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Determine the impulse response for the cascade of two LTI systems having impulse responses h1(n)=(1/2)2 u(n) and h2(n)= (1/4)2 u(n). 
  • a)
    (1/2)n[2-(1/2)n], n<0
  • b)
    (1/2)n[2-(1/2)n], n>0
  • c)
    (1/2)n[2+(1/2)n], n<0
  • d)
    (1/2)n[2+(1/2)n], n>0
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
Determine the impulse response for the cascade of two LTI systems havi...
Explanation: Let h2(n) be shifted and folded.
so, h(k)=h1(n)*h2(n)=
For k<0, h1(n)= h2(n)=0 since the unit step function is defined only on the right hand side.
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Most Upvoted Answer
Determine the impulse response for the cascade of two LTI systems havi...
To find the impulse response of the cascade of two LTI systems, we need to convolve their individual impulse responses.

h1(n) = (1/2)2u(n)

h2(n) = (1/4)2u(n)

h1(n) * h2(n) = [(1/2)2u(n)] * [(1/4)2u(n)]

= (1/8)4u(n) * u(n)

= (1/8)4u(n)

= (1/2)2u(n)

Therefore, the impulse response of the cascade of the two LTI systems is h(n) = (1/2)2u(n), which is the same as the impulse response of the first system.

So, there is no need to calculate a new impulse response, as it is the same as the first system. The answer is h(n) = (1/2)2u(n), which can also be written as (1/4)n.
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Determine the impulse response for the cascade of two LTI systems having impulse responses h1(n)=(1/2)2u(n) and h2(n)= (1/4)2u(n).a)(1/2)n[2-(1/2)n], n<0b)(1/2)n[2-(1/2)n], n>0c)(1/2)n[2+(1/2)n], n<0d)(1/2)n[2+(1/2)n], n>0Correct answer is option 'B'. Can you explain this answer?
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Determine the impulse response for the cascade of two LTI systems having impulse responses h1(n)=(1/2)2u(n) and h2(n)= (1/4)2u(n).a)(1/2)n[2-(1/2)n], n<0b)(1/2)n[2-(1/2)n], n>0c)(1/2)n[2+(1/2)n], n<0d)(1/2)n[2+(1/2)n], n>0Correct answer is option 'B'. Can you explain this answer? for Electrical Engineering (EE) 2024 is part of Electrical Engineering (EE) preparation. The Question and answers have been prepared according to the Electrical Engineering (EE) exam syllabus. Information about Determine the impulse response for the cascade of two LTI systems having impulse responses h1(n)=(1/2)2u(n) and h2(n)= (1/4)2u(n).a)(1/2)n[2-(1/2)n], n<0b)(1/2)n[2-(1/2)n], n>0c)(1/2)n[2+(1/2)n], n<0d)(1/2)n[2+(1/2)n], n>0Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Electrical Engineering (EE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Determine the impulse response for the cascade of two LTI systems having impulse responses h1(n)=(1/2)2u(n) and h2(n)= (1/4)2u(n).a)(1/2)n[2-(1/2)n], n<0b)(1/2)n[2-(1/2)n], n>0c)(1/2)n[2+(1/2)n], n<0d)(1/2)n[2+(1/2)n], n>0Correct answer is option 'B'. Can you explain this answer?.
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