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.
The autocorrelation function R_x[n] of a discrete signal satisfies:
Answer: B
Autocorrelation is an even function: R_x[n] = E[x[m]x[m+n]] = E[x[m]x[m-n]] = R_x[-n].
Q.162Medium
In a Butterworth filter design, increasing the filter order primarily:
Answer: C
Higher-order filters provide steeper roll-off (slope = -20N dB/decade for Butterworth). They reduce transition width and are more complex computationally.
Q.163Medium
The group delay of a filter is defined as:
Answer: B
Group delay τ_g(ω) = -dφ(ω)/dω represents the delay of signal envelope.
Q.164Medium
Which window function has the narrowest main lobe but highest side lobes?
Answer: A
Rectangular window has the narrowest main lobe (~4π/N) but -13 dB side lobe level. Other windows trade main lobe width for lower side lobes.
Q.165Medium
For a real signal x[n], if X[k] is its DFT, then X[N-k] equals:
Answer: B
For real signals, DFT exhibits conjugate symmetry: X[N-k] = X*[k].
Q.166Medium
An analog signal with bandwidth 10 kHz is sampled at 30 kHz. What is the aliased frequency of a 25 kHz component?
Answer: A
Aliased frequency = |f_original - k×f_s| where k is chosen to bring frequency into [-f_s/2, f_s/2]. For 25 kHz with f_s=30 kHz: |25-30| = 5 kHz.
Q.167Medium
For a causal discrete-time LTI system with H(z) = 1/(1-0.5z⁻¹), the system is:
Answer: B
Pole at z=0.5 (inside unit circle) makes the system stable. The denominator has z⁻¹ term, making it IIR (infinite impulse response).
Q.168Medium
A real continuous-time signal has Fourier transform X(f) with magnitude |X(f)| symmetric about f=0. Which property is satisfied?
Answer: A
For a real signal, X(f) exhibits Hermitian symmetry: X(-f) = X*(f). Magnitude symmetry |X(-f)| = |X(f)| indicates even symmetry in x(t).
Q.169Medium
The pole-zero diagram of a causal system shows poles at z = 0.3 and z = 0.7, with a zero at z = 0. The system is:
Answer: B
Zero at z=0 (DC) causes attenuation at low frequencies. Poles near z=1 allow high frequencies to pass, characteristic of a high-pass filter.
Q.170Medium
The inverse Fourier transform of X(f) = δ(f-f₀) + δ(f+f₀) is:
Answer: A
IFT{δ(f-f₀)} = e^(j2πf₀t) and IFT{δ(f+f₀)} = e^(-j2πf₀t). Sum = 2cos(2πf₀t), but accounting for delta properties, result is cos(2πf₀t).
Q.171Medium
For a finite impulse response (FIR) filter of length M=5, the maximum linear phase is achieved when:
Answer: A
Linear phase FIR filters require symmetric (even) or antisymmetric (odd) impulse responses about the center. For length 5, center is n=2.
Q.172Medium
A system has step response s(t) = 1 - e^(-2t)u(t). Its impulse response h(t) is:
