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(Solved): Question 5: (2 marks) A discrete system is represented by the following difference equation: y[n+3]- ...



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

.

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