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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}
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
The impulse response of a LTI system is h(n)={1,1,1}. What is the resp...
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}.
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Most Upvoted Answer
The impulse response of a LTI system is h(n)={1,1,1}. What is the resp...
Given:

h(n) = {1, 1, 1} (impulse response of LTI system)

x(n) = {1, 2, 3} (input signal)

To find:

y(n) = output signal

Solution:

The output signal y(n) can be obtained by convolving the input signal x(n) with the impulse response h(n) of the LTI system.

y(n) = x(n) * h(n)

where, * denotes convolution operation.

Substituting the given values, we get:

y(n) = {1, 2, 3} * {1, 1, 1}

y(n) = {1*1, 1*2+1*1, 1*3+1*2+1*1, 1*3+1*2, 1*3}

y(n) = {1, 3, 6, 5, 3}

Therefore, the response of the signal to the input x(n)={1,2,3} is {1, 3, 6, 5, 3}.

Hence, the correct option is (c).
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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}Correct answer is option 'C'. Can you explain this answer?
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