From blixt@charcoal.eg.bucknell.edu Tue Sep 16 22:12 EDT 1997
Date: Tue, 16 Sep 1997 22:12:19 -0400
From: blixt@charcoal.eg.bucknell.edu (Blixt Zachary Robert '99)

%  Zach Blixt
% Sample MATLAB program for Homework 8:  Problem 1.34 in the Kamen/Heck text.
%
% ELEC 320, Fall 1997, 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]')

% Part b: x[n] = 2u[n], output y2[n]

x = 2;
y2(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 = 2;
  y2(i) = 0.5*y2(i-1) + x;
end

figure(2)	% Plot output signal y1[n]
stem(n, y2)
title('Problem 1.34 (b)')
xlabel('Time index (n)')
ylabel('y2[n]')

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

x = sin(0);
y3(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 = sin(3.14/4);
  y3(i) = 0.5*y3(i-1) + x;
end

figure(3)	% Plot output signal y1[n]
stem(n, y3)
title('Problem 1.34 (c)')
xlabel('Time index (n)')
ylabel('y3[n]')

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

x = 2+sin(0);
y4(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 = 2+sin(3.14/4);
  y4(i) = 0.5*y4(i-1) + x;
end

figure(4)	% Plot output signal y1[n]
stem(n, y4)
title('Problem 1.34 (d)')
xlabel('Time index (n)')
ylabel('y1[n]')

figure (5)
stem(n, 2*y1+y3)
title('Problem 1.34 (d2)')
xlabel('Time index (n)')
ylabel('y1[n]')


