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What is the inverse of the system with impulse response h(n)=(1/2)nu(n)?
- a)δ(n)+1/2 δ(n-1)
- b)δ(n)-1/2 δ(n-1)
- c)δ(n)-1/2 δ(n+1)
- d)δ(n)+1/2 δ(n+1)
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
What is the inverse of the system with impulse response h(n)=(1/2)nu(n...
Explanation: Given impulse response is h(n)=(1/2)nu(n)
The system function corresponding to h(n) is
H(z)=1/(1-1/2 z-1 ) ROC:|z|>1/2
This system is both stable and causal. Since H(z) is all pole system, its inverse is FIR and is given by the system function
HI(z)= 1- 1/2 z-1
Hence its impulse response is δ(n)-1/2 δ(n-1).
The system function corresponding to h(n) is
H(z)=1/(1-1/2 z-1 ) ROC:|z|>1/2
This system is both stable and causal. Since H(z) is all pole system, its inverse is FIR and is given by the system function
HI(z)= 1- 1/2 z-1
Hence its impulse response is δ(n)-1/2 δ(n-1).
Most Upvoted Answer
What is the inverse of the system with impulse response h(n)=(1/2)nu(n...
The inverse of the system with impulse response h(n) = (1/2)nu(n) is not well-defined because the system is not invertible. The impulse response h(n) is a causal signal, meaning it is non-zero only for n >= 0. In order for a system to be invertible, its impulse response must be non-zero for all values of n. Since h(n) is zero for n < 0,="" it="" is="" not="" possible="" to="" determine="" the="" input="" signal="" uniquely="" from="" the="" output="" signal,="" and="" thus="" the="" system="" is="" not="" invertible.="" 0,="" it="" is="" not="" possible="" to="" determine="" the="" input="" signal="" uniquely="" from="" the="" output="" signal,="" and="" thus="" the="" system="" is="" not="" />
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