Signals and Control Systems Flashcards
7 cards from real BEE practice questions. Tap to flip, then mark Knew It or Still Learning — missed cards come back until you master them.
Read the first 7 Signals and Control Systems flashcards as text
What does the Region of Convergence (ROC) of the z-transform determine about a signal?
Answer: Whether the signal is causal, anti-causal, or two-sided
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.
For a second-order underdamped system, the peak overshoot Mp in the step response is determined by:
Answer: Damping ratio ζ only
Peak overshoot Mp = exp(−πζ/√(1−ζ²)) depends solely on the damping ratio ζ, not on the natural frequency.
In a Bode magnitude plot, a simple pole at s = −a contributes a slope of how many dB/decade beyond the corner frequency?
Answer: −20 dB/decade
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.
The convolution of two rectangular pulses of duration T each produces a signal of what shape?
Answer: Triangular pulse of duration 2T
Convolving two equal-width rectangular pulses yields a triangular pulse whose total duration is twice the original pulse width.
The Nyquist sampling theorem states that to perfectly reconstruct a band-limited signal with maximum frequency fmax, the sampling frequency must be:
Answer: At least 2fmax
The Nyquist theorem requires a sampling rate of at least 2fmax (the Nyquist rate) to avoid aliasing and enable perfect reconstruction.
Which root locus rule states that the number of branches going to infinity equals the number of open-loop poles minus the number of open-loop zeros?
Answer: Number of asymptotes rule
The number of asymptotes (branches going to infinity) equals P − Z, where P is the number of poles and Z is the number of finite zeros.
An energy signal x(t) has finite energy E. Its Parseval's relation states that E equals:
Answer: ∫|X(f)|²df from −∞ to ∞
Parseval's theorem equates the total energy computed in the time domain to the integral of the squared magnitude spectrum: E = ∫|X(f)|²df.