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.
For a linear-phase FIR filter, the impulse response h[n] must satisfy:
Answer: C
Linear phase requires either symmetric (Type I, II) or antisymmetric (Type III, IV) impulse response.
Q.22Medium
In a multirate DSP system, downsampling by factor M introduces aliasing if the signal is not:
Answer: D
To prevent aliasing in downsampling, the signal must be bandlimited to π/M and preceded by an anti-aliasing lowpass filter.
Q.23Medium
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.24Medium
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.25Medium
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.26Medium
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.27Medium
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.28Medium
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.29Medium
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.30Medium
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.31Medium
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.32Medium
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.33Medium
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.34Medium
A system has step response s(t) = 1 - e^(-2t)u(t). Its impulse response h(t) is:
