbP50ThsLCQh555BFcXFzo06cP8+fPJzk5\nudLzEhMTqxXg7UyePJkDBw6QmJjIQw89xPTp0wFITk5mzZo1JCcns3HjRsaNGycTL4WWujYsIYQQ\nhqDzpEcbGxuGDh3K9u3b2bp1K1u3buWVV17BysqKESNG0KlTJ8LDw2nbti3m5jfX64+Ojmbfvn01\nHriDw81H4/Lz83FzcwMgLi6O4cOHY2lpia+vL82aNSMhIYGwsDCt8xdMWYCHUj3GbudgR5PAJgSH\nqsfQkhLUma6Uq1fu/O8chm1J6nL34GCjKDvZbeXnBCue6OWgtd//3+k2ZXc6ZWOqxlzu3DnYqOKp\ni+WybcYSj5SlrGs5Pj6J2NhfAfD2rv6cMp1fb926dWsOHjwIQEZGBtu2bWPbtm38/vvvpKWlaY6z\ns7OjQ4cOhIeH07FjR5555hnOnTtX7UAr8vrrr7NixQpsbW1JSEjAycmJCRMmEBYWxsiRIwEYO3Ys\n/fr1Y8iQIZrz5PXWhuEYs5pu4cb3uujfDrry1qrmbH9vh9Z2U3y9tRBC6Kq6r7fWeUji6aef1nzv\n5eXFY489xtKlSzlx4gT//PMPX375JWPGjKFBgwb8+eefvPfeewwZMoQLFy5UObiIiAiCg4PLff38\n888AzJw5k9OnTzNmzBheeuml215HoZAJbrXBGOcwAIQ0ucyBNEfqwkiVjPvqn7SxYUg7Gz+dhyTG\njx9/233e3t48/vjjPP7444D6nRPbtm1jw4YNrFmzpsrBbdmyRafjRowYQf/+/QFQKpVaEyAzMjJQ\nKpVVjkHUPfXti3BxKOLE2Xr4e16t7XCEEMIk3NXLp3Tl4+PDqFGjWL16NT4+PvqogpSUFM33cXFx\nhISEABAZGUlsbCyFhYWkpaWRkpJCaGioXmIQd2aM6zCUCfK+wpF0039SQp5d1z9pY8OQdjZ+Ovcw\nVJWrq6terjtlyhSOHTuGubk5TZs25ZNPPgEgKCiIqKgogoKCsLCwYPHixTIkIcoJ9MrnaIY9kfcZ\n57CJEEIYG70nDOvXr9fLdb/99tvb7ps6dSpTp07VS71Cd4mns+kWXttRVKyFVz47j5n+OyVunb0v\n9EPa2DCknY2fXoYkbuXhYbzd0uLe1cIrv04MSQghhKHoPWEQ9y5jnsPQ4t8hiWo8YWQU5I5M/6SN\nDUPa2fhVOiSxYMEC8vLyarRSJyenOz4GKYS+uTsVYm6m4lyeFR7OhbUdjhBCGL1KEwYfHx+uXLlS\no5XeukqjqLuMeQ4DlA1LOODhXPW1QmqbjPvqn7SxYUg7G79KE4bBgwcbIg4hDK5sWKJ7sOkmDEII\nYSgyh0HojTHPYQAI9M43+bdWyh2Z/kkbG4a0s/HTa8JQXFzMxYsXuXbtmj6rEaJKWijVPQxCCCEq\nV+MJw7p163j00Udxc3PDysoKV1dX7O3tcXFxoX///vzyyy81XaUwUsb6LokyZUMSpkzW39c/aWPD\nkHY2fjW6cNOiRYv45ptvePjhhxk6dCj16tXDysqK/Px8rly5QkpKClOnTuXEiRO88MILNVm1EHfN\nx/06Zy9aU1ikwMrSxJ+vFEIIPavRhOH06dNs3779jse89dZbTJo0qSarFUbK2OcwWFqoaORSwOnz\ntjTzNM1hMxn31T9pY8OQdjZ+NTokoctbIc3MzPD09KyxOufNm4eZmRm5ubmabbNnz8bf358WLVqw\nefPmGqtL1D1NPK6Rds6utsMQQgijV6MJQ2pqKjNnzuTIkSNcv35da19hYSHHjh1j1qxZHDp0qEbq\nS09PZ8uWLTRu3FizLTk5mTVr1pCcnMzGjRsZN24cpaWlNVKfuDvGPocBwM/jGmnZppswyLiv/kkb\nG4a0s/