BEE Signals and Control Systems 2

Question 1

Which property of the Fourier Transform states that a time shift in a signal results in a phase shift in its frequency domain representation?

Accepted Answer

Time-shifting property

Answer

The time-shifting property states that if x(t) ↔ X(jω), then x(t−t₀) ↔ X(jω)e^(−jωt₀), introducing a linear phase shift.

Question 2

A system has the transfer function H(s) = 10/(s² + 4s + 10). What is the damping ratio ζ?

Accepted Answer

0.632

Answer

Comparing with the standard form ωn²/(s² + 2ζωns + ωn²), ωn = √10 ≈ 3.162 and 2ζωn = 4, so ζ = 4/(2×3.162) ≈ 0.632.

Question 3

The z-transform of the unit step sequence u[n] is:

Accepted Answer

z/(z−1), |z| > 1

Answer

The z-transform of u[n] = Σ z^(−n) for n≥0 sums to z/(z−1) for |z| > 1.

Question 4

In a PID controller, which component is added primarily to reduce steady-state error to zero for step inputs?

Accepted Answer

Integral term

Answer

The integral term accumulates past error over time, forcing the steady-state error to zero by continuously correcting any residual offset.

Question 5

Which of the following is NOT a property of a Linear Time-Invariant (LTI) system?

Accepted Answer

Output depends on future inputs

Answer

LTI systems are causal in most practical applications, meaning their output depends only on present and past inputs, not future inputs.

BEE - Bachelor of Electrical Engineering Practice Test