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 signal x(t) is time-limited to 0 to T seconds. What is the minimum sampling rate required to avoid aliasing if its bandwidth is B Hz?
Answer: B
According to Nyquist sampling theorem, minimum sampling rate = 2×(maximum frequency) = 2B Hz.
Q.23Medium
An LTI system has impulse response h(t) = e^(-3t)u(t). Is this system stable?
Answer: A
For stability, ∫|h(t)|dt must be finite. Here, ∫₀^∞ e^(-3t)dt = 31, which is finite. System is stable.
Q.24Medium
The output of a system is y[n] = 0.5y[n-1] + x[n]. What is the transfer function H(z)?
Answer: A
From y[n] = 0.5y[n-1] + x[n], taking Z-transform: Y(z) = 0.5z⁻¹Y(z) + X(z). So H(z) = Y(z)/X(z) = 1/(1-0.5z⁻¹).
Q.25Medium
A sinusoidal signal x(t) = 5sin(2πf₀t + π/4) is sampled at fs = 10f₀. What is the Nyquist frequency?
Answer: C
Nyquist frequency = fs/2 = 10f₀/2 = 5f₀. The Nyquist rate is 2×(highest frequency) = 2f₀.
Q.26Medium
Which window function provides the narrowest main lobe but highest side lobes in frequency domain?
Answer: B
Rectangular window has the narrowest main lobe (4π/N) but the highest side lobes (-13 dB). Other windows trade main lobe width for lower side lobes.
Q.27Medium
For a sequence x[n] = {1, 2, 1, -1}, what is the circular convolution with itself using 4-point DFT?
Answer: B
Circular convolution in time domain equals multiplication in frequency domain. y[n] = IDFT{X[k]×X[k]} = IDFT{X[k]²}.
Q.28Medium
A signal has autocorrelation R_x(τ) = Ae^(-2|τ|). What is its bandwidth (3dB) approximately?
Answer: A
Power spectral density S_x(ω) = Fourier transform of R_x(τ) = 4A/(4+ω²). At 3dB point: 4+ω² = 8, so ω ≈ 2 rad/s.
Q.29Medium
A filter has poles at z = 0.7 and z = 0.9. What can we infer about its stability and response?
Answer: B
For discrete-time systems, stability requires all poles inside the unit circle (|z| < 1). Both 0.7 and 0.9 satisfy this, so the filter is stable.
Q.30Medium
An analog filter has magnitude response |H(jω)| = 1/√(1+(ω/ωc)⁴). What is the order of the filter?
Answer: B
The denominator power indicates filter order: (ω/ωc)⁴ represents 4th-order filter response.
Q.31Medium
A real discrete signal x[n] has DTFT X(e^jω). What is the relationship between X(e^jω) and X(e^-jω)?
Answer: A
For real signals, the DTFT exhibits Hermitian symmetry: X(e^-jω) = X*(e^jω), meaning magnitude is even and phase is odd.
Q.32Hard
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.33Hard
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.34Hard
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.35Hard
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.36Hard
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.37Hard
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.38Easy
A continuous-time signal x(t) = 5cos(2π×100t) is sampled at 250 Hz. What is the Nyquist frequency required?
Answer: B
Nyquist frequency = 2 × maximum frequency = 2 × 100 = 200 Hz. Since sampling rate (250 Hz) > Nyquist frequency, no aliasing occurs.
Q.39Easy
For a causal LTI system with transfer function H(z) = 1/(1-0.5z^-1), the system is:
Answer: C
Pole is at z = 0.5, which lies inside the unit circle. For causality and stability, all poles must be inside |z| < 1.
Q.40Easy
The energy of a discrete-time signal x[n] = (0.5)^n u[n] is:
