# 0.1 Lab 1 - discrete and continuous-time signals

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Questions or comments concerning this laboratory should be directedto Prof. Charles A. Bouman, School of Electrical and Computer Engineering, Purdue University, West Lafayette IN 47907;(765) 494-0340; bouman@ecn.purdue.edu

## Introduction

The purpose of this lab is to illustrate the properties of continuous and discrete-time signals using digital computersand the Matlab software environment. A continuous-time signal takes on a value at every pointin time, whereas a discrete-time signal is only defined at integer values of the “time” variable.However, while discrete-time signals can be easily stored and processed on a computer,it is impossible to store the values of a continuous-time signal for all points along a segment of the real line.In later labs, we will see that digital computers are actuallyrestricted to the storage of quantized discrete-time signals. Such signals are appropriately known as digital signals.

How then do we process continuous-time signals? In this lab, we will show that continuous-time signalsmay be processed by first approximating them by discrete-time signals using a process knownas sampling. We will see that proper selectionof the spacing between samples is crucial for an efficient and accurate approximationof a continuous-time signal. Excessively close spacing will lead to too much data,whereas excessively distant spacing will lead to a poor approximation of the continuous-time signal.Sampling will be an important topic in future labs, but for now we will use sampling to approximatelycompute some simple attributes of both real and synthetic signals.

Be sure to read the guidelines for the written reports.

## Matlab review

Practically all lab tasks in the ECE438 lab will be performed using Matlab. Matlab (MATrix LABoratory) is a technical computing environmentfor numerical analysis, matrix computation, signal processing, and graphics.In this section, we will review some of its basic functions. For a short tutorial and some Matlab examples click here .

## Starting matlab and getting help

You can start Matlab (version 7.0) on your workstation by typing the command

matlab

in a command window. After starting up, you will get a Matlab window.To get help on any specific command, such as “plot”, you can type the following

help plot

in the “Command Window” portion of the Matlab window. You can do a keyword search for commands related to a topic by using thefollowing.

lookfor topic

You can get an interactive help window using the function

helpdesk

or by following the Help menu near the top of the window.

## Matrices and operations

Every element in Matlab is a matrix. So, for example, the Matlab command

$a=\left[\begin{array}{ccc}1& 2& 3\end{array}\right]$

creates a matrix named “ $a$ ” with dimensions of $1×3$ . The variable “ $a$ ” is stored in what is called the Matlab workspace. The operation

$b=a.\text{'}$

stores the transpose of “ $a$ ” into the vector “ $b$ ”. In this case, “ $b$ ” is a $3×1$ vector.

Since each element in Matlab is a matrix, the operation

$c=a*b$

computes the matrix product of “ $a$ ” and “ $b$ ” to generate a scalarvalue for “ $c$ ” of $14=1*1\phantom{\rule{3.33333pt}{0ex}}+\phantom{\rule{3.33333pt}{0ex}}2*2\phantom{\rule{3.33333pt}{0ex}}+\phantom{\rule{3.33333pt}{0ex}}3*3\phantom{\rule{2pt}{0ex}}\text{.}$

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Cied
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the Beer law works very well for dilute solutions but fails for very high concentrations. why?
how did you get the value of 2000N.What calculations are needed to arrive at it
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