Question

How to take the impulse response of 1/3 n⋅u(n−1)?

A) Time-domain analysis
B) Laplace transform
C) Fourier transform
D) Z-transform

Answer 1

To find the impulse response of 1/3 n⋅u(n−1), we can use time-domain analysis and the unit step function.

Step-by-step explanation:

To find the impulse response of the function 1/3 n⋅u(n−1), we can use time-domain analysis. The impulse response of a discrete-time system is the output when an input impulse of unity magnitude is applied.

In this case, the function describes a discrete-time system with a delay of 1. So, when the input impulse is applied at n=0, the output will be zero. At n=1, the output will be 1/3. And for n>1, the output will be zero again.

Therefore, the impulse response of 1/3 n⋅u(n−1) is given by:

h(n) = 1/3u(n-1), where u(n) is the unit step function.