Question 5: (2 marks) A discrete system is represented by the following difference equation:
y[n+3]-2y[n+1]+3y[n]=x[n+2]-x[n+1]
with the initials conditions
y[-3]=-3,y[-2]=-2
, and
y[-1]=-1
. Solve this difference equation recursively for the input
x[n]=r[n]
by finding the system output
y[n]
at
n=0,1,2,3
. Question 6: (2 marks) Determine the output
^()
u [n]
of the discrete-time system whose input and impulse response are given by
x[n]=(4)^(u^(?))u[n-2]
and
h[n]=(2)^(')u[n]
, respectively. Use direct expression. Hint:
\sum_(k=m)^n r^(k)=(r^(n+1)-r^(m))/(r-1),r!=1
.