How to get y(k) values of a difference equation?

Hi, I need to know how do I get first 10 values of y(k) (from 0 to 9) in a difference equiation by Matlab, I got on paper but I need to know how to get it by Matlab. I have this difference equation:

0.5y(k - 2) - 1.5y(k - 1) + y(k) = µ(k) - µ(k - 1); if y(-1) = 2, y(-2) = 1 and µ(k) is a step signal.

They ask me solve it by Matlab but I don´t know how to do it, I do it on paper to verify the results on Matlab but I didn´t find how to solve it. I tried to search on my own but I didn't find something relevant, you are my last hope people. Thank you for help me.

Answer 1

[Harshal Ritwik]

Hi,

As per my understanding of your question you want to know how we can use display the desired 10 values of y(k) with the help of the given initial conditions. The following Code Snippet may help.

%Code Section

% Define the range of data you want 
k = 0:9; 
% Define initial conditions here y(-1) is taken as y(1) to get %all indexes to positive side 
y = zeros(1, length(k)+2); 
y(1) = 1; 
y(2) = 2; 
% Defining the step signal 
mu = [ones(1, length(k)+2) 0]; 
% Implement the difference equation for k = 3 and onwards 
for n = 3:length(k)+2 
y(n) = (mu(n) - mu(n-1) + 1.5*y(n-1) - 0.5*y(n-2)) / 1; 
end 
% Display the first 10 values in the Command Window 
disp(y(3:12));

Please refer to the following documentation for more information

https://in.mathworks.com/help/matlab/programming-and-data-types.html

I hope it helps!

Thanks.

[Paul]

Should the values of y(1) and y(2) reversed?

[Harshal Ritwik]

Hi Paul!

Yes I missed that we need to do that

I have done the changes.

Thanks