BEE Signals & Systems 2

Question 1

A discrete-time signal x[n] is defined as x[n] = u[n] - u[n-4]. What is the duration of this signal?

Accepted Answer

4 samples

Answer

x[n] is nonzero for n = 0, 1, 2, 3, giving exactly 4 samples.

Question 2

The Z-transform of δ[n - k] for k > 0 is:

Accepted Answer

z^(-k)

Answer

By the time-shifting property of the Z-transform, δ[n-k] ↔ z^(-k).

Question 3

Which condition must hold for a system described by H(z) to be causal and stable?

Accepted Answer

All poles inside the unit circle

Answer

A causal, stable discrete-time LTI system requires all poles to lie strictly inside the unit circle.

Question 4

The energy of the complex exponential signal x(t) = e^(jω₀t) over one period T₀ is:

Accepted Answer

T₀

Answer

|e^(jω₀t)|² = 1, so integrating over one period T₀ yields energy = T₀.

Question 5

The cross-correlation of two signals x(t) and y(t) evaluated at τ = 0 equals:

Accepted Answer

The inner product ∫x(t)y(t)dt

Answer

R_xy(0) = ∫x(t)y(t)dt, which is the inner product of x and y.

BEE - Bachelor of Electrical Engineering Practice Test