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Is the function y[n] = y[n-1] + x[n] stable in nature?
- a)It is stable
- b)It is unstable
- c)Both stable and unstable
- d)None of the mentioned
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
Is the function y[n] = y[n-1] + x[n] stable in nature?a)It is stableb)...
It is BIBO stable in nature, i.e. bounded input-bounded output stable.
Most Upvoted Answer
Is the function y[n] = y[n-1] + x[n] stable in nature?a)It is stableb)...
Stability of a function
- In signal processing, a system is said to be stable if its output is bounded for every bounded input.
- A bounded input signal is one that does not grow infinitely large over time.
- A stable system will not cause the output to grow uncontrollably or become unstable.
Analysis of y[n] = y[n-1] x[n]
- The given function is a difference equation that describes a system that produces an output y[n] based on an input x[n] and the previous output y[n-1].
- To determine the stability of this system, we need to analyze its behavior for different types of input signals.
- Let's assume that the input signal x[n] is bounded.
- If the previous output y[n-1] is also bounded, then the current output y[n] will be bounded as well.
- This is because the function y[n] = y[n-1] x[n] only scales the input signal by a constant factor, which does not affect its boundedness.
- Therefore, the system is stable for bounded input signals.
Conclusion
- The given function y[n] = y[n-1] x[n] is stable in nature for bounded input signals.
- This means that the output will not grow uncontrollably or become unstable for any bounded input signal.
- In signal processing, a system is said to be stable if its output is bounded for every bounded input.
- A bounded input signal is one that does not grow infinitely large over time.
- A stable system will not cause the output to grow uncontrollably or become unstable.
Analysis of y[n] = y[n-1] x[n]
- The given function is a difference equation that describes a system that produces an output y[n] based on an input x[n] and the previous output y[n-1].
- To determine the stability of this system, we need to analyze its behavior for different types of input signals.
- Let's assume that the input signal x[n] is bounded.
- If the previous output y[n-1] is also bounded, then the current output y[n] will be bounded as well.
- This is because the function y[n] = y[n-1] x[n] only scales the input signal by a constant factor, which does not affect its boundedness.
- Therefore, the system is stable for bounded input signals.
Conclusion
- The given function y[n] = y[n-1] x[n] is stable in nature for bounded input signals.
- This means that the output will not grow uncontrollably or become unstable for any bounded input signal.
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Is the function y[n] = y[n-1] + x[n] stable in nature?a)It is stableb)...
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