Gr0YRh7ty5ZGdn07FjR+rVq4e5uTm2traar7CwME6ePMmiRYtqpL5JkyYxd+5crW1xcXEM\nHz4cS0tLfH19adasGQkJCTVSn6h7mjS8atIJgxBCGEqNzmGws7Pjo48+4r333uPYsWNkZ2eTm5uL\ng4MDjRo1om3btlhY1EyVcXFxeHl50bp1a63tWVlZhIWFacpeXl5kZmaWO3/BlAV4KNVj7HYOdjQJ\nbEJwqHoMLSlBnelKuXrlzv/OYdiWpC53Dw42urKfx3WWbD7JtqTj+PsB3LzTKRtTNeZy587BRhVP\nXSyXbTOWeKQsZV3L8fFJxMb+CoC3d/XnlClUKsO/fmfdunUMHDiw0uMiIiI4e/Zsue0zZ85k1qxZ\nbN68GUdHR/z8/Ni7dy+urq5MmDCBsLAwRo4cCcDYsWPp37+/1oqVCoWCn47+VHM/kKiQY8xquoUP\nr+0w7mjHkfpMXNaS3R/8RWb+aqwjjDteIYSoKnf3SKrzJ79WVnr84YcfdDpuy5YtJCUllftq0qQJ\naWlptGnTBj8/PzIyMmjfvj3Z2dkolUrS09M118jIyNBpMqaoeaYwh8HL7QaZF2xqO4wqk3Ff/ZM2\nNgxpZ+NXo0MSzz//PNevX79tBqNQKFCpVMTFxbFs2bIq19OqVSuys2/+MfLz8+Pvv//GxcWFyMhI\nRowYwaRJk8jMzCQlJYXQ0NAq1yXqtkb1b3Auz5riEkVthyKEEEatRnsYOnXqpHkCoqKkQaVSVas7\n5HYUipsf9kFBQURFRREUFES/fv1YvHix1n5hOMa+DgOo12JwdyzgTK51bYdSJfLsuv5JGxuGtLPx\nq9EehpEjR5KYmMgHH3xwx+OefPLJmqyWkydPapWnTp3K1KlTa7QOUXd5ud0g44ItPl61HYkQQhiv\nGu1hUCgUOnX/P/zwwzVZrTBSpjCHAcDL9QYZOaY5j0HGffVP2tgwpJ2NX41PeoyKiqr0GF2ekBDC\nULzdrpOeY1vbYQghhFGrVsLw/vvvs3///kqPO3r0KHFxcVy6dKk61QkTYwpzGAC83K6TYaJPSsi4\nr/5JGxuGtLPxq1bC8PXXX1NYWHjHY5YuXUqrVq148sknue+++7h2zTRf8iPqLk+XArJyTTNhEEII\nQ6lWwtC7d28CAwP5+OOPiYmJoaCgQGt/QUEBr7zyCq+//jo5OTmMHTuWzz77rFoBC9NhKnMYPJwL\nOHfJNJ+SkHFf/ZM2NgxpZ+NXrYShefPmtG7dmgkTJhAdHU14eDg3btzQ7P/777+5fPmyZl7DpEmT\n2LFjR/UiFqKGNXAqINtEEwYhhDCUaiUMu3fvJjIyknXr1vHtt9/i6enJxx9/rNl/+vRpAHx9fQEw\nNzfHxka6fu8VpjKHwcO5gHN5VrUdRpXIuK/+SRsbhrSz8avWOgwlJSV89NFHmnJkZCRjxozRlMvm\nK9SrV0+zTRIGYWxcHQq5dNWS4hIzpJ9BCCEqVq0eBisr7bsyCwsLHBwcNOXS0tJy51y/fr06VQoT\nYipzGMzNwcW+iAuXHWs7lLsm4776J21sGNLOxq9aCUN2djY//fQTN27cIDc3l48//hg3NzfN/vPn\nzwNw5coVQN3jkJ+fX50qhdALD+cCk0wYhBDCUKo1JDFp0iQiIiIoLi5GpVLh5ubGyJEjWbJkCcnJ\nySxbtoxevXqxaNEipk6dysKFC+nSpUtNxS6MnKnMYQBo4FzA+Tyn2g7jrsm4r/5JGxuGtLPxq1YP\nQ9euXdmwYQMDBw5k9OjR7N69m+nTp+Pt7U337t1JTk7m559/ZtWqVbi5ubF06VKeffbZGgn87bff\nxsvLi5CQEEJCQtiwYYNm3+zZs/H396dFixZs3ry5RuoTdZv0