1. What does state-space analysis provide in system representation?
a) Frequency domain representation
b) Time domain representation
c) Both frequency and time domain representation
d) None of the above
Answer: b) Time domain representation
Explanation: State-space analysis represents a dynamic system in the time domain using state variables and their derivatives.
2. What does the state-transition matrix describe in a system?
a) The relationship between inputs and outputs
b) The evolution of state variables over time
c) The steady-state behavior of the system
d) None of the above
Answer: b) The evolution of state variables over time
Explanation: The state-transition matrix describes how the state variables of a system evolve from one time instant to the next.
3. In multi-input, multi-output systems, how many input-output pairs are considered simultaneously?
a) One input and one output
b) Multiple inputs and one output
c) One input and multiple outputs
d) Multiple inputs and multiple outputs
Answer: d) Multiple inputs and multiple outputs
Explanation: Multi-input, multi-output (MIMO) systems consider multiple input-output pairs simultaneously, allowing for more complex system representations.
4. What is the role of the Sampling Theorem?
a) To convert continuous-time signals into discrete-time signals
b) To reconstruct continuous-time signals from discrete-time samples
c) To analyze the frequency content of continuous-time signals
d) None of the above
Answer: a) To convert continuous-time signals into discrete-time signals
Explanation: The Sampling Theorem dictates the conditions under which a continuous-time signal can be accurately represented by discrete samples.
5. What does the Sampling Theorem imply about the sampling rate compared to the signal frequency?
a) The sampling rate must be higher than the signal frequency
b) The sampling rate must be lower than the signal frequency
c) The sampling rate must be equal to the signal frequency
d) There is no relationship between sampling rate and signal frequency
Answer: a) The sampling rate must be higher than the signal frequency
Explanation: According to the Nyquist-Shannon Sampling Theorem, the sampling rate must be at least twice the highest frequency component of the signal.
6. How does undersampling affect the reconstructed signal?
a) It introduces distortion and aliasing
b) It improves the signal quality
c) It has no effect on the reconstructed signal
d) It reduces the signal amplitude
Answer: a) It introduces distortion and aliasing
Explanation: Undersampling occurs when the sampling rate is insufficient to capture the signal adequately, leading to distortion and aliasing in the reconstructed signal.
7. What information does the spectrum of a sampled signal provide?
a) Time-domain characteristics
b) Frequency-domain characteristics
c) Both time and frequency-domain characteristics
d) None of the above
Answer: b) Frequency-domain characteristics
Explanation: The spectrum of a sampled signal reveals the frequency content of the signal after sampling.
8. What is the purpose of reconstruction in signal processing?
a) To increase the signal amplitude
b) To convert discrete-time signals into continuous-time signals
c) To reduce the frequency content of the signal
d) None of the above
Answer: b) To convert discrete-time signals into continuous-time signals
Explanation: Reconstruction involves converting discrete-time signals back into their continuous-time counterparts.
9. How does the reconstruction process typically occur in practice?
a) By filtering and interpolation
b) By amplifying the signal
c) By reducing the sampling rate
d) None of the above
Answer: a) By filtering and interpolation
Explanation: Reconstruction often involves filtering out aliasing and interpolating between sampled points to reconstruct the continuous signal.
10. What happens if the sampling rate is too low during reconstruction?
a) Signal distortion
b) Signal amplification
c) Signal attenuation
d) None of the above
Answer: a) Signal distortion
Explanation: If the sampling rate is too low during reconstruction, it can result in signal distortion due to aliasing and insufficient information to reconstruct the original signal accurately.