Question

A discrete time linear shift-invariant system has an impulse response h[n] with h[0] =1, h[1] = -1, h[2] = 2, and zero otherwise. The system is given an input sequence x[n] with x[0] = x[2]=1 and zero otherwise. The number of nonzero samples in the output sequence y[n], and the value of y[2] are, respectively

• A.
  5, 3
• B.
  6, 2
• C.
  5, 2
• D.
  6, 1

Answer 1

The correct option is A

5, 3
$L_1=3,L_2=3$
$\Rightarrow \text{Number of samples in output =}{L}_1+L_2-1=5$
$y\left[n\right]=\underset{k=-\infty }{\overset{\infty }{\int }}x\left[k\right]h[n-k]$$y\left[2\right]=\underset{k=-\infty }{\overset{\infty }{\int }}x\left[k\right]h[2-k]$


$\Rightarrow y\left(2\right)=3$