{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#CHAPTER 1: INTRODUCTION"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example 1.1, Page Number: 18"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Populating the interactive namespace from numpy and matplotlib\n"
     ]
    },
    {
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      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x55761d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
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      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7eccf30>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
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       "+VHgAAAAAElFTkSuQmCC\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7e0acd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "As x(-t)=-x(t), x(t) is an odd signal\n"
     ]
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy\n",
    "import math\n",
    "%pylab inline\n",
    "\n",
    "#Given\n",
    "t=numpy.arange(-1.0,1.0,0.01)                     #Time Base\n",
    "x=sin(math.pi*t)                                  #x(t), T is assumed to be 1  \n",
    "y1=sin(-math.pi*t)                                #y1=x(-t)\n",
    "y2=-sin(math.pi*t)                                #y2=-x(t)\n",
    "\n",
    "# Plots\n",
    "\n",
    "#To plot x(t)\n",
    "plt.plot(t,x)\n",
    "plt.title('x(t)')\n",
    "plt.xlabel('t')\n",
    "plt.ylabel('x(t)')\n",
    "plt.grid(True)\n",
    "plt.show()\n",
    "\n",
    "#To plot x(-t)\n",
    "plt.plot(t,y1)\n",
    "plt.title('x(-t)')\n",
    "plt.xlabel('t')\n",
    "plt.ylabel('x(-t)')\n",
    "plt.grid(True)\n",
    "plt.show()\n",
    "\n",
    "#To plot -x(t)\n",
    "plt.plot(t,y2)\n",
    "plt.title('-x(t)')\n",
    "plt.xlabel('t')\n",
    "plt.ylabel('-x(t)')\n",
    "plt.grid(True)\n",
    "plt.show()\n",
    "\n",
    "#Result\n",
    "print \"As x(-t)=-x(t), x(t) is an odd signal\"\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example 1.2, Page Number: 19"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Populating the interactive namespace from numpy and matplotlib\n"
     ]
    },
    {
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       "5P8DmSwkOvA53rsAAAAASUVORK5CYII=\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x8b224f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
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      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7bb0d70>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
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       "YmZmLXMxMTOzlrmYmJlZy/4fjDot7dV1ElYAAAAASUVORK5CYII=\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x5402130>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy\n",
    "import math\n",
    "%pylab inline\n",
    "\n",
    "#Given\n",
    "t=numpy.arange(-4.0,4.0,0.01)          #Time Base\n",
    "x=(math.e**(-2*t))*cos(t)              #Given Signal\n",
    "\n",
    "#Calculation\n",
    "x_e=0.5*(cos(t)*math.e**(-2*t)+cos(-t)*math.e**(2*t))       #Even Component\n",
    "x_o=0.5*(cos(t)*math.e**(-2*t)-cos(-t)*math.e**(2*t))       #Odd Component\n",
    "\n",
    "#Results\n",
    "\n",
    "#To plot x(t)\n",
    "plt.plot(t,x)\n",
    "plt.title('x(t)')\n",
    "plt.xlabel('t')\n",
    "plt.ylabel('x(t)')\n",
    "plt.grid(True)\n",
    "plt.show()\n",
    "\n",
    "#To plot x_e(t)\n",
    "plt.plot(t,x_e)\n",
    "plt.title('Even Component of x(t)')\n",
    "plt.xlabel('t')\n",
    "plt.ylabel('x_e(t)')\n",
    "plt.grid(True)\n",
    "plt.show()\n",
    "\n",
    "#To plot x_o(t)\n",
    "plt.plot(t,x_o)\n",
    "plt.title('Odd Component of x(t)')\n",
    "plt.xlabel('t')\n",
    "plt.ylabel('x_o(t)')\n",
    "plt.grid(True)\n",
