Objectives:

To introduce Matlab.

To plot waves$/$signals using Matlab.

To explore sine waves and understand their characteristics.

To use Fourier analysis in decomposing complex signals.

Instructions:

Take a screen snapshot $($Alt$+$Prnt Scrn$)$ of all the commands and graphs that you type in Matlab and paste it under its corresponding step below.

Part I: Matlab Introduction

Matlab stands for Matrix Laboratory. It is a very good tool for manipulating matrices.

In matlab, you create a $1xN$ matrix by typing the following command:

$matri{x}_n$ame $=[$ element $1$ element $2$dots elementN $]$

To create a matrix named myMatrix, for example, with the numbers from zero to five you would type the following command:

myMatrix $=\left[\begin{array}{cccccc}0& 1& 2& 3& 4& 5\end{array}\right]$

a$.$ Create a $112$ matrix named months with elements $1$ to $12.$

b$.$ You can create matrices more quickly using this command:

$matri{x}_n$ame $=$ element$1$:increment:elementN

Using this command a matrix is created whose first element is element$1,$ and element $2=$ element $1+$ increment, element $3=$ element $2+$ increment and so on$.$

c$.$ Create a $112$ matrix called monthsQuick with elements $1$ to $12$ but using the command in step $b.$

d$.$ Sampling is reading a value of a signal at specific times. Assume we want to sample a signal every $0\mathrm{.}5$ seconds, starting from time zero to time $10.$ Create a matrix named samplingTimes with the times at which we will sample such a signal.