B CompE Bachelor of Computer Engineering Signals and Systems 2

Question 1

A Linear Time-Invariant (LTI) system must satisfy which two fundamental properties?

Accepted Answer

Linearity and time-invariance

Answer

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:

Accepted Answer

The output when the input is a unit impulse δ(t)

Answer

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:

Accepted Answer

The impulse response h(t)

Answer

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:

Accepted Answer

2 × f_max

Answer

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:

Accepted Answer

The sampling rate is less than twice the signal bandwidth

Answer

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.

B CompE Bachelor of Computer Engineering Practice Test

B CompE Bachelor of Computer Engineering Practice Test

B CompE Bachelor of Computer Engineering Signals and Systems 2