    "plt.show()\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##Example 1.3, Page Number: 29"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 128,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Populating the interactive namespace from numpy and matplotlib\n"
     ]
    },
    {
     "data": {
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      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x8c582d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
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       "xg6+gpMsAAAAAElFTkSuQmCC\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x8c6b990>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy\n",
    "%pylab inline\n",
    "\n",
    "#Given\n",
    "\n",
    "#To define x(t), assuming T1=1 and T2=2\n",
    "t1=numpy.arange(-1.0,0.0,.01)\n",
    "t2=numpy.arange(0.0,2.0,0.01)\n",
    "\n",
    "x=zeros(300)                             #x(t)\n",
    "for i in range(0,100):\n",
    "    x[i]=1+t1[i]\n",
    "    \n",
    "for i in range(0,200):\n",
    "    x[i+100]=1-0.5*t2[i]\n",
    "    \n",
    "#Plots\n",
    "#To plot x(t)\n",
    "t=numpy.arange(-1.0,2.0,0.01)    \n",
    "plt.plot(t,x)\n",
    "plt.xlabel('t')\n",
    "plt.ylabel('x(t)')\n",
    "plt.title('x(t)')\n",
    "plt.ylim(0,2)\n",
    "plt.xlim(-3,3)\n",
    "plt.grid(True)\n",
    "plt.show()\n",
    "\n",
    "\n",
    "#Calculation\n",
    "#To flip the signal\n",
    "x1=zeros(size(x))\n",
    "\n",
    "for i in range (0,300):\n",
    "    x1[i]=x[299-i]\n",
    "\n",
    "#To plot flipped signal\n",
    "\n",
    "t3=numpy.arange(-2.0,1.0,0.01)    \n",
    "plt.plot(t3,x1)\n",
    "plt.xlabel('t')\n",
    "plt.ylabel('x(-t)')\n",
    "plt.title('Reflection of x(t)')\n",
    "plt.ylim(0,2)\n",
    "plt.xlim(-3,3)\n",
    "plt.grid(True)\n",
    "plt.show()  \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example 1.4, Page Number: 29"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Populating the interactive namespace from numpy and matplotlib\n"
     ]
    },
    {
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       "krRgbPyStGBs/JK0YP4fh4Hv+J+BOykAAAAASUVORK5CYII=\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x8b494b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
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       "krHxS9KSsfFL0pKx8UvSkrHxS9KS+f9+6AnuzPxpPAAAAABJRU5ErkJggg==\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x77c2cd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy\n",
    "%pylab inline\n",
    "\n",
    "#Given\n",
    "#x(t)\n",
    "t=numpy.arange(-2.5,2.5,0.01)\n",
    "x=zeros(500)\n",
    "for i in range(200,300):\n",
    "    x[i]=1\n",
    "\n",
    "#y(t)=x(t-2)\n",
    "y=zeros(500)\n",
    "for i in range(400,500):\n",
    "    y[i]=1\n",
    "\n",
    "#Plots\n",
    "plt.plot(t,x)\n",
    "plt.xlabel('t')\n",
    "plt.ylabel('x(t)')\n",
    "plt.title('x(t)')\n",
    "plt.ylim(0,2)\n",
    "plt.xlim(-2.5,2.5)\n",
    "plt.grid(True)\n",
    "plt.show()\n",
    "\n",
    "plt.plot(t,y)\n",
    "plt.xlabel('t')\n",
    "plt.ylabel('y(t)')\n",
    "plt.title('y(t)=x(t-2)')\n",
    "plt.ylim(0,2)\n",
    "plt.xlim(-2.5,2.5)\n",
    "plt.grid(True)\n",
    "plt.show()\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example 1.5, Page Number: 31"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Populating the interactive namespace from numpy and matplotlib\n"
     ]
    },
    {
     "data": {
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      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x79d2dd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x8c268d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
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       "gg==\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x860f290>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy\n",
    "%pylab inline\n",
    "\n",
    "#Given\n",
    "#x(t)\n",
    "x=zeros(800)\n",
    "for i in range(300,500):\n",
    "    x[i]=1\n",
