BEE FREE Bachelor of Electrical Engineering Signals & Systems Questions and Answers 2 — Questions and Answers
Question 1: What is the Nyquist sampling rate for a signal with a maximum frequency component of 4 kHz?
- 4 kHz
- 8 kHz (Correct answer)
- 16 kHz
- 2 kHz
Correct answer: 8 kHz
The Nyquist rate is twice the maximum frequency, so 2 × 4 kHz = 8 kHz.
Question 2: Which property of the Fourier Transform states that multiplication in the time domain corresponds to convolution in the frequency domain?
- Linearity
- Duality
- Convolution theorem (Correct answer)
- Parseval's theorem
Correct answer: Convolution theorem
The convolution theorem states that multiplication in one domain equals convolution in the other domain.
Question 3: A system with impulse response h(t) = e^(-2t)u(t) is classified as what type of system?
- Unstable and non-causal
- Stable and causal (Correct answer)
- Stable and non-causal
- Unstable and causal
Correct answer: Stable and causal
The impulse response is zero for t < 0 (causal) and absolutely integrable (stable).
Question 4: What does the Region of Convergence (ROC) of a causal signal in the Laplace domain look like?
- A vertical strip
- The entire s-plane
- A right-half plane extending to the right of the rightmost pole (Correct answer)
- A left-half plane
Correct answer: A right-half plane extending to the right of the rightmost pole
For causal signals, the ROC is a right-half plane to the right of the rightmost pole.
Question 5: If x(t) is an even signal, what can be said about its Fourier Transform X(ω)?
- X(ω) is purely imaginary
- X(ω) is purely real (Correct answer)
- X(ω) is complex with equal real and imaginary parts
- X(ω) is always zero
Correct answer: X(ω) is purely real
The Fourier Transform of a real and even signal is purely real and even.
Question 6: In a discrete-time LTI system, what operation is used to find the output given the input x[n] and impulse response h[n]?
- Multiplication
- Correlation
- Discrete convolution (Correct answer)
- Differentiation
Correct answer: Discrete convolution
The output of a discrete-time LTI system is the discrete convolution of x[n] and h[n].
BEE FREE Bachelor of Electrical Engineering Signals & Systems Questions and Answers 2
What is the Nyquist sampling rate for a signal with a maximum frequency component of 4 kHz?