% Sample MATLAB program for Homework 7:  Problem 1.34 in the Kamen/Heck text.
%
% ELEC 320, Rich Kozick

% NOTE:  MATLAB does not allow an index of zero in vectors.
%        Thus the array index will be one greater than the time index.
%        In other words, the discrete-time signal value y[n] will be
%        stored at array location y[n+1].

% Parts a-d:  y[n] = 0.5*y[n-1] + x[n],  n = 0, 1, ..., 10
%             with initial condition y[-1] = 0.

yinit = 0;
n = 0:10;	% Vector of times at which we will evaluate system output.
                % This will be used for plotting.

% Part a: x[n] = u[n], output y1[n]

x = 1;
y1(1) = 0.5*yinit + x;	% Do time n=0 separately to handle initial condition.

for i=2:11	% Compute system outputs for times 1, 2, ..., 10
  x = 1;
  y1(i) = 0.5*y1(i-1) + x;
end

figure(1)	% Plot output signal y1[n]
stem(n, y1)
title('Problem 1.34 (a)')
xlabel('Time index (n)')
ylabel('y1[n]')

