{
"cells": [
 {
		   "cell_type": "markdown",
	   "metadata": {},
	   "source": [
       "# Chapter 2: Discrete Signals"
	   ]
	},
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 2.1a: Signal_energy_and_power.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"//example 2.1.a,pg no.11\n",
"for i=1:1:50\n",
"    x(1,i)=3*(0.5)^(i-1);\n",
"end\n",
"//summation of x\n",
"E=0\n",
"for i=1:1:50\n",
"    E=E+x(1,i)^2;\n",
"end\n",
"disp('the energy of given signal is')\n",
"E"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 2.1b: Average_power_of_periodic_signals.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"//example 2.1b,pg.no.11\n",
"n=1:1:10;\n",
"xn=6*cos((2*%pi*n')/4);\n",
"a=4;\n",
"p=0;\n",
"for i=1:1:a\n",
"    p=p+abs(xn(i)^2);\n",
"end\n",
"P=p/a;\n",
"disp('The average power of given signal is')\n",
"P"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 2.1c: Average_power_of_periodic_signals.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"//example 2.1c,pg.no.11\n",
"n=1:4;\n",
"xn=6*%e^((%i*%pi*n')/2);\n",
"a=4;\n",
"p=0;\n",
"for i=1:1:a\n",
"    p=p+abs(xn(i)^2);\n",
"end\n",
"P=p/a;\n",
"disp('The average power of given signal is')\n",
"P"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 2.2: Operations_on_Discrete_Signals.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"//example 2.2,pg no.12\n",
"x=[0 2 3 4 5 6 7];\n",
"n1=-3:1:3;\n",
"y=x;\n",
"n2=0:1:6;\n",
"f=x;\n",
"n3=-5:1:1;\n",
"g=x(length(x):-1:1);\n",
"n4=-3:1:3;\n",
"h=x(length(x):-1:1);\n",
"n5=-2:1:4;\n",
"s=x(length(x):-1:1);\n",
"n6=-5:1:1;\n",
"a=gca();\n",
"subplot(231);\n",
"plot2d3('gnn',n1,x);\n",
"ylabel('x[n]');\n",
"subplot(232);\n",
"plot2d3('gnn',n2,y);\n",
"ylabel('y[n]=x[n-3]');\n",
"subplot(233);\n",
"plot2d3('gnn',n3,f);\n",
"ylabel('f[n]=x[n+2]');\n",
"subplot(234);\n",
"plot2d3('gnn',n4,g);\n",
"ylabel('g[n]=x[-n]');\n",
"subplot(235);\n",
"plot2d3('gnn',n5,h);\n",
"ylabel('h[n]=x[-n+1]');\n",
"subplot(236);\n",
"plot2d3('gnn',n6,s);\n",
"ylabel('s[n]=x[-n-2]');"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 2.3a: Even_and_Odd_parts_of_Discrete_signals.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"//example 2.3a pg.no.14\n",
"clear;clc;close;\n",
"n=-2:2;\n",
"x1=[4 -2 4 -6 0];\n",
"x2=0.5*x1//x[n]\n",
"x3=0.5*[x1(length(x1):-1:1)];//x[-n]\n",
"xe=(x2+x3);//even part\n",
"xo=(x2-x3);//odd part\n",
"a=gca();\n",
"a.thickness=2;\n",
"a.x_location='middle';\n",
"a.y_location='middle';\n",
"plot2d3('gnn',n,xe,rect=[-4 -6 4 6])\n",
"xtitle('graphical representation of even part of x[n]','n','x[n]')\n",
"xset('window',1)\n",
"b=gca();\n",
"b.thickness=2;\n",
"b.y_location='middle';\n",
"b.x_location='middle';\n",
"plot2d3('gnn',n,xo,rect=[-2 -4 2 4])\n",
"xtitle('graphical representation of odd part of x[n]','n','x[n]')"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 2.3b: Even_and_Odd_parts_of_Discrete_signals.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"//example 2.3a pg.no.14\n",
"clear;clc;close;\n",
"x1=[0 0 0 0 0 1 1 1 1 ];\n",
"n=-4:4;\n",
"x2=0.5*x1//x[n]\n",
"x3=0.5*[x1(length(x1):-1:1)]//x[-n]\n",
"xe=(x2+x3);//even part\n",
"xo=(x2-x3);//odd part\n",
"a=gca();\n",
"a.thickness=2;\n",
"a.y_location='middle';\n",
"a.x_location='middle';\n",
"plot2d3('gnn',n,xe,rect=[-4 -1 4 1]);\n",
"xtitle('graphical representation of even part of x[n]','n','x[n]')\n",
"xset('window',1)\n",
"b=gca();\n",
"b.thickness=2;\n",
"b.y_location='middle';\n",
"b.x_location='middle';\n",
"plot2d3('gnn',n,xo,rect=[-4 -1 4 1]);\n",
"xtitle('graphical representation of odd part of x[n]','n','x[n]')"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 2.4a: Decimation_and_Interpolation_of_Discrete_signals.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"//example 2.4a pg.no.17\n",
"x=[1 2 5 -1];\n",
"xm=2;//denotes 2nd sample has pad.\n",
