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 system is described by y[n] = 0.8y[n-1] + x[n]. The steady-state gain is:
Answer: D
DC gain H(z)|_{z=1} = 1/(1-0.8) = 5. Alternatively, setting y[n] = y[n-1] = y_ss: y_ss = 0.8y_ss + x_ss gives gain = 5.
Q.42Easy
Which of the following is a property of the Discrete-Time Fourier Transform (DTFT)?
Answer: B
The DTFT X(e^jω) is periodic with period 2π because e^j(ω+2π)n = e^jωn.
Q.43Medium
An IIR filter has poles at z = 0.6e^j0.4π and z = 0.6e^-j0.4π. The filter order is:
Answer: B
Two distinct poles indicate a second-order filter. Complex conjugate pairs count as one pole pair.
Q.44Medium
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.45Easy
A signal x[n] has Z-transform X(z) = 1 + 2z^-1 + 3z^-2 for |z| > 0. The signal values are:
Answer: A
By definition, X(z) = Σx[n]z^-n. Comparing coefficients: x[0]=1, x[1]=2, x[2]=3.
Q.46Medium
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.47Easy
The convolution of x[n] = {1, 2, 3} and h[n] = {1, 1} yields a sequence of length:
Answer: C
Length of convolution = M + N - 1 = 3 + 2 - 1 = 4.
Q.48Medium
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.49Easy
A signal has power spectral density S_x(f) that is nonzero only for |f| ≤ 2 kHz. The minimum sampling frequency is:
Answer: B
By Nyquist theorem, f_s ≥ 2×f_max = 2×2 = 4 kHz.
Q.50Easy
A finite-duration signal x[n] has length N=8. Its DFT X[k] has length:
Answer: B
DFT length equals the input signal length unless zero-padding is applied. For N-point signal, DFT yields N frequency bins.
Q.51Medium
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.52Medium
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.53Medium
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.54Medium
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.55Medium
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.56Easy
The Z-transform of x[n] = n·(0.8)^n u[n] is:
Answer: A
Using the property that Z{n·a^n·u[n]} = az/(z-a)², with a=0.8, we get X(z) = 0.8z/(z-0.8)².
Q.57Easy
A signal x(t) = sin(2πf₀t) is sampled at fs = 5f₀. What is the Nyquist sampling rate required?
Answer: B
Nyquist rate = 2 × maximum frequency = 2f₀. The given sampling rate (5f₀) exceeds this, ensuring no aliasing.
Q.58Medium
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.59Easy
The energy of signal x[n] = {1, 2, 1, -1} over the given support is:
