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.
Which window function has the BEST frequency resolution but WORST spectral leakage?
Answer: C
Rectangular window has narrowest main lobe (best resolution) but highest sidelobe (worst leakage)
Q.62Hard
Parseval's theorem states that energy in time domain equals energy in frequency domain. For discrete signals:
Answer: B
Parseval's theorem for discrete-time: ∑|x[n]|² = (21π)∫|X(e^jω)|²dω over 2π
Q.63Hard
For a stable IIR filter with difference equation y[n] = 0.5y[n-1] + x[n], the DC gain is:
Answer: C
DC gain = H(z=1) = 1/(1-0.5) = 01.5 = 2
Q.64Hard
The concept of 'group delay' in filters refers to:
Answer: B
Group delay τ_g(ω) = -dθ(ω)/dω represents dispersion in filter's phase response
Q.65Hard
A linear phase FIR filter of length N has which characteristic for group delay?
Answer: A
Linear phase FIR filters have constant group delay = (N-1)/2 samples, which is why they're preferred for applications requiring minimal distortion.
Q.66Hard
A speech signal is band-limited to 4 kHz and sampled at 8 kHz. If 1000 samples are collected, what is the frequency resolution of its DFT?
Answer: C
Frequency resolution = fs/N = 10008000 = 8 Hz. This is the minimum frequency spacing in DFT.
Q.67Hard
A system with H(s) = (s+2)/((s+1)(s+3)) is analyzed. What is the steady-state response to u(t) = 10sin(2t)?
Answer: A
For sinusoidal input, steady-state output is |H(jω)|×A at angle ∠H(jω). Here ω=2, so output amplitude = |H(j2)|×10.
Q.68Hard
In multirate signal processing, if a signal is decimated by factor M and then interpolated by factor M, what is the output relationship to input?
Answer: B
Decimation-interpolation by same factor M recovers original signal only with ideal lowpass filters. Non-ideal filters cause distortion and aliasing.
Q.69Hard
A minimum-phase system has a zero at z = 2. Where should its mirror zero be placed for a linear-phase equivalent system?
Answer: A
For linear phase from minimum-phase, zeros must be placed symmetrically: if z₀ is a zero, then 1/z₀* must also be a zero. For z=2, mirror is z=21.
Q.70Hard
A signal undergoes spectral analysis using FFT with windowing. If spectral leakage is observed, which of the following is NOT a solution?
Answer: D
Spectral leakage is reduced by increasing observation window length, using better windows, or zero-padding FFT. Reducing fs would worsen aliasing and doesn't address leakage.
Q.71Hard
For a complex exponential signal e^(j2πf₀t) sampled at fs = 10 kHz with f₀ = 3 kHz, aliasing occurs at frequency:
Answer: B
Aliased frequency = |f₀ - kfs| = |3 - 10| = 7 kHz (for k=1). The signal appears as a 7 kHz component in the baseband.
Q.72Hard
A second-order system has poles at s = -1 ± j2. Its natural frequency ωn is:
Answer: C
For poles at σ ± jωd, ωn = √(σ² + ωd²) = √(1 + 4) = √5.
Q.73Hard
A causal stable filter has H(s) = (s+3)/((s+1)(s+2)). Using partial fractions, the impulse response contains:
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.75Hard
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.
