From vallone@charcoal.eg.bucknell.edu Wed Sep 17 01:07 EDT 1997
Date: Wed, 17 Sep 1997 01:07:13 -0400
From: vallone@charcoal.eg.bucknell.edu (Vallone Michael Anthony '99)

% 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]
% Part b: x[n] = 2u[n], output y2[n]
% Part c: x[n] = sin(pi*n/4)u[n], output y3[n]
% Part d: x[n] = 2u[n] + sin(pi*n/4)u[n], output 2y1[n] + y3[n]


x = 1;
y1(1) = 0.5*yinit + x;	% Do time n=0 separately to handle initial condition.
y2(1) = 0.5*yinit + 2*x; % Do time n=0 separately to handle initial condition.
y3(1) = 0.5*yinit + sin(pi*x/4)*x; % Do time n=0 separately to handle initial conditions.
y4(1) = 0.5*yinit + 2*x + sin(pi*x/4)*x; % Do time n=0 separately to handle initial conditions.


for i=2:11	% Compute system outputs for times 1, 2, ..., 10
  x = 1;
  y1 (i) = 0.5*y1(i-1) + x;
  y2 (i) = 0.5*y2(i-1) + 2*x;
  y3 (i) = 0.5*y3(i-1) + sin(pi*x/4)*x;
  y4 (i) = 0.5*y4(i-1) + 2*x + sin(pi*x/4)*x; 



end

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