MAghxJ1V++VTPXv2pGfPnlrb+vbt\nq1WOj4/nt99+o2vXrtjb21e3SkD93opJkyYxadIkre3JycmsWbOG5ORkMjMz6d27N8ePH8fMrMZX\nwRaVSDydTbfw2o5CNw2cCk2yhyE+PknuzPRM2tgwpJ2NX429rfLcuXPs3buXwsJCWrduTZMmTTT7\nnJyc9PLCqYpelR0XF8fw4cOxtLTE19eXZs2akZCQQFhYWI3XL+oON8cCsq/UTDIrhBB1UbUThsuX\nL/PCCy+watUqiouLAfXdf//+/Vm+fDnu7u7VDvJ2Fi1axFdffUWHDh2YN28ezs7OZGVlaSUHXl5e\nZGZmljt3wZQFeCjVY+x2DnY0CWxCcKg6u01KUM/WlXL1yp3/ncOwLUld7h4cbLTl83nnuXzDCyjQ\nzNYuu9sx5nLnzsFGFU9dLJdtM5Z4pCxlXcvx8UnExv4KgLd39eeUKVQV3abr6Pr169x///1cvXqV\nsLAwnJ2duXbtGmfOnOHPP/+kUaNG7Nmzp8rDEBEREZw9e7bc9pkzZxIWFqZJRt58803OnDnDsmXL\nmDBhAmFhYYwcORKAsWPH0r9/fwYPHqw5X6FQ8NPRn6oUk9CdY8xquoUPr+0wdPL1NiXf7b7G5z9e\nrO1QhBBCL9zdIyvsmddVtXoY3n//fYYMGcKUKVPK7SsqKmLBggXMnj2bmTNnVun6W7Zs0em4sWPH\nMmjQIACUSiXp6emafRkZGSiVyirVL6rHlOYwONcr4lK+PWBaCYOM++qftLFhSDsbv2rNBDx06FCF\nyQKApaUlr776KseOHatOFbd15swZzfc//PADwf92L0dGRhIbG0thYSFpaWmkpKQQGhqqlxhE3eFc\nr4jL1+xqOwwhhDBa1ephcHFxqfSY/64GWVNee+01EhMTUSgU+Pn5ad6CGRQURFRUFEFBQVhYWLB4\n8WIUCoVeYhB3ZkrrMDjbm2bCIHdk+idtbBjSzsavWglDbm5upcdcvny5OlXc1ldffXXbfVOnTmXq\n1Kl6qVfUTc71irl8tV7lBwohxD2qWkMSLVq0YO7cuRXuKykp4fXXX6dNmzbVqUKYMFN5lwSohyTy\nTLCHQdbf1z9pY8OQdjZ+1ephmDx5MuHh4cTExBAeHo6zszNFRUWcOXOG7du34+TkxJ49e2oqViH0\nxs66hOIScwoKzLC2Lv/SNCGEuNdVK2Gwt7dn27ZtjBs3juXLl2vt69evH8uXL9d6e6W4t5jSHAaF\nAhztrnH5sgXu7oW1HY7OZNxX/6SNDUPa2fhVe+EmFxcXYmNjmTdvHgkJCZSWltKmTRuaNWtWE/EJ\nYTDqhMHSpBIGIYQwlBp7wYJSqeThhx9myJAhWsnCvHnzaqoKYWJMaQ4DgFO9q+TlWdZ2GHdFxn31\nT9rYMKSdjZ9e38ikUqn48MMP9VmFEDXG0e6aySUMQghhKDoNSXz00Ud8+OGHKBQKnZeVVCgUXLt2\njfPnz1crQGG6TGkOA4CjCfYwyLiv/kkbG4a0s/HTeQ5DdnY2Dz74INbW1jpfPD8/n++//75KgQlh\naHbWBVy7ZlPbYQghhFHSKWFwdXXlqaeeYuHChXddQYsWLe76HFE3mNK7JACsLIopLNTrKF2Nk/X3\n9U/a2DCknY2fTglDjx49aNu2bZUqWLRoUZXOE8LQrCyLTC5hEEIIQ9EpYfD09MTT07PCfdeuXSMv\nLw8bGxscHR0xNzfX2h8REVH9KIVJMrU5DNYWxRQUmFbCIHdk+idtbBjSzsbvrj8d//rrL8aOHUuL\nFi2wtbXFwcEBLy8v3NzcsLW1pXnz5owdO5Y//vhDH/FqWbRoEYGBgbRq1YrXXntNs3327Nn4+/vT\nokULNm/erPc