From keeney@charcoal.eg.bucknell.edu Wed Sep 17 08:59 EDT 1997
Date: Wed, 17 Sep 1997 08:59:34 -0400
From: keeney@charcoal.eg.bucknell.edu (Keeney Shawn Patrick Grad/Sp)

% Sample MATLAB program for Homework 8:  Problem 1.34 in the Kamen/Heck text.
%
% 
% 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) = 0.1*yinit*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) = 0.1*y1(i-1)^2 + x;
end

% part b: x[n]=2*u[n], output y2[n]
x = 2;
y2(1) = 0.1*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) = 0.1*y2(i-1)^2 + x;
end

%part c: x[n]=sin(pi*n/4)u[n]
x = sin(pi/4);
y3(1) = 0.1*yinit + x;
for i=2:11
  x = sin(pi*i/4);
  y3(i) = 0.1*y3(i-1)^2 + x;
end

%part d: x[n]=sin(pi*n/4)u[n] + 2*u[n]
x = sin(pi/4)+2;
y4(1) = 0.1*yinit + x;
for i=2:11
  x = sin(pi*i/4)+2;
  y4(i) = 0.1*y4(i-1)^2 + x;
end

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

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

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

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

figure(5)	% Plot output signal y1[n]
stem(n, 2*y1+y3)
title('Problem 1.34 (b)')
xlabel('Time index (n)')
ylabel('2*y1+y3')





