0.1 Lab 1 - discrete and continuous-time signals  (Page 2/5)

Often, you may want to apply an operation to each elementof a vector. For example, you many want to square each value of “ $a$ ”. In this case, you may use the following command.

$c=a.*a$

The dot before the * tells Matlab that the multiplication should be applied to each corresponding element of “ $a$ ”. Therefore the .* operation is not a matrix operation. The dot convention works with many other Matlab commandssuch as divide ./ , and power .^ . An error results if you try to perform element-wise operations on matrices that aren't the same size.

Note also that while the operation $a.\text{'}$ performs a transpose on the matrix " $a$ ", the operation $a\text{'}$ performs a conjugate transpose on " $a$ " (transposes the matrix and conjugates each number in the matrix).

Matlab scripts and functions

Matlab has two methods for saving sequences of commands as standard files. These two methods are called scripts and functions . Scripts execute a sequence of Matlab commandsjust as if you typed them directly into the Matlab command window. Functions differ from scripts in that they accept inputs and return outputs, and variables defined within a function are generally local to that function.

A script-file is a text file with the filename extension ".m". The file should contain a sequence of Matlab commands.The script-file can be run by typing its name at the Matlab prompt without the .m extension.This is equivalent to typing in the commands at the prompt. Within the script-file, you can access variables youdefined earlier in Matlab. All variables in the script-file are global,i.e. after the execution of the script-file, you can access its variables at the Matlab prompt.For more help on scripts click here .

To create a function called func , you first create a text file called func.m . The first line of the file must be

function output = func(input)

where input designates the set of input variables, and output are your output variables. The rest of the function file then contains the desired operations.All variables within the function are local; that means the function cannot access Matlab workspace variables that you don't pass as inputs.After the execution of the function, you cannot access internal variables of the function.For more help on functions click here .

Continuous-time vs. discrete-time

The "Introduction" mentioned the important issue of representing continuous-time signals on a computer.In the following sections, we will illustrate the process of sampling , and demonstrate the importance of the sampling interval to the precision of numerical computations.

Analytical calculation

Compute these two integrals. Do the computations manually.

1. $${\int }_0^{2\pi }si{n}^2\left(5t\right)dt$$
2. $${\int }_0^1{e}^{t}dt$$

Displaying continuous-time and discrete-time signals in matlab

For help on the following topics, visit the corresponding link: Plot Function , Stem Command , and Subplot Command .

It is common to graph a discrete-time signal as dots in a Cartesian coordinate system.This can be done in the Matlab environment by using the stem command. We will also use the subplot command to put multiple plots on a single figure.