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+{
+"cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Chapter 2: Signals An Introduction"
+ ]
+ },
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 2.10: Laplace_Transform.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"\n",
+"\n",
+"//x(t) = del(t)\n",
+"syms t s;\n",
+"\n",
+"L =laplace('delta(t)',t,s)\n",
+"disp(L)\n",
+"// x(t) = u(t)\n",
+"\n",
+"L1 =laplace('1',t,s);\n",
+"disp(L1)\n",
+"//x(t) = sin(w0*t)u(t)\n",
+"\n",
+"L2 =laplace('sin(w0*t)',t,s);\n",
+"disp(L2)"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 2.11: Z_transform.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"\n",
+"clc;\n",
+"clear;\n",
+"\n",
+"// a) z-transform of unit impulse function\n",
+"syms n z;\n",
+"x=1;\n",
+"X=symsum(x*(z^-n),n,0,0);\n",
+"disp(X,'X(z)=');\n",
+"\n",
+"//b) z-transform of unit step function\n",
+"\n",
+"y=ones(1);\n",
+"Y=symsum(y*(z^-n),n,0,%inf);\n",
+"disp(Y,'Y(z)=');"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 2.1_A: Periodicity.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"\n",
+"clear;\n",
+"clc;\n",
+" //a) periodicity os 5sin(6t-pi/4)\n",
+"t=0:0.001:1;\n",
+"w=6;\n",
+"theta=%pi/4;\n",
+"T=2*%pi/w;\n",
+"x=cos(t*w+theta);\n",
+"y=cos((t+T)*w+theta);\n",
+"if ceil(x)==ceil(y) then\n",
+" disp(' a) cos(6t+pi/4) is periodic with T=2*pi/6 (sec) ')\n",
+" \n",
+"else\n",
+" disp('nonperiodic')\n",
+"end\n",
+"\n",
+"\n",
+" //b) periodicity of e^(j3t)\n",
+" \n",
+" w=3; \n",
+" t=0:0.001:1;\n",
+" T=2*%pi/w;\n",
+" x=exp(3*%i*t);\n",
+" y=exp(3*%i*(t+T));\n",
+" if ceil(x)==ceil(y) then\n",
+" disp(' b) exp(j3t) is periodic with T=2*pi/3 (sec) ')\n",
+" \n",
+"else\n",
+" disp('nonperiodic')\n",
+"end\n",
+" \n",
+" \n",
+" //c) periodicity of cot(3t+theta)\n",
+" \n",
+" t=0:0.001:1;\n",
+"w=5;\n",
+"T=%pi/w;\n",
+"\n",
+" x=cotg(t*w+theta);\n",
+" y=cotg((t+T)*w+theta);\n",
+"if ceil(x)==ceil(y) then\n",
+" disp(' c) cot(3t+Theta) is periodic with T=pi/5 (sec) ')\n",
+" \n",
+"else\n",
+" disp('nonperiodic')\n",
+"end\n",
+" \n",
+" "
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 2.2_A: Even_and_Odd_Part_of_function.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"clc;\n",
+"clear;\n",
+"t = 0:1:10;\n",
+"\n",
+"for i = 1:length(t)\n",
+" x(i) = (t(i)^6) + 2*(t(i)^4)+ 3*(t(i)^2)+4 ;\n",
+"end\n",
+"\n",
+"for i = 1:length(t)\n",
+" y(i) = ((-t(i))^6)+ 2*((-t(i))^4)+ 3*((-t(i))^2)+4 ;\n",
+"end\n",
+"\n",
+"// checking if the function is even x(t)=x(-t)\n",
+"if x==y then\n",
+" disp('the function is even');\n",
+"end\n",
+"//odd part of the signal=0.5(x(t)-x(-t))\n",
+"\n",
+"z=0.5*(x-y);\n",
+"if z==0 then\n",
+" disp('the odd part is 0')\n",
+"end"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 2.2: Real_and_Imaginary_part.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"clc;\n",
+"clear;\n",
+"\n",
+"/// e^j(*2*pi*f*t+theta)\n",
+"\n",
+"syms pi f0 t theta A\n",
+"K=2*pi*f0*t+theta;\n",
+"\n",
+"disp('the given signal is complex');\n",
+"disp('e^(j*theta) can be written as');\n",
+"disp('cos(theta)+j*sin(theta)');\n",
+"\n",
+"Re=A*cos(K);\n",
+"Img=A*sin(K);\n",
+"mag=sqrt(Re^2+Img^2);\n",
+"\n",
+"disp(Re,'real part is ');\n",
+"disp(Img,'the imaginary part ');\n",
+"disp(mag,'Magnitude of signal is |A|=');\n",
+"disp(K,'phase of the signal ');"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 2.3_A: Power_and_Rms_power_of_Signal.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"clear;\n",
+"clc;\n",
+"\n",
+" //x(t)=5u(t)....\n",
+" amp=5; //amplitude is 5\n",
+"t=0:0.01:1;\n",
+"x0=0;\n",
+"x1=0:0.1:10; // over a time interval of T\n",
+"disp('the power of the signal (in watts) is');\n",
+" X=(integrate('25','x',x0,10)/(2*10)); // power of the signal\n",
+"disp(X);\n",
+"\n",
+"rms=amp/sqrt(2);\n",
+"disp(rms,'the rms value of power is (in watts)');"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 2.3: Energy_of_Signal.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"clc;\n",
+"clear;\n",
+"\n",
+"//x(t)=2 over an interval of (-2,2)\n",
+"\n",
+"disp('the energy of the signal (in J)is');\n",
+" Ex=(integrate('4','x',-2,2)); // energy content of the signal\n",
+"disp(Ex);"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 2.5: Properties_of_Impulse_Signal.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"clc;\n",
+"clear;\n",
+"\n",
+"\n",
+"//delta(t)\n",
+"\n",
+" for j = 1:1000\n",
+" if j==1\n",
+" delta(j)=1;\n",
+" else\n",
+" delta(j)=0;\n",
+" end\n",
+" end\n",
+"\n",
+"// a)\n",
+"figure(1)\n",
+" t=-1;\n",
+" plot2d4(t,0);\n",
+" for j=1:1:10\n",
+" t=t+1;\n",
+" z(j)=(cosd(j-1)*delta(j));\n",
+" plot2d3(t,z(j));\n",
+" disp(z(j));\n",
+" \n",
+" end\n",
+"\n",
+"\n",
+"//b)\n",
+"figure(2)\n",
+" t=1.5;\n",
+" plot2d4(t,0);\n",
+" for j=3:1:10\n",
+" t=t+1;\n",
+" z(j)=abs(cosd(2.5)*delta(2*j-5));\n",
+" plot2d3(t,z(j));\n",
+" \n",
+" end\n",
+"\n",
+"//c)\n",
+"syms t;\n",
+"\n",
+"A=(-1)*exp(-1*t); //property 8\n",
+"disp(diff(A,t));\n",
+"\n",
+"disp('when t=3');\n",
+"\n",
+"A=exp(-3);\n",
+"disp(A);\n",
+"\n",
+"\n",
+"\n",
+" \n",
+"\n",
+"\n",
+"\n",
+"\n",
+"\n",
+"\n",
+" "
+ ]
+ }
+],
+"metadata": {
+ "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
+}
generated by cgit (git 2.34.1) at 2025-07-14 08:23:32 +0000