Question
Download Solution PDFThe impulse response h[n] of an LTI system is
h[n] = u[n + 3] + u[n - 2] - 2u[n - 7].
Then the system is:
1. Stable
2. Casual
3. Unstable
4. Not casual.
Which of these are correct?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
- LTI system is causal when h[n] = 0 for n < 0
- LTI system is stable when \(\mathop \sum \nolimits_{n = - \infty }^\infty \left| {h\left[ n \right]} \right| < \infty \) i.e. It should be absolutely summable.
Calculation:
h[n] = u(n + 3) + u(n – 2) – 2 u(n – 7)
∵ h[n] ≠ 0 n < 0 ….. system is Non causal
\(\mathop \sum \nolimits_{n = - \infty }^\infty h\left( n \right) < \infty \) i.e. given impulse response is summable hence it is stable.
Last updated on Jul 2, 2025
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