BEE Signals & Systems 3

Question 1

A continuous-time LTI system has impulse response h(t) = e^(-2t)u(t). What is the system's time constant?

Accepted Answer

0.5 seconds

Answer

For h(t) = e^(-αt)u(t), the time constant τ = 1/α = 1/2 = 0.5 seconds.

Question 2

The discrete Fourier transform (DFT) of a sequence of length N has how many unique frequency components?

Accepted Answer

N

Answer

The N-point DFT produces exactly N complex-valued frequency coefficients.

Question 3

If X(jω) is the Fourier transform of x(t), then the Fourier transform of x*(t) is:

Accepted Answer

X*(-jω)

Answer

Conjugation in time corresponds to complex conjugation and frequency reversal: FT{x*(t)} = X*(-jω).

Question 4

A second-order system has transfer function H(s) = ω_n²/(s² + 2ζω_n·s + ω_n²). For ζ = 0, the system is:

Accepted Answer

Marginally stable with pure oscillation

Answer

When ζ = 0, the poles are purely imaginary (±jω_n), producing undamped, sustained oscillation.

Question 5

The region of convergence (ROC) of a right-sided sequence's Z-transform is:

Accepted Answer

Outside a circle

Answer

A right-sided (causal) sequence has an ROC that is the exterior of a circle |z| > r.

BEE - Bachelor of Electrical Engineering Practice Test