    "    \n",
    "#v(t)=x(t+3) \n",
    "v=zeros(800)\n",
    "for i in range(0,200):\n",
    "    v[i]=1\n",
    "\n",
    "#y(t)\n",
    "y=zeros(800)\n",
    "for i in range(200,300):\n",
    "    y[i]=1\n",
    "    \n",
    "\n",
    "#To plot x(t)    \n",
    "t1=numpy.arange(-4.0,4.0,0.01)\n",
    "plt.plot(t1,x)\n",
    "plt.xlabel('t')\n",
    "plt.ylabel('x(t)')\n",
    "plt.title('x(t)')\n",
    "plt.ylim(0,2)\n",
    "plt.xlim(-4,4)\n",
    "plt.grid(True)\n",
    "plt.show()\n",
    "\n",
    "#To plot x(t+3)\n",
    "plt.plot(t1,v,'b')\n",
    "plt.xlabel('t')\n",
    "plt.ylabel('v(t)')\n",
    "plt.title('x(t+3)')\n",
    "plt.ylim(0,2)\n",
    "plt.xlim(-4,4)\n",
    "plt.grid(True)\n",
    "plt.show()\n",
    "\n",
    "#To plot y(t)\n",
    "plt.plot(t1,y,'b')\n",
    "plt.xlabel('t')\n",
    "plt.ylabel('y(t)')\n",
    "plt.title('y(t)=x(2t+3)')\n",
    "plt.ylim(0,2)\n",
    "plt.xlim(-4,4)\n",
    "plt.grid(True)\n",
    "plt.show()\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example 1.6, Page Number: 33"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Populating the interactive namespace from numpy and matplotlib\n"
     ]
    },
    {
     "data": {
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      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x8882a50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
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      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x91fa3d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
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       "RQIAUIsiAQCoRZEAANSiSAAAav0/7YYc6B310o0AAAAASUVORK5CYII=\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x8572b30>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy\n",
    "%pylab inline\n",
    "\n",
    "#Given \n",
    "x=[0,0,0,-1,-1,0,1,1,0,0,0]\n",
    "\n",
    "#Calculation \n",
    "x1=zeros(11)\n",
    "for i in range(0,6):\n",
    "    x1[2*i]=x[2*i]\n",
    "\n",
    "#Plots\n",
    "\n",
    "n1=numpy.arange(-5,6,1)\n",
    "plt.stem(n1,x)\n",
    "plt.xlabel('n')\n",
    "plt.ylabel('x[n]')\n",
    "plt.title('x[n]')\n",
    "plt.grid(True)\n",
    "plt.show()\n",
    "\n",
    "n2=numpy.arange(-2,9,1)\n",
    "plt.stem(n2,x)\n",
    "plt.xlabel('n')\n",
    "plt.ylabel('v[n]')\n",
    "plt.title('v[n]=x[n+3]')\n",
    "plt.xlim(-2,6)\n",
    "plt.grid(True)\n",
    "plt.show()\n",
    "\n",
    "n3=numpy.arange(-6.0,5.0,1)\n",
    "plt.stem(n3,x1)\n",
    "plt.xlabel('n')\n",
    "plt.ylabel('y[n]')\n",
    "plt.title('y[n]=x[2n+3]')\n",
    "plt.grid(True)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example 1.7, Page Number: 38"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 127,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The common fundamental period is 2.0\n",
      "Therefore, output signal is:\n",
      "y[n]= 2.0 cos(5*pi*n -0.52 )\n"
     ]
    }
   ],
   "source": [
    "import numpy\n",
    "import math\n",
    "\n",
    "#Given\n",
    "A1=-1                           #Amplitude of x1 (in terms of cos)\n",
    "A2=math.sqrt(3)                #Amplitude of x2\n",
    "\n",
    "#Calculation\n",
    "\n",
    "#To find angular frequency\n",
    "m=1                                 #Initialise m to 1\n",
    "while((m*2.0/5!=int(m*2.0/5))):     #To find smallest integer value   \n",
    "    m=m+1\n",
    "\n",
    "\n",
    "N=2*m*math.pi/(5*math.pi)\n",
    "\n",
    "#To find amplitude and phase angle\n",
    "phi=math.atan(A1/A2)                #Phase angle in radians\n",
    "A=-1/math.sin(phi)                  #Amplitude\n",
    "\n",
    "#Results\n",
    "\n",
    "print \"The common fundamental period is\",N\n",
    "print \"Therefore, output signal is:\"\n",
    "print \"y[n]=\",A,\"cos(5*pi*n\",round(phi,2),\")\"\n",
    "\n",
    "\n"
   ]
  }
 ],
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