B CompE Bachelor of Computer Engineering Signals and Systems 1 β Questions and Answers
Question 1: Which of the following best describes a continuous-time signal?
- A signal defined only at integer time instants
- A signal defined for all real values of time (Correct answer)
- A signal that takes only discrete amplitude values
- A signal with finite energy and finite duration
Correct answer: A signal defined for all real values of time
A continuous-time signal is defined for every real value of t, distinguishing it from discrete-time signals that are defined only at integer time instants.
Question 2: The Fourier Transform of a time-domain signal decomposes it into:
- A series of polynomial functions
- A product of exponential decay terms
- A continuous spectrum of sinusoidal components at different frequencies (Correct answer)
- A set of discrete amplitude levels sampled periodically
Correct answer: A continuous spectrum of sinusoidal components at different frequencies
The Fourier Transform represents a signal as a continuous spectrum of sinusoids, revealing how signal energy is distributed across frequencies.
Question 3: The integral of the unit impulse function Ξ΄(t) over all time equals:
- 0
- β
- 1 (Correct answer)
- -1
Correct answer: 1
By definition, β«Ξ΄(t)dt = 1 over all time; this normalization is the fundamental property that makes the impulse useful in system analysis.
Question 4: Convolution of two signals in the time domain corresponds to which operation in the frequency domain?
- Addition
- Differentiation
- Multiplication (Correct answer)
- Integration
Correct answer: Multiplication
The Convolution Theorem states that convolution in the time domain equals pointwise multiplication in the frequency domain, simplifying computation.
Question 5: The Laplace Transform of the unit impulse function Ξ΄(t) is:
- 1/s
- 1 (Correct answer)
- s
- e^(βs)
Correct answer: 1
Applying the sifting property, L{Ξ΄(t)} = β«Ξ΄(t)e^(βst)dt = e^0 = 1 for all valid s.
Question 6: The fundamental period of the signal x(t) = sin(2Οt) is:
- 2Ο seconds
- Ο seconds
- 0.5 seconds
- 1 second (Correct answer)
Correct answer: 1 second
For x(t) = sin(2Οt), the angular frequency Οβ = 2Ο rad/s, so the period T = 2Ο/Οβ = 2Ο/2Ο = 1 second.
Question 7: The Z-transform is primarily used for analyzing:
- Continuous-time analog signals
- Electromagnetic wave propagation
- Discrete-time signals and systems (Correct answer)
- Thermal noise in resistors
Correct answer: Discrete-time signals and systems
The Z-transform is the discrete-time counterpart of the Laplace Transform and is the standard tool for analyzing discrete-time signals and digital systems.
B CompE Bachelor of Computer Engineering Signals and Systems 1
Which of the following best describes a continuous-time signal?