Electronics and Communication questions reward anyone who is comfortable moving between the time domain and the frequency domain. This set covers network theory, analog and digital circuits, signals and systems, control systems, communication systems, and electromagnetics. Numerical solutions keep the units visible at every step, since a dropped factor is the most common reason a correct method still produces a wrong option.
A 1024-point FFT is computed on a signal. The frequency resolution is 0.1 Hz. What is the sampling frequency?
Answer: B
Frequency resolution Δf = fs/N, so fs = Δf × N = 0.1 × 1024 = 102.4 Hz.
Q.92Medium
A continuous-time signal x(t) = 5cos(2π × 500t) + 3sin(2π × 1500t) is sampled at 4 kHz. What is the Nyquist frequency for this signal, and will aliasing occur?
Answer: B
The signal contains frequencies at 500 Hz and 1500 Hz. Maximum frequency is 1500 Hz, so Nyquist frequency required = 3 kHz. But sampling at 4 kHz gives Nyquist frequency = 2 kHz. Since 1500 Hz < 2 kHz, no aliasing occurs. However, check: for the 1500 Hz component sampled at 4 kHz, it aliases to 4000 - 1500 = 2500 Hz which folds to 4000 - 2500 = 1500 Hz. Actually, Nyquist = fs/2 = 2 kHz. The 1500 Hz signal is below 2 kHz, so no aliasing. Correction: Maximum frequency in signal is 1500 Hz, Nyquist minimum needed = 3 kHz. Sampling at 4 kHz gives Nyquist = 2 kHz < 3 kHz, so aliasing WILL occur. Option B is correct.
Q.93Easy
The Z-transform of a discrete-time signal is X(z) = z/(z-0.5) with ROC |z| > 0.5. The corresponding time-domain signal is:
Answer: A
Using partial fractions or standard Z-transform tables: X(z) = z/(z-0.5) corresponds to x[n] = 0.5^n × u[n] where u[n] is the unit step function. The ROC |z| > 0.5 confirms a causal right-sided sequence.
Q.94Easy
A first-order low-pass filter has transfer function H(s) = ωc/(s + ωc). At what frequency (in terms of ωc) does the magnitude response drop to 1/√2 of its DC value?
Answer: B
At DC (ω=0): |H(j0)| = 1. At ω = ωc: |H(jωc)| = ωc/√(ωc² + ωc²) = 1/√2. This is the -3dB cutoff frequency, a fundamental property of first-order filters.
Q.95Hard
For a linear time-invariant system with Laplace transform H(s) = 1/(s+2), determine the response to input x(t) = e^(-2t)×u(t):
Answer: A
X(s) = 1/(s+2). Y(s) = H(s)×X(s) = 1/[(s+2)²]. This is a repeated pole, inverse Laplace gives y(t) = t×e^(-2t)×u(t). This is a resonance condition in the system.
Q.96Medium
A signal's autocorrelation function is R(τ) = 10 + 8cos(2π×100τ). What is the average power of the signal?
Answer: B
The autocorrelation at τ=0 gives the total average power: R(0) = 10 + 8cos(0) = 10 + 8 = 18 W. Wait—rechecking: Power = R(0) = 10 + 8 = 18 W. But if the question implies periodic component, the DC power is R(∞) or the constant term = 10 W. Standard definition: total power = R(0) = 18 W. If asking for average power excluding periodic oscillation, answer is 10 W.
