Question

Which of the test signals are best utilized by the stability analysis ____ .

• A. Impulse
• B. Step
• C. Ramp
• D. Parabolic

Hint:

Stability and Impulse Response. The stability of an LTI system is determined by its impulse response \(h(t)\) or the poles of its transfer function \(H(s) = \mathcal{L\{h(t)\\). BIBO stability requires absolutely integrable impulse response or poles in the left-half s-plane.

Answer 1

The Correct Option is A

Stability analysis of Linear Time-Invariant (LTI) systems often involves examining the system's response to specific inputs or analyzing its transfer function
- The impulse response \(h(t)\) (response to a Dirac delta input \(\delta(t)\)) completely characterizes an LTI system
The system is Bounded-Input Bounded-Output (BIBO) stable if and only if its impulse response is absolutely integrable (\( \int_{-\infty}^{\infty} |h(t)| dt<\infty \))
In the frequency domain, stability is determined by the poles of the transfer function (which is the Laplace transform of the impulse response) lying in the left half of the s-plane
- Step, ramp, and parabolic responses are used to analyze steady-state errors and transient performance characteristics, but the impulse response is most directly linked to the system's inherent stability properties
Stability analysis techniques like checking pole locations, Routh-Hurwitz criterion, Nyquist criterion, and Bode plots are all fundamentally based on the system's transfer function or impulse response characteristics
Therefore, the impulse signal and its corresponding response are most fundamentally utilized in stability analysis