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What is the inverse of the system with impulse response h(n)= δ(n)-1/2 δ(n-1)?
- a)(1/2)nu(n)
- b)-(1/2)nu(-n-1)
- c)(1/2)nu(n) & -(1/2)nu(-n-1)
- d)None of the mentioned
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
What is the inverse of the system with impulse response h(n)= δ(...
Explanation: The system function of given system is H(z)= 1- 1/2 z-1
The inverse of the system has a system function as H(z)= 1/(1-1/2 z-1 )
Thus it has a zero at origin and a pole at z=1/2.So, two possible cases are |z|>1/2 and |z|<1/2
So, h(n)= (1/2)nu(n) for causal and stable(|z|>1/2)
and h(n)= -(1/2)nu(-n-1) for anti causal and unstable for |z|<1/2.
The inverse of the system has a system function as H(z)= 1/(1-1/2 z-1 )
Thus it has a zero at origin and a pole at z=1/2.So, two possible cases are |z|>1/2 and |z|<1/2
So, h(n)= (1/2)nu(n) for causal and stable(|z|>1/2)
and h(n)= -(1/2)nu(-n-1) for anti causal and unstable for |z|<1/2.
Most Upvoted Answer
What is the inverse of the system with impulse response h(n)= δ(...
To find the inverse of a system with impulse response h(n), we need to find a system with impulse response g(n) such that the convolution of h(n) and g(n) is equal to the impulse response of the identity system, which is a Kronecker delta function.
Mathematically, we need to solve the following equation for g(n):
h(n) * g(n) = δ(n),
where * represents convolution and δ(n) is the Kronecker delta function.
In general, finding the inverse of a system is a complex task and may require advanced techniques such as Fourier transform or z-transform. The specific inverse of a system with impulse response h(n) cannot be determined without additional information about the system.
Mathematically, we need to solve the following equation for g(n):
h(n) * g(n) = δ(n),
where * represents convolution and δ(n) is the Kronecker delta function.
In general, finding the inverse of a system is a complex task and may require advanced techniques such as Fourier transform or z-transform. The specific inverse of a system with impulse response h(n) cannot be determined without additional information about the system.
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What is the inverse of the system with impulse response h(n)= δ(n)-1/2 δ(n-1)?a)(1/2)nu(n)b)-(1/2)nu(-n-1)c)(1/2)nu(n) & -(1/2)nu(-n-1)d)None of the mentionedCorrect answer is option 'C'. Can you explain this answer?
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