How to create functions in MATLAB, Digital Signaling Processing

DIGITAL SIGNALING PROCESSING

FUNCTIONS AND FUNCTION FILES IN MATLAB

OBJECTIVE: To understand concept of Function in MATLAB and to make function files.

Many functions are programmed inside MATLAB as built-in functions, and can be used in mathematical expressions simply by typing their name with an argument example

 are sin (x), cos (x), sqrt(x), and exp (x). Frequently, in computer programs, there is a need to calculate the value of functions that are not built-in. When a function expression is simple and needs to be calculated only once, it can be typed as part of the program. However, when a function needs to be evaluated many times for different value of arguments it is convenient to create a ''user defined" function. Once the new function is created (saved) it can be used just like the built-in functions.

CREATING A FUNCTION FILE:  Function files are created and edited, like script files, in the Editor/Debugger Window. This window is opened from the Command Window. In the File menu, select New, and then select m-file.

FUNCTION DEFINITION LINE: -

The first executable line in a function file must be the function definition line. Otherwise the file is considered a script file. The function definition line:

• Defines the file as a function file

• Defines the name of the function.

• Defines the number and order of the input and output arguments.

Function [output arguments] =function_name [input arguments]

INPUT AND OUTPUT ARGUMENTS: -

The input and output arguments are used to transfer data into and out of the function. The input arguments are listed inside parentheses following the function name. Usually, there is at least one

input argument, although it is possible to have a function that has no input arguments. If there are more than one, the input arguments are separated with commas.

EXAMPLE:

Write a function file for the function of the following expression. For the input to the function is x and output is f(x).

Write the function such that x can be a vector. Use the function to calculate:

a1)       f(x) for x =6.

a2)       f(x) for x = 1,3,5,7,9, and 11.

Open the Editor/Debugger Window. This window is opened from the Command Window. In the File menu, select New, and then select m-file. Once the Editor/Debugger Window opens write the following function in it

     function [y] = exp4one(x)

     y= (x.^4.*sqrt(3*x+5))./(x.^2+1.^2);

a     1)      Calculating the function for x = 6 can be done by typing exp4one(6) in the Command window

>> exp4one(6)

ans = 167.9837

2)      To calculate the function for several values of x, a vector with the values of x is

 first created, and then used for the argument of the function.

>> x = 1:2:11

x =

     1     3     5     7     9    11

>> exp4one(x)

ans = 1.4142   30.3074  107.5033  244.8549  452.6173  739.7802

    EXERCISE:

Q.1: Write down a function that takes value of frequency and at output gives a cosine wave.

Q.2: Write down a function that takes value of frequency and generate sawtooth, square and triangular wave in on plot window. (Frequency =0.5)

function [y] = freq(x)

n=0:0.1:40;

y=sawtooth(2*pi*x*n);

subplot(311)

    plot(y);

    y=square(2*pi*x*n);

subplot(312)

    plot(y);

   t = 0:0.1:15;

y=sawtooth(t,x);

subplot(313)

plot(t,y);

Q.3: Write down a function which solve the numerical problems of chapter 1 of your text book (detail of this question will be explained in the lab)

function [y] = exp4one(x)

    y= (x.^6.*sqrt(3))./(x.^2+x.^9);