Question

Solve using MAT-LAB codes: A. Solve the following difference equations using the sequential method: ylk] +1.5y[k-1]+0.5y[k-2] x[k]+ x[k-1] where 0.8 uk] and and y[-2] = y[ - 1] 0 xk] B. Plot the results for the range 0 s ks 20.

Answer 1

MATLAB Code:

close all
clear
clc

num = [1 1]; % 1*x[k] + 1*x[k-1]
den = [1 1.5 0.5]; % 1*y[k] + 1.5*y[k-1] + 0.5*y[k-2]
k = 0:1:20;
x = 0.8.^k; % x[k] and since k >= 0 , u[k] = 1
x_conds = [0 0]; % [x[-2] x[-1]]
y_conds = [0 0]; % [y[-2] y[-1]]
initconds = filtic(num, den, y_conds, x_conds); % initial conditions
y = filter(num, den, x, initconds);
plot(k,y,'-o'), title('Solution'), xlabel('k'), ylabel('y[k]')

Plot:

Solution 1G 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0 2 4 6 8 10 12 14 16 18 20 k