"y=[x(1:2:xm-2),x(xm:2:length(x))]//decimation\n",
"h=[x(1:1/3:length(x))]//step interpolated\n",
"g=h;\n",
"for i=2:3\n",
"    g(i:3:length(g))=0;\n",
"end\n",
"//zero interpolated\n",
"x1=1:3:3*length(x);\n",
"s=interpln([x1;x],1:10)//linear interpolated"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 2.4b: Decimation_and_Interpolation_of_Discrete_signals.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"//example 2.4 b,c.pg.no.17\n",
"x=[3 4 5 6];\n",
"xm=3;//denotes 3rd sample has pad\n",
"xm=xm-1;//shifting\n",
"g=[x(xm-2:-2:1),x(xm:2:length(x))]//decimation\n",
"xm=3;\n",
"h=[x(1:1/2:length(x))]//step interpolated"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 2.4c: Decimation_and_Interpolation_of_Discrete_signals.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"//example 2.4c,pg.no.17\n",
"x=[3 4 5 6];\n",
"xm=3;\n",
"xm=xm+1*(xm-1);//shift in pad due to interpolation\n",
"xm=xm-2//normal shifting\n",
"x1=[x(1:1/3:length(x))]//step interpolated\n",
"xm=3;\n",
"xm=xm+2*(xm-1)//shift in pad due to interpolation\n",
"y=[x1(1:2:xm-2),x1(xm:2:length(x1))]//decimation"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 2.4d: Decimation_and_Interpolation_of_Discrete_signals.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"//example 2.4d,pg.no.17\n",
"x=[2 4 6 8]\n",
"xm=3;//denote 3rd sample has pad\n",
"x1=[1 3 5 7]\n",
"x2=interpln([x1;x],1:6)\n",
"xm=xm+1*(xm-1);//shift in pad due to interpolation\n",
"xm=xm-1//shift in pad due to delay\n",
"y=[x2(2:2:xm-2),x2(xm:2:length(x2))]//decimation"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 2.5: Describing_Sequences_and_signals.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"//example 2.5,pg.no.20\n",
"x=[1 2 4 8 16 32 64];\n",
"y=[0 0 0 1 0 0 0];\n",
"z=x.*y;\n",
"a=0;\n",
"for i=1:length(z)\n",
"    a=a+z(i);\n",
"end\n",
"z,a//a=summation of z"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 2.6: Discrete_time_Harmonics_and_Periodicity.sci"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"//example 2.6 pg.no.23\n",
"function[p]=period(x)\n",
"for i=2:length(x)\n",
"    v=i\n",
"    if (abs(x(i)-x(1))<0.00001)    \n",
"        k=2\n",
"        for j=i+1:i+i\n",
"            if (abs(x(j)-x(k))<0.00001)   \n",
"                v=v+1\n",
"            end\n",
"        k=k+1;      \n",
"        end\n",
"     end \n",
"    if (v==(2*i)) then\n",
"        break\n",
"    end\n",
"end\n",
"p=i-1\n",
"endfunction\n",
"for i=1:60\n",
"    x1(i)=cos((2*%pi*8*i)/25);\n",
"end\n",
"for i=1:60\n",
"    x2(i)=exp(%i*0.2*i*%pi)+exp(-%i*0.3*i*%pi);\n",
"end\n",
"for i=1:45\n",
"    x3(i)=2*cos((40*%pi*i)/75)+sin((60*%pi*i)/75);\n",
"end\n",
"period(x1)\n",
"period(x2)\n",
"period(x3)"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 2.7: Aliasing_and_its_effects.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"//example 2.7.pg.no.27\n",
"f=100;\n",
"s=240;\n",
"s1=s;\n",
"aliasfrequency(f,s)\n",
"s=140;\n",
"s1=s;\n",
"aliasfrequency(f,s,s1)\n",
"s=90;\n",
"s1=s;\n",
"aliasfrequency(f,s,s1)\n",
"s=35;\n",
"s1=s;\n",
"aliasfrequency(f,s,s1)"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 2.8: Signal_Reconstruction.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"f=100;\n",
"s=210;\n",
"s1=420;\n",
"aliasfrequency(f,s,s1)\n",
"s=140;\n",
"aliasfrequency(f,s,s1)"
   ]
   }
],
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		  "kernelspec": {
		   "display_name": "Scilab",
		   "language": "scilab",
		   "name": "scilab"
		  },
		  "language_info": {
		   "file_extension": ".sce",
		   "help_links": [
			{
			 "text": "MetaKernel Magics",
			 "url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md"
			}
		   ],
		   "mimetype": "text/x-octave",
		   "name": "scilab",
		   "version": "0.7.1"
		  }
		 },
		 "nbformat": 4,
		 "nbformat_minor": 0
}