4RN0gPQxCCHF7Ok96LCkpITo6mhUrVgDqeQ2NGzfGxsYGhULB1atXyc/PJyMjg+XL\nl7N8+XIef/xxli5diqVlzc88//333/npp584ePAglpaWmqcxkpOTWbNmDcnJyWRmZtK7d2+OHz+O\nmZn8ITA0U5zDYGo9DDLuq3/SxoYh7Wz8dE4YZs+ezaFDh1i1ahURERG4urpWeJxKpeLUqVP8/PPP\nLFq0iLfeeotZs2bVWMBlPvnkE6ZMmaJJRtzd3QGIi4tj+PDhWFpa4uvrS7NmzUhISCAsLEzr/AVT\nFuChVHeZ2znY0SSwCcGh6l/WpAT1AiJSrl657N2P25LU5e7BwUZdtrL0Ja/QjPj4JEpKFNSvH05w\n8GXNgjJlH2ZSvrfKhw6dNKp46mq5jLHEUxfK8fFJxMb+CoC3d/WHiBUqHRdWiIyM5Ntvv8XKykrn\ni1+5coXIyEh+//33Kgd4OyEhITz44INs3LgRGxsbPvjgAzp06MCECRMICwtj5MiRAIwdO5Z+/fox\nZMgQzbkKhYKfjv5U4zEJbY4xq+kWPry2w9DZjG9zSbfqyuzZh1iyxI/p0wNJTNyKm5ssFS2EMH3u\n7pE6r6VUEZ17GBo3bnxXyQKAg4NDtR6rjIiI4OzZs+W2z5w5k+LiYi5evMiuXbvYs2cPUVFRnDx5\nssLrKBSKKscg7h1lQxLFxQrmz/cnJOQSX3/tw4svptZ2aEIIUet0HrA9efIkRUVFd3Xxa9eukZpa\n9Q/bLVu2kJSUVO4rMjISLy8vBg8eDEDHjh0xMzMjJycHpVJJenq65hoZGRkolcoqxyCqztTeJVE2\n6TEnxwozMxWvvXaMjRuN+0kPWX9f/6SNDUPa2fjpnDB06NCBTp06sWbNGi5dunTHY2/cuMEPP/xA\neHg47dq1q3aQFXnooYf47bffADh+/DiFhYW4ubkRGRlJbGwshYWFpKWlkZKSQmhoqF5iEHVLWQ9D\ndrYNDRoUEBh4hePHHahGD54QQtQZOg9JvPnmm5w5c4bhw4ejUChwc3PD1dUVW1tbzdoLKpWKS5cu\ncerUKUpKSujfvz8zZszQS+DR0dFER0cTHByMlZUVX331FQBBQUFERUURFBSEhYUFixcvliGJWmJy\n6zD828Nw7pw1Hh43cHUtxMqqlOxsaxo2LNA6dvPmBly6ZElUVGYtRasms8r1T9rYMKSdjZ/OCYOF\nhQWff/45o0ePJiYmhj/++IOUlBRKSko0x9ja2uLn58dLL73Egw8+SJcuXfQSNIClpaXmEc//mjp1\nKlOnTtVb3aJuKuthOHfOmgYN1AlCQIC6l+HWhOGPP9yYPDmYkhIF7u6F9OghL1gTQtR9OicMZTp3\n7kznzp0BKC4u5tKlS9y4cQNnZ2fs7e1rPEBhukxuHYZ/exjKhiQAAgLyOXbMnq5dczTHrVjhwwsv\npOLqWsj//te0VhMGeXZd/6SNDUPa2fhVa5UaCwsL3Nzc8PLykmRBmLyyl0+VDUkA+Pvnc+LEzd/t\nq1fN+fXXBgwenEVExDn273cmN9e0XokthBBVcVcJQ2lpKZ988gk9evQgKCiIyMhIfvqp/HoGI0eO\nZPTo0cyaNUteb30PM8U5DAUF5lpDEh4eNzh37uYr3Y8dc8DP7yrOzkXY2ZXQrVsOmzbV3s8pd2T6\nJ21sGNLOxk/nIYnS0lIGDRrEhg0bNNuOHj3KunXriIqK4quvvtKs0/D1119z4cIF2rRpw5kzZ7Tm\nOQhhrLQnPaoTBlfXQnJybiYMR486EBh4RVMOC7vA/v31GT48o9z10tNteeqp9iiV11m4MBF7e/l/\nIIQwXTr3MCxevJiNGzfyyCOPsHLlSjZt2sSSJUvo1asX33zzDQ8++