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The impulse response h(t) of a continuous time, linear time invariant system is described by h(t) = eat u(t) + ebt u(-t) where, u(t) denots the unit step function and a and b are real constants. This system is stable if 
  • a)
    both a and b are positive
  • b)
    a is positive and b is negative
  • c)
    a is negative and b is positive 
  • d)
    both a and b are negative
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
The impulse response h(t) of a continuous time, linear time invariant ...
Concept:
An LTI system is stable if and only if its impulse response is absolutely integrable.
Calculation:
Given,
h(t) = eat u(t) + ebt u(-t)
h(t) = h1(t) + h2(t)
∵ τ > 0 therefore, for absolute integrability a < 0
∵ τ < 0 therefore, for absolute integrability b > 0
∴ h(t) should be in the form shown in the figure below:
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The impulse response h(t) of a continuous time, linear time invariant system is described by h(t) = eatu(t) + ebtu(-t) where, u(t) denots the unit step function and a and b are real constants. This system is stable ifa)both a and b are positiveb)a is positive and b is negativec)a is negative and b is positived)both a and b are negativeCorrect answer is option 'C'. Can you explain this answer?
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