Matlab Workshop III.pptx

7/28/2019 Matlab Workshop III.pptx

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Wavez 2011-2012


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Using Functions

Solving Differential Equations

Signal Processing


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Syntax :

function[out1, out2, ] = func_name (input1, input2, )

Note that you need not have any output values, in

which case you simply type:

function function_name (input1, input2, )


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All functions are defined in a separate .m file.

Each of these .m file names should be the same

as the function name

You can also include sub-functions under each

function (kind of like nested functions)


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There are multiple functions, like ode45, ode23,

bvp4c, and others for solving differential equations

Well only be covering ode45 today, as its a basic

and essential solver.


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ode45 is a solver for an initial-value type of

differential equation.

We need to specify the domain (x-region) in which

we need to solve the equation.

We also need to specify the initial value of the

function at the beginning of the domain.


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The following is an example code to solve y = 3x + 5 , y(0) = 1 on

the domain [0,10] :

function my_solver()

x_dom = [0 10]

y_init = 1;

[X,Y] = ode45( @func, x_dom, y_init);

plot(X,Y);

end

function dy = func(x,y)dy = 3*x + 5;

end


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Now lets try it for the function y = y , y(0) = 1 on the domain [0,10]

:


x_dom = [0 10]

y_init = 1;


plot(X,Y);

end

function dy = func(x,y)dy = y;

end


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Now lets try it for the functions y1 = y1y2, y2=-3y1 , y1(0) = 1,y2(0)=1 on the domain [0,10] :

function my_solver()x_dom = [0 10]

y_init = [1 1];[X,Y] = ode45( @func, x_dom, y_init);plot(X,Y);

end

function dy = func(x,y)

dy = zeros(2,1);dy(1) = y(1)*y(2);dy(2) = -3*y(1);

end


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Technically, this can only solve for first degree equations.

We can manipulate this to solve higher order equations

in the following way:

For the equation y=-3y, y(0) = 1, y(0) = 1, we

create new functions to represent the higher powers, like

this:

y1 = y

y2= y


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Once again, for y=-3y, y(0) = 0, y(0) = 3:


x_dom = [0 10]

y_init = [0 3];


plot(X,Y);

end

function dy = func(x,y)

dy(1) = y(2); % y = y2dy(2) = -3*y(1); % y = -3y

end


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Most of our signal processing takes place

in a Matlab toolbox called Simulink.

You can get to Simulink by going to

Matlab Start > Simulink > Library

Browser


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For today, well be dealing with the DataAcquisition toolbox, and the Simulink>Sinksblockset.

The Data Acquisition toolbox allows youaccept analog signals, particularly from yourmicrophone, and save them to a variable

The Sinks blockset allows you to output thisdata in forms that we can read.


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First, from the library, create a new file.

Next, go to Data Acquisition and drag the

Analog Input block into the new file.

Now go to the Sinks blockset, and drag the

To Workspace block into the file.


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Configure the Analog Input block by double-

clicking on it.

For now, check the Asynchronous option, makesure your microphone is selected, set the sample

rate as anything greater than 8000

samples/second, and select only one Hardware

Channel (dont select both)

Once youre finished, close the window.


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Drag an arrow from the Analog Input to the To

Workspace block.

Double-click the To Workspace block to configure it.

Change the name of the variable to which it saves

the data, and set it as a Structure with Time type.

For now, dont change anything else, and close the

window.


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Also, if you want to view your signal, open the Sinks blockset

again, and drag the Scope block into your file.

Pull out an arrow from the Scopes input, and connect it to the

previous line.

Now run the file by pressing the Play button at the top.

Once youve recorded enough, stop the code by pressing the

Stop button.

Double-click on the scope to view your signal. Also, youll find that

this signal has been saved to your workspace in the variable you

mentioned earlier.


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We now use the Fast Fourier Transform

function to find out the frequencies present

in the signal you recorded.

This code will give us the amplitude of

each frequency present in the signal.


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Finito

End

Fin

Graci

as

ByeB

ye

Documents

Matlab Workshop III.pptx