Using a For Loop to plot a sample range for a difference equation

Basically I cant figure out how to intitally set up my code to run x(n) and y(n) for 101 to 500 samples. any help is much appreciated.

Answer 1

[Voss]

Given in the question:

% input signal
% x(n) = cos(pi/60*n), n = 0,1,2,...,999
% 
% output signal
% from difference equation
% y(n) = 0.5*y(n-1) + x(n)
% and initial condition
% y(-1) = 0

Since the output signal y(n) has to start at n = -1, the vector y (to be constructed in MATLAB) has to have 1001 elements (for n = -1 to n = 999). It is convenient for the vector x to have the same size as y, so that the ith element of x corresponds to the ith element of y (but this is not strictly necessary).

The point is that indexing starts at 1 in MATLAB, so index 1 in vectors x and y will correspond to n = -1 in signals x(n) and y(n). (So the vector x will have 1001 elements with the 1st element corresponding to n = -1, but the first element of x won't be used.)

N = 1000;

% n = -1 to n = 999:
n = -1:N-1;

% x(n) at n=-1 is NaN, after that x(n)=cos(pi/60*n):
x = [NaN cos(pi/60*n(2:end))];

% initialize vector y to have 1001 elements:
y = NaN(1,N+1);

% y(n)=0 at n=-1:
y(1) = 0; % n=-1 corresponds to index 1 in vector y

% y(n) = 0.5*y(n-1) + x(n):
for ii = 2:N+1 % n = 0,...,999 <-> ii = 2:1001
    y(ii) = 0.5*y(ii-1) + x(ii);
end

% a table to summarize the situation
t = table(n.',(1:N+1).',x.',y.', ...
    'VariableNames',{'signal index n','vector index ii','x=cos(pi/60*n)','y'});
head(t)

ans = 8×4 table
    signal index n    vector index ii    x=cos(pi/60*n)      y   
    ______________    _______________    ______________    ______

          -1                 1                  NaN             0
           0                 2                    1             1
           1                 3              0.99863        1.4986
           2                 4              0.99452        1.7438
           3                 5              0.98769        1.8596
           4                 6              0.97815         1.908
           5                 7              0.96593        1.9199
           6                 8              0.95106         1.911