CDFxcWa411dXXF2dtZL0MI0\nmOI6DLc+VgnqhOHChZsLlh054kCLFjcThpYtL3P4sGOF13v11db06HGO0lIFH3/cVC8xy7Pr+idt\nbBjSzsZP5x6GL774gsWLF/PMM89obX/yySfZuXMnY8aMYeTIkaxZs6bGgxTCEMrmMOTlWeLiol4O\n2tW1QCthOHrUgW7dbk6AbNnyMsnJDpSWwq3vNzt1yo79+5344os9nD9vTa9eXXn++RPSyyCEMFk6\n9zBcvXq1XLJQplOnTuzbtw/gtseIe4+pzWGwsizixg1z8vMtcHBQr2rq4lLEpUuWlI2qHTvmQPPm\nN3sY6tcvwsmpiH/+sdO61o8/ejJ4cBa2tqX4+Fyndes8/vrLrcZjlnFf/ZM2NgxpZ+Onc8Lg4XHn\nD387OztiY2NxdnZm/Pjx1Q5MCEOztigmN9cSe/ti/l2LDAsLFY6OxVy8aIVKBefPW9Ow4Q2t8wID\nr3D0qIPWtr//rk+nThc05d69z7Fly+3/D/3+uzshIb148sn2FBXJQmNCCOOjc8LQsmVL9u7dC0B8\nfDyffvppucmMCoWCOXPm0KpVK15++WVZYfEeZ4pzGEpKzHBy0n5nStmwxOXLFtjalmBpqb1WtLf3\ndTIzbTVllQr27XOmXbubS6j36nWO3393r7DeS5csGT++LXPnJnH1qgULFvjrHLOM++qftLFhSDsb\nP50ThnfffZfJkyfz3XffMWDAAJ5//nm++eabCo999tln6dmzJ//880+NBSqEvllZqCftlk8Y1BMf\nL1ywwtW1/KuuPT2vc+aMjaaclaX+Xqm8rtnWrFk+Fy9aculS+TUbfvqpEWFhuUREnGPGjMPExDSm\nsFCSbSGEcdE5YXBxceHHH38kMTGRpk2bEhoaqlnxsSIDBgxg27ZttGzZskYC/a9hw4YREhJCSEgI\nfn5+hISEaPbNnj0bf39/WrRowebNm/VSv6icqc1hsDAvQaFQ4eionTC4uakfrczNtdJMhrxVw4Y3\nyMq62cNw4IAzbdrkcWsHm5mZeujiyBGHcud//72SwYPV76QICMjH3z+fzZtv33YlJTB/vj/TpwfS\nrl2bu/0xxV2SsXXDkHY2fne1NLSjoyPvvPMO77zzjk7Ht2vXjoMHD1YpsMrExsZqvn/llVc0j3Am\nJyezZs0akpOTyczMpHfv3hw/fhwzs2otainuAQoFWFuX4uxccQ+DrW1JhQmDp+cNrR6G06dt8fW9\nWu64oCD1I5idOuVqtl25YkFiojO9ep3TbOvb9yx//OHOwIFnK4xz7tzmxMe74upayIQJbVm6dN9d\n/6xCCHG3TP6vqEql4ptvvmH48OEAxMXFMXz4cCwtLfH19aVZs2YkJCTUcpT3JlObwwBgZVVabkjC\n2bmQvDxLLlyouIfB0/O6ZhgCIDPTVms4okxQ0GWSk7XXbDh0yJHAwMvY2JRqtoWH57Jjh2uF8V2+\nbMHSpX4sW/Y3n3++jz/+OMzRo7Isuz7J2LphSDsbv7t++ZSx2b59Ox4eHjRtql4YJysri7CwMM1+\nLwajJU0AACAASURBVC8vMjPLv4J4wZQFeCjV3b52DnY0CWxCcKi6SywpQf2LK+Xqleuhti1JXe4e\nHGzUZX8/dQ9Dfv5fxMef0nSRnj27i/PnVVhZtcfFpVDzwVa2/9SpBDIzVahU6l6Kgwf3Y2+fCzQC\nbn4QBga68N13XlrnHzjgRIMGm4iPT9NcLy/vLzIyCjl3zooGDbTri4vzpGXLn0hNPUbnzsH063eW\nd9+14rnnTmrO/298H3yQyTffeDF4cACTJx9j507t/f89Xsra5UOHThpVPHW1XMZY4qkL5fj4JGJj\nfwXA27v6Q8QKlUqlqvyw2hEREcHZs+W7ZWfNmsWgQYMAeO655wgICGDixIkATJgwgbCwMEaOHAnA\n2LFj6d+/P4MHD9acr1Ao+Olo+XdgiJrlGLOabuHDazsMnWXmr+a+V5cycmQ6r756XLN9/nx/btww\no7RUgb19MS+9lFru3KZN+7J376/Ur19E375dmDHjMKGhF7WOOX3alsjIcBITf9Vse+65EO6/P4cR\nI9K1jo2Kuo+xY9Po0+ec1vahQ+/j8cf/0QxXnDxZj4ce6sSBA1up6KGk06dtiYi4nwULDvD++wE8\n/XQaw4aVX8ZaCFH3ubtHUp0/+Ubdw7Bly5Y77i8uLuaHH37QLBoFoFQqSU+/+eGbkZGBUqnUW4yi\nbrGyKj+HwdKylCtXLMjLs8Tb+1qF5zVqpJ7HUL9+EZmZNhUOSTRseIPz5621VoVMSnJi3LgT5Y71\n988nNdVeK2EoLYW9e+vzv//t12zz87uKQqFOHJo2LT9vYvHipowe/Q/9+mVTv34R48aF8MgjmVhY\n3P5D48gRB+LjXRk06IzmnRpCCGHScxi2bt1KYGAgnp6emm2RkZHExsZSWFhIWloaKSkphIaG1mKU\n9y5TnMNgbV1a7ikJS8tSCgvNbvuUBICjYxFXrlhQVKTgwgXrCv/QWlmpcHIq5vx59cusVCp1D4Cf\nX/k/9P7++aSkaM9NSEmxx8WlEHf3mzHs2JFE1645/Pln+VUkS0rg558bMWyYOoEOC8ulfv1CEhLq\n3/bnP3zYgYcf7sRff7kRFRXG9esm/RFRI2Rs3TCknY2fSX8arFmzRjPZsUxQUBBRUVEEBQXRr18/\nFi9eLAtICZ1VNOnR0lJFUZE6YahoHQYAe/tirl614OxZG9zdC257B9+w4c01Gy5dssTSUlXh+yUq\nShj27q1Phw4Xyx0bFnaBvXvLJwG7drnSsOENmjS52SvSr99ZNmxoWGFsAO+/35yJE1P44ou9NGly\nlSVL/G57bJkDB5xYu1aJvJRWiLrNpBOGL774gqeffrrc9qlTp5KamsrRo0d54IEHaiEyAaa3DgOA\ni0thuaWfraxKKSxUcOWKxW1fHlWvXgn5+RacO2etedNlRcqGLkC9wFNFQxegXujpxAnthOHQISfa\ntLmkta1z52CaN7/CsWPl13fYvduFrl1ztLY98EA2mzZV/O9y+rQtu3a58Pjjp1Eo4PnnU1m50oc7\nDXn++acbw4bdx/Llvjz1VPvbH2jCZH0Aw5B2Nn4mnTAIUdNWr06gbds8rW2WlqUUF5tRVGSGlVXF\nCYO9fTH5+RZcvWqBvX1xhceA9poNWVm2eHreqPC4Bg0KKCw04+LFmytD/vOPHY0bl59DERCgnu9Q\nWqq9PTHRibZttROMli0vc/68tdZ1y/z6awN69TqHnZ36Z2zf/hJWVir27Kl4CKO0FF5+uTWLFiUS\nF7eDQ4ecKhwa+e85CxY0Y/r0QPLzze94rBDCuEjCIPTGFOcwVDSUoO5hMKOw0Awrq9IKziobkjDn\n2jVz6tW7fcLQqNHNVSGzsmxo1KjiHgaFovyS06dPl08Y4uOTcHQsxsmpiPR0W619iYnO5RIGMzNo\n1eoySUlO5er8/Xd3evQ4rxVDz57niI+veE2InTtdsbcvpnfvc1hZqZg48TiffXbnIYx33w1k69YG\nZGbaEh3d4Y69F2UKCsxq9YVcMrZuGNLOxk8SBiEqYWGhnsNQUGCGtXXFCUO9euo5DFevWmju0CvS\nsOENsrNv9jDcbkgCwN29oNwESR+fip/SaN78CseP3xyWyM625sYNc3x8yl+/des8Dh7UThhKSuCv\nv9zo1u281vZOnS6wc2fFCcO33yoZMuTmGif9+59lxw7X2/YcnD9vxVdf+RDz/+2daVRUV7bH/7eg\nKKBkFChQkEJGSxBKEdDn0IjGNkbikGiUIIrDisY2Melo2+89JyIGTUwkHROJQkzyFKKuBDVKpJVS\nDCga1KgocWBGZplkrKrzPlRXwbUmVBCI57cWH+rUufeeu3XV3fe/99n7m8v48stsFBebaC1QpeS3\n3yzh7z8J3t5TkJFhrXMuhULpWajDQOkx+mMOgya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"text": [ "" ] } ], "prompt_number": 5 }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Example\n", "\n", "In the following, let's consider the performance of the filter with two equal-amplitude single-frequency tones, one in the passband and one in the stopband." ] }, { "cell_type": "code", "collapsed": false, "input": [ "# two-tone example using filter\n", "\n", "t = arange(0,Ns)/fs\n", "x = cos(2*pi*30*t)+cos(2*pi*200*t)\n", "X = fft.fft(x,N)\n", "\n", "y=signal.lfilter(hn,1,x)\n", "Y = fft.fft(y,N)\n", "\n", "fig,ax = subplots()\n", "fig.set_size_inches((10,4))\n", "ax.plot(arange(N)/N*fs,20*log10(abs(X)),'r-',label='filter input')\n", "ax.plot(arange(N)/N*fs,20*log10(abs(Y)),'g-',label='filter output')\n", "ax.set_xlim(xmax = fs/2)\n", "ax.set_ylim(ymin=-20)\n", "ax.set_ylabel(r'dB',fontsize=22)\n", "ax.set_xlabel(\"frequency (Hz)\",fontsize=18)\n", "ax.grid()\n", "ax.annotate('attenuated in\\nstopband',fontsize=16,xy=(200,32),\n", " xytext=(50,3),textcoords='offset points',\n", " arrowprops=dict(arrowstyle='->',lw=3),\n", " )\n", "ax.legend(loc=0);\n", "\n", "# fig.savefig('figure_00@.png', bbox_inches='tight', dpi=300)\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "pyout", "prompt_number": 6, "text": [ "" ] }, { "output_type": "display_data", "png": 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scEDCxo0bufnmm0lJSQHgiy++IDs7m8cff5yioiK6d+/Oww8/zN13333ScyYk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\n8r5LEVpbW9HU1AQAaGlpwaZNmzBhwgRr+68bkjF6n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"text": [ "" ] } ], "prompt_number": 6 }, { "cell_type": "markdown", "metadata": {}, "source": [ "The figure above shows the frequency domain input and the corresponding filtered output. Because second tone is in the stopband, and its relative energy is approximately 40 dB, it is completely extinguished by the filter, whose attenuation in the stopband is 60 dB. I invite you to download the IPython Notebook corresponding to this section and try different amplitude values for the tone in the stopband." ] }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Summary" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The window design method is the easiest FIR design method to understand and it draws upon intuitions regarding window function that we have previously developed. The Kaiser-Bessel method is widely used because it provides design flexibility and easy-to-understand filter specifications. Furthermore, there are many closed form approximations to the various derived terms (e.g. $\\beta$, $M$) which means that time-consuming iterative algorithms are not necessary and that engineering trade-offs appear explicitly in a formula.\n", "\n", "In the next section we consider Parks-McClellan FIR design that solves for the desired filter sequence using a powerful iterative exchange algorithm that generally results in filters with fewer taps for the same level of performance." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "As usual, the corresponding IPython notebook for this post is available for download [here](https://github.com/unpingco/Python-for-Signal-Processing/blob/master/Filtering_Part2.ipynb). \n", "\n", "Comments and corrections welcome!" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "References\n", "---------------\n", "\n", "* Proakis, John G. ,*Digital signal processing: principles algorithms and applications*. Pearson Education India, 2001.\n", "\n", "* Oppenheim, Schafer, \"Discrete-Time Signal Processing\", p.475-476." ] } ], "metadata": {} } ] }