Govt. Exams
Entrance Exams
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Topics in Electronics (ECE)
For a real signal x(t), its Fourier transform X(f) satisfies:
Correct Answer:
B. X(-f) = X*(f)
EXPLANATION
For real signals, Fourier transform exhibits conjugate symmetry: X(-f) = X*(f)
The inverse Fourier transform of δ(f-f₀) is:
Correct Answer:
A. e^(j2πf₀t)
EXPLANATION
IFT of δ(f-f₀) = e^(j2πf₀t) using sifting property of delta function
A signal is called energy signal if:
Correct Answer:
B. Its energy is finite and power is zero
EXPLANATION
Energy signal has 0 < E < ∞ and P = 0. Power signal has P > 0 and E = ∞
For a discrete-time LTI system with H(z) = 1/(1-0.5z⁻¹), the ROC should be:
Correct Answer:
B. |z| > 0.5
EXPLANATION
For a causal system, ROC is outside the outermost pole. Pole at z=0.5, so |z| > 0.5
A signal x[n] is time-reversed to get x[-n]. This operation is:
Correct Answer:
C. Linear but time-variant
EXPLANATION
Time reversal is linear (satisfies superposition) but time-variant (violates shift invariance)
Which property does NOT apply to the Laplace transform?
Correct Answer:
D. Periodicity preservation
EXPLANATION
The Laplace transform does not preserve periodicity of signals in the frequency domain
The energy of signal x(t) = e^(-2t)u(t) is:
Correct Answer:
B. 0.25 J
EXPLANATION
E = ∫₀^∞ e^(-4t)dt = [-e^(-4t)/4]₀^∞ = 1/4 = 0.25 J
A system is BIBO stable if:
Correct Answer:
B. ∑|h[n]| < ∞
EXPLANATION
Bounded Input Bounded Output stability requires the impulse response to be absolutely summable: ∑|h[n]| < ∞
The Fourier transform of a rectangular pulse rect(t/T) is:
Correct Answer:
A. T·sinc(πfT)
EXPLANATION
The Fourier transform of rect(t/T) is T·sinc(πfT) where sinc(x) = sin(x)/x
