BEE Signals & Systems 3 — Questions and Answers
Question 1: A continuous-time LTI system has impulse response h(t) = e^(-2t)u(t). What is the system's time constant?
- 2 seconds
- 0.5 seconds (Correct answer)
- 1 second
- e seconds
Correct answer: 0.5 seconds
For h(t) = e^(-αt)u(t), the time constant τ = 1/α = 1/2 = 0.5 seconds.
Question 2: The discrete Fourier transform (DFT) of a sequence of length N has how many unique frequency components?
- N/2
- N-1
- N (Correct answer)
- 2N
Correct answer: N
The N-point DFT produces exactly N complex-valued frequency coefficients.
Question 3: If X(jω) is the Fourier transform of x(t), then the Fourier transform of x*(t) is:
- X*(jω)
- X*(-jω) (Correct answer)
- X(-jω)
- -X*(jω)
Correct answer: X*(-jω)
Conjugation in time corresponds to complex conjugation and frequency reversal: FT{x*(t)} = X*(-jω).
Question 4: A second-order system has transfer function H(s) = ω_n²/(s² + 2ζω_n·s + ω_n²). For ζ = 0, the system is:
- Overdamped
- Critically damped
- Underdamped
- Marginally stable with pure oscillation (Correct answer)
Correct answer: Marginally stable with pure oscillation
When ζ = 0, the poles are purely imaginary (±jω_n), producing undamped, sustained oscillation.
Question 5: The region of convergence (ROC) of a right-sided sequence's Z-transform is:
- The entire z-plane
- Inside a circle
- Outside a circle (Correct answer)
- An annular ring
Correct answer: Outside a circle
A right-sided (causal) sequence has an ROC that is the exterior of a circle |z| > r.
Question 6: Parseval's theorem for continuous-time signals states that:
- ∫|x(t)|²dt = (1/2π)∫|X(jω)|²dω (Correct answer)
- ∫x(t)dt = X(0)
- ∫|X(jω)|dω = ∫|x(t)|dt
- ∫x(t)h(t)dt = X(jω)H(jω)
Correct answer: ∫|x(t)|²dt = (1/2π)∫|X(jω)|²dω
Parseval's theorem equates signal energy in time and frequency domains with the 1/2π normalization factor.
Question 7: A linear phase FIR filter is preferred in applications requiring:
- Maximum stopband attenuation
- Minimum filter order
- No phase distortion across all frequencies (Correct answer)
- Recursive implementation
Correct answer: No phase distortion across all frequencies
Linear phase FIR filters introduce a constant group delay, preserving waveshape and avoiding phase distortion.
BEE Signals & Systems 3
A continuous-time LTI system has impulse response h(t) = e^(-2t)u(t).
What is the system's time constant?