BEE Signals & Systems 5 โ Questions and Answers
Question 1: The bilateral Laplace transform differs from the unilateral Laplace transform in that it integrates from:
- 0 to โ
- -โ to โ (Correct answer)
- -โ to 0
- 0 to T
Correct answer: -โ to โ
The bilateral (two-sided) Laplace transform integrates over all time from -โ to โ, capturing non-causal signals.
Question 2: The frequency response H(e^(jฯ)) of a discrete-time system is evaluated from H(z) by substituting:
- z = ฯ + jฯ
- z = e^(jฯ) (Correct answer)
- z = jฯ
- z = 1/jฯ
Correct answer: z = e^(jฯ)
The DTFT is obtained by evaluating the Z-transform on the unit circle, i.e., z = e^(jฯ).
Question 3: An all-pass system has a magnitude response |H(jฯ)| that is:
- Zero for all ฯ
- A linear function of ฯ
- Constant (unity) for all ฯ (Correct answer)
- Maximum at ฯ = 0
Correct answer: Constant (unity) for all ฯ
An all-pass filter passes all frequencies with equal gain (unity magnitude) while altering only the phase.
Question 4: The group delay of a system is defined as:
- -dฯ(ฯ)/dฯ (Correct answer)
- dฯ(ฯ)/dฯ
- ฯ(ฯ)/ฯ
- -ฯ(ฯ)/ฯ
Correct answer: -dฯ(ฯ)/dฯ
Group delay ฯ_g(ฯ) = -dฯ(ฯ)/dฯ, representing the delay experienced by a narrowband signal centered at ฯ.
Question 5: A signal x(t) is said to be even if:
- x(t) = -x(-t)
- x(t) = x(-t) (Correct answer)
- x(t) = x(t + T)
- x(t) = jx(-t)
Correct answer: x(t) = x(-t)
An even signal satisfies x(t) = x(-t), meaning it is symmetric about the vertical axis.
Question 6: The output of a causal LTI system before the input is applied (t < 0) is zero because of:
- Linearity
- Time-invariance
- Causality (Correct answer)
- Stability
Correct answer: Causality
Causality requires that the system output depends only on present and past inputs, so no output exists before excitation.
Question 7: The CTFT of a rectangular pulse of width ฯ centered at the origin is:
- A sinc function in frequency (Correct answer)
- Another rectangular pulse
- A Gaussian function
- A complex exponential
Correct answer: A sinc function in frequency
The Fourier transform of a rectangular pulse rect(t/ฯ) is ฯยทsinc(fฯ), a sinc function in the frequency domain.
BEE Signals & Systems 5
The bilateral Laplace transform differs from the unilateral Laplace transform in that it integrates from: