B CompE Bachelor of Computer Engineering Signals and Systems 2 — Questions and Answers
Question 1: A Linear Time-Invariant (LTI) system must satisfy which two fundamental properties?
- Causality and stability
- Linearity and time-invariance (Correct answer)
- Periodicity and symmetry
- Memorylessness and invertibility
Correct answer: Linearity and time-invariance
LTI systems must obey the superposition principle (linearity) and behave identically regardless of when the input is applied (time-invariance).
Question 2: The impulse response h(t) of an LTI system is defined as:
- The output when the input is a unit ramp function
- The output when the input is a unit impulse δ(t) (Correct answer)
- The Fourier Transform of the system's transfer function
- The integral of the step response
Correct answer: The output when the input is a unit impulse δ(t)
The impulse response is defined as the output of an LTI system when excited by a unit impulse δ(t), and it completely characterizes the system's behavior.
Question 3: The transfer function H(s) of an LTI system is the Laplace Transform of:
- The input signal x(t)
- The output signal y(t)
- The impulse response h(t) (Correct answer)
- The step response s(t)
Correct answer: The impulse response h(t)
H(s) = L{h(t)}, the Laplace Transform of the impulse response, which relates the output to the input in the s-domain via Y(s) = H(s)X(s).
Question 4: According to the Nyquist sampling theorem, a band-limited signal with maximum frequency f_max must be sampled at a minimum rate of:
- f_max
- f_max / 2
- 2 × f_max (Correct answer)
- 4 × f_max
Correct answer: 2 × f_max
The Nyquist criterion requires the sampling frequency f_s ≥ 2 × f_max to prevent aliasing and allow perfect reconstruction of the signal.
Question 5: Aliasing in a sampled signal occurs when:
- The sampling rate equals exactly twice the signal bandwidth
- The sampling rate exceeds twice the signal bandwidth
- The sampling rate is less than twice the signal bandwidth (Correct answer)
- The signal has no high-frequency components
Correct answer: The sampling rate is less than twice the signal bandwidth
Aliasing occurs when f_s < 2 × f_max (below the Nyquist rate), causing high-frequency components to fold back and appear as spurious low-frequency components.
Question 6: A system is BIBO stable if and only if:
- Its impulse response is absolutely integrable (∫|h(t)|dt < ∞) (Correct answer)
- Its input signal is always bounded
- Its transfer function has poles on the imaginary axis
- Its impulse response is periodic and bounded
Correct answer: Its impulse response is absolutely integrable (∫|h(t)|dt < ∞)
BIBO (Bounded-Input Bounded-Output) stability requires that ∫|h(t)|dt < ∞, guaranteeing that every bounded input produces a bounded output.
Question 7: A causal system is one in which the output depends only on:
- Past and present values of the input (Correct answer)
- Future values of the input
- The derivative of the input signal
- The frequency content of the input
Correct answer: Past and present values of the input
A causal system can only depend on current and past inputs (not future inputs), making it physically realizable in real-time applications.
