# Signals & Systems Questions and Answers – BIBO Stability & Systems in the Time Domain

This set of Signals & Systems Multiple Choice Questions & Answers focuses on “BIBO Stability & Systems in the Time Domain”.

1. What is the full form of BIBO?
a) Boundary input Boundary Output
b) Boundary Input Bounded Output
c) Bonded Input Bonded Output
d) Bounded Input, Bounded Output

Explanation: BIBO stands for Bounded input, Bounded Output. It gives the stability of a system through a simple explanation that a system will be stable if it’s both input and output are bounded i.e it is not infinity.

2. When is a system said to be BIBO stable?
a) When the boundary conditions of the system are stable
b) When there is stability in the overall system
c) Every Bounded input results in a bounded output
d) When the input and output conditions are stable

Explanation: A system is said to be stable if, for any bounded input x(t), the response y(t) is also Bounded.
i.e |x(t)|≤Bx<∞ implies |y(t)≤Bx<∞.

3. When does a signal say to be bounded?
a) When it is stable
b) When it gives slow responses
c) Magnitude does not grow without bound
d) When it has small inputs

Explanation: A signal x(t) is said to be bounded if its magnitude does not grow without bound.
i.e |x(t)|≤Bx<∞.

4. How do you describe a stable system informally?
a) When small inputs lead to responses that do not diverge
b) When small inputs lead to responses that diverge
c) When large inputs lead to diverging outputs
d) All inputs lead to outputs that converge

Explanation: When small inputs lead to output responses that do not tend to infinity. The output of such systems does not diverge if the input does not diverge.

5. The system is stable when y(t)= tx(y).
a) True
b) False

Explanation: Here we can see,
|x(t)|≤Bx<∞, for all t.
Using the input output relation we have y(t)= tx(y). And so we may write, |Y(t)|=|tx(t)|=|t||x(t)|=|t|Bx.
As tends to infinity, the output also tends to infinity. That is it is unbounded. So it is unstable.
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6. How is a time domain system analyzed?
a) Study of a system in accordance to changes in its inputs over time
b) Study of a system in accordance to changes in its over time
c) Study of a system in accordance to changes in its overall structure over time
d) Study of a system in accordance to how a system change itself overall in a time

Explanation: Analysis in the time domain by done in how signals behave over time. That is, a system or a signal is studied in accordance to how it changes itself overall in time.

7. What is the frequency domain?
a) Analysis of signals in a frequency range
b) Analysis of signals in their bandwidth
c) Analysis of a signal with respect to its frequency
d) Study of a system in accordance to changes in its overall frequency

Explanation: Though this answer is a bit confusing frequency domain is defined as an analysis of a signal or a system with respect to its frequency. This concept has emerged from the transformations and the ‘spectrum’ concept.

8. Time domain is easier for mathematical operation than frequency domain.
a) True
b) False

Explanation: Time domain analysis is much tedious and difficult to perform when it comes to lengthy solvable problems. Whereas, in a frequency domain, it is very quick to perform. Even stability is easily attained in frequency domain analysis.

9. What are the mathematical tools to convert a system from a time domain to frequency domain?
a) Fourier series, Fourier transform, Laplace transform, Z-transform
b) Fourier series only
c) Fourier series and Laplace transform only
d) Fourier series, Fourier transform and Laplace transform only

Explanation: Fourier series, Fourier transform, Laplace transform, z-transform are some tools to convert a system from a time domain to frequency domain analysis to make it simpler. In fact, the concept of frequency domain has emerged from these transformations. It was first given by Joseph Fourier.

10. One of the main limitations of time domain analysis is the noise and frequency.
a) True
b) False

Explanation: True, one of the main limitations of time domain analysis is the noise and frequency. This is because it is easier in the frequency domain to read it and detect it and solve it. Time domain analysis is much tedious and difficult to perform when it comes to lengthy solvable problems.

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