BEE Signals and Control Systems 3

Question 1

What does the Region of Convergence (ROC) of the z-transform determine about a signal?

Accepted Answer

Whether the signal is causal, anti-causal, or two-sided

Answer

The ROC determines the nature of the corresponding time-domain signal: a right-half ROC (|z| > r) indicates a causal signal, while a left-half ROC indicates an anti-causal signal.

Question 2

For a second-order underdamped system, the peak overshoot Mp in the step response is determined by:

Accepted Answer

Damping ratio ζ only

Answer

Peak overshoot Mp = exp(−πζ/√(1−ζ²)) depends solely on the damping ratio ζ, not on the natural frequency.

Question 3

In a Bode magnitude plot, a simple pole at s = −a contributes a slope of how many dB/decade beyond the corner frequency?

Accepted Answer

−20 dB/decade

Answer

A single real pole introduces a −20 dB/decade roll-off slope in the magnitude plot for frequencies well above the pole's corner frequency.

Question 4

The convolution of two rectangular pulses of duration T each produces a signal of what shape?

Accepted Answer

Triangular pulse of duration 2T

Answer

Convolving two equal-width rectangular pulses yields a triangular pulse whose total duration is twice the original pulse width.

Question 5

The Nyquist sampling theorem states that to perfectly reconstruct a band-limited signal with maximum frequency fmax, the sampling frequency must be:

Accepted Answer

At least 2fmax

Answer

The Nyquist theorem requires a sampling rate of at least 2fmax (the Nyquist rate) to avoid aliasing and enable perfect reconstruction.

BEE - Bachelor of Electrical Engineering Practice Test

BEE - Bachelor of Electrical Engineering Practice Test

BEE Signals and Control Systems 3