Topic: Signals and Systems
Two discrete time systems have impulse response $h_{1}[n]=\delta[n-3]$ and $h_{2}[n]=\delta[n-5]$. If these two systems are cascaded then the overall impulse response of the cascaded system is
- A. $\delta[n-8]$
- B. $\delta[n-3]+\delta[n-5]$
- C. $\delta[n-1]*\delta[n-2]$
- D. $\delta[n-2]$
Answer: A. $\delta[n-8]$
Explanation: The overall impulse response of cascaded systems is the convolution of their individual impulse responses.
$h[n] = h_1[n] * h_2[n] = \delta[n-3] * \delta[n-5] = \delta[n - (3+5)] = \delta[n-8]$.