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 {
		   "cell_type": "markdown",
	   "metadata": {},
	   "source": [
       "# Chapter 5: Frequency Domain Analysis"
	   ]
	},
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 5.1: Sinusoidal_plots_for_increasing_frequency.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"// Sinusoidal plots for increasing frequency\n",
"// 5.1\n",
"\n",
"exec('stem.sci',-1);\n",
"\n",
"n=0:16;\n",
"subplot(2,2,1), stem(n,cos(n*%pi/8))\n",
"xgrid,xtitle('','n','cos(n*pi/8)')\n",
"subplot(2,2,2), stem(n,cos(n*%pi/4))\n",
"xgrid,xtitle('','n','cos(n*pi/4)')\n",
"subplot(2,2,3), stem(n,cos(n*%pi/2))\n",
"xgrid,xtitle('','n','cos(n*pi/2)')\n",
"subplot(2,2,4), stem(n,cos(n*%pi))\n",
"xgrid,xtitle('','n','cos(n*pi)')\n",
""
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 5.2: Bode_plots.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"// Bode plots for Example 5.7 on page 141\n",
"// 5.2\n",
"\n",
"exec('label.sci',-1);\n",
"\n",
"omega = linspace(0,%pi);\n",
"g1 = 0.5 ./ (cos(omega)-0.5+%i*sin(omega));\n",
"mag1 = abs(g1);\n",
"angle1 = phasemag(g1);\n",
"g2 = (0.5+0.5*cos(omega)-1.5*%i*sin(omega)) ...\n",
"   * 0.25 ./ (1.25-cos(omega));\n",
"mag2 = abs(g2);\n",
"angle2 = phasemag(g2);\n",
"subplot(2,1,1)\n",
"plot(omega,mag1,omega,mag2,'--');\n",
"label('',4,' ','Magnitude',4);\n",
"subplot(2,1,2); \n",
"plot(omega,angle1,omega,angle2,'--');\n",
"label('',4,'w (rad/s)','Phase',4);\n",
""
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 5.3: Bode_plot_of_the_moving_average_filter.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"// Bode plot of the moving average filter, discussed in Example 5.5 on page 129\n",
"// 5.3\n",
"\n",
"exec('label.sci',-1);\n",
"\n",
"w = 0.01:0.01:%pi;\n",
"subplot(2,1,1);\n",
"mag = abs(1+2*cos(w))/3;\n",
"plot2d('ll',w,mag,2);\n",
"label('',4,' ','Magnitude',4);\n",
"subplot(2,1,2);\n",
"plot2d('ln',w,phasemag(1+2*cos(w)),style = 2,rect  =[0.01 -0.5 10 200]);\n",
"label('',4,'w','Phase',4)\n",
""
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 5.4: Bode_plot_of_the_differencing_filter.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"// Bode plot of the differencing filter, discussed in Example 5.6 on page 130\n",
"// 5.4\n",
"\n",
"exec('label.sci',-1);\n",
"\n",
"w = 0.01:0.01:%pi;\n",
"G = 1-exp(-%i*w);\n",
"subplot(2,1,1)\n",
"plot2d1('gll',w,abs(G),style = 2);\n",
"label('',4,' ','Magnitude',4);\n",
"subplot(2,1,2)\n",
"plot2d1('gln',w,phasemag(G),style = 2);\n",
"label('',4,'w','Phase',4)\n",
"\n",
""
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 5.5: Bode_plot_of_minimum_and_nonminimum_phase_filters.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"// Bode plot of minimum and nonminimum phase filters, discussed in Example 5.9 on page 145\n",
"// 5.5\n",
"\n",
"exec('label.sci',-1);\n",
"\n",
"omega = linspace(0,%pi);\n",
"ejw = exp(-%i*omega);\n",
"G1 = 1.5*(1-0.4*ejw); \n",
"mag1 = abs(G1); angle1 = phasemag(G1);\n",
"G2 = -0.6*(1-2.5*ejw);\n",
"mag2 = abs(G2); angle2 = phasemag(G2);\n",
"subplot(2,1,1);\n",
"plot(omega,mag1,omega,mag2,'--');\n",
"label('',4,' ','Magnitude',4);\n",
"subplot(2,1,2);\n",
"plot(omega,angle1,omega,angle2,'--');\n",
"label('',4,'w (rad/s)','Phase',4);\n",
""
   ]
   }
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		   "help_links": [
			{
			 "text": "MetaKernel Magics",
			 "url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md"
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