#### EE342.01: MATLAB M-FILE FOR RECURSIVELY SOLVING A DIFFERENCE EQUATION

MATLAB M-File example4.m:
```%
%  Filename:  example4.m
%
%  Description:  This m-file demonstrates how a difference
%                equation can be recursively solved.
%

N = 10;                      % maximum n for recursion
yprev = 0;                   % initial y value, y[-1] = 0

for n=0:N,                   % recursion loop

if (n == 0)                % x[n] = 2delta[n]
x = 2;
else
x = 0;
end

y = x + 0.5*yprev;         % compute y[n]
yprev = y;                 % store current y value for next interation

nvec(n+1) = n;             % store n and y into vectors for plotting
yvec(n+1) = y;

end;

n_and_y = [nvec' yvec']      % view n and y

stem(nvec, yvec,'filled');   % plot y vs n
xlabel('n');                 % label plot
ylabel('y[n]');
title('EE342 Example 4: Plot of y[n] from Recursion');
```
MATLAB Output Generated:
```n_and_y =

0    2.0000
1.0000    1.0000
2.0000    0.5000
3.0000    0.2500
4.0000    0.1250
5.0000    0.0625
6.0000    0.0312
7.0000    0.0156
8.0000    0.0078
9.0000    0.0039
10.0000    0.0020
```
MATLAB Plot Generated: