BEE Signals and Control Systems 5

Question 1

The transfer function of an ideal differentiator in the Laplace domain is:

Accepted Answer

s

Answer

Differentiation in the time domain corresponds to multiplication by s in the Laplace domain, so the transfer function of a differentiator is H(s) = s.

Question 2

A minimum-phase system is one in which:

Accepted Answer

Both poles and zeros are in the left-half s-plane

Answer

A minimum-phase system has all its poles AND zeros in the open left-half s-plane, ensuring the system and its inverse are both stable and causal.

Question 3

For a discrete-time LTI system to be BIBO stable, the impulse response h[n] must satisfy:

Accepted Answer

Σ|h[n]| < ∞ (absolutely summable)

Answer

BIBO stability requires that the impulse response be absolutely summable: Σ|h[n]| < ∞, which guarantees bounded output for any bounded input.

Question 4

The phase margin of a control system is measured at:

Accepted Answer

The gain crossover frequency

Answer

Phase margin is measured at the gain crossover frequency (where |G(jω)H(jω)| = 1, or 0 dB) and equals 180° plus the actual phase angle at that frequency.

Question 5

Which of the following correctly represents the relationship between the DTFT X(e^jω) and the z-transform X(z)?

Accepted Answer

X(e^jω) = X(z)|_{z=e^jω}

Answer

The DTFT is the z-transform evaluated on the unit circle |z| = 1, i.e., X(e^jω) = X(z)|_{z=e^jω}.

BEE - Bachelor of Electrical Engineering Practice Test

BEE - Bachelor of Electrical Engineering Practice Test

BEE Signals and Control Systems 5