Govt. Exams
Entrance Exams
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Topics in Electronics (ECE)
A system with H(s) = (s+2)/((s+1)(s+3)) is analyzed. What is the steady-state response to u(t) = 10sin(2t)?
Correct Answer:
A. |H(j2)|×10 at angle ∠H(j2)
EXPLANATION
For sinusoidal input, steady-state output is |H(jω)|×A at angle ∠H(jω). Here ω=2, so output amplitude = |H(j2)|×10.
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?
Correct Answer:
C. 8 Hz
EXPLANATION
Frequency resolution = fs/N = 8000/1000 = 8 Hz. This is the minimum frequency spacing in DFT.
A linear phase FIR filter of length N has which characteristic for group delay?
Correct Answer:
A. Constant and equal to (N-1)/2
EXPLANATION
Linear phase FIR filters have constant group delay = (N-1)/2 samples, which is why they're preferred for applications requiring minimal distortion.
The concept of 'group delay' in filters refers to:
Correct Answer:
B. The negative derivative of phase with respect to frequency
EXPLANATION
Group delay τ_g(ω) = -dθ(ω)/dω represents dispersion in filter's phase response
For a stable IIR filter with difference equation y[n] = 0.5y[n-1] + x[n], the DC gain is:
Correct Answer:
C. 2
EXPLANATION
DC gain = H(z=1) = 1/(1-0.5) = 1/0.5 = 2
Parseval's theorem states that energy in time domain equals energy in frequency domain. For discrete signals:
Correct Answer:
B. ∑|x[n]|² = (1/2π)∫|X(e^jω)|²dω
EXPLANATION
Parseval's theorem for discrete-time: ∑|x[n]|² = (1/2π)∫|X(e^jω)|²dω over 2π
Which window function has the BEST frequency resolution but WORST spectral leakage?
Correct Answer:
C. Rectangular window
EXPLANATION
Rectangular window has narrowest main lobe (best resolution) but highest sidelobe (worst leakage)
