Question

The impulse response of a LTI system is h(n)={1,1,1}. What is the response of the signal to the input x(n)={1,2,3}?

(a) {1,3,6,3,1}

(b) {1,2,3,2,1}

(c) {1,3,6,5,3}

(d) {1,1,1,0,0}

This question was addressed to me in an internship interview.

My doubt stems from Analysis of Discrete time LTI Systems in division Discrete Time Signals and Systems of Digital Signal Processing

Answer 1

The correct option is (c) {1,3,6,5,3}

The explanation: Let y(n)=x(n)*h(n)(‘*’ symbol indicates convolution symbol)

From the formula of convolution we get,

y(0)=x(0)h(0)=1.1=1

y(1)=x(0)h(1)+x(1)h(0)=1.1+2.1=3

y(2)=x(0)h(2)+x(1)h(1)+x(2)h(0)=1.1+2.1+3.1=6

y(3)=x(1)h(2)+x(2)h(1)=2.1+3.1=5

y(4)=x(2)h(2)=3.1=3

Therefore, y(n)=x(n)*h(n)={1,3,6,5,3}.