Question

MatLab only

Problem B-2-17 Matlab only y Solve the following difference equation: x(k + 2) = x(k + 1) + 0.25x(k) - u(k + 2) where x(0) - 1 and x(1) - 2. The input function u(k) is given by u(k) = 1, k = 0,1,2,... Solve this problem lasti enabytíonlig maabcomputationally with MATLAB,

Answer 1

Script:

clc;close all;clear all;

k=0:1:50;

%Initial values

x(1)=1;x(2)=2;

%Input

u=1.*(k>=0);

%using recursive method

for m=3:1:length(k)

%delayed difference equation

x(m)=(x(m-1)-0.25*x(m-2)+u(m));

end

figure;

stem(k,x);grid;

xlabel('n');ylabel('x(n)')

title('output x(n)')

output x(n) 3.5 3 2.5 2 FO 1.5 16 0.5 30 50 10 20 40 4)

Script2:

k=0:1:50;

%using filter command

b=1;a=[1 -1 0.25];

sys=tf(b,a);

x=filter(b,a,u);

figure;

stem(k,x);grid;

xlabel('n');ylabel('x(n)')

title('output x(n)')

output x(n) 3.5 3 2.5 2 FO 1.5 16 0.5 30 50 10 20 40 4)