Home Subjects Electronics (ECE) Signals & Systems

Electronics (ECE)
Signals & Systems

Analog/digital electronics, communication

34 Q 4 Topics Take Mock Test
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Difficulty: All Easy Medium Hard 1–10 of 34
Topics in Electronics (ECE)
A first-order low-pass filter has transfer function H(s) = ωc/(s + ωc). At what frequency (in terms of ωc) does the magnitude response drop to 1/√2 of its DC value?
A ω = ωc/2
B ω = ωc
C ω = 2ωc
D ω = ωc/√2
Correct Answer:  B. ω = ωc
EXPLANATION

At DC (ω=0): |H(j0)| = 1. At ω = ωc: |H(jωc)| = ωc/√(ωc² + ωc²) = 1/√2. This is the -3dB cutoff frequency, a fundamental property of first-order filters.

Test
The Z-transform of a discrete-time signal is X(z) = z/(z-0.5) with ROC |z| > 0.5. The corresponding time-domain signal is:
A x[n] = 0.5^n × u[n]
B x[n] = δ[n] + 0.5^n × u[n]
C x[n] = 0.5^(n-1) × u[n-1]
D x[n] = δ[n-1] × 0.5^n
Correct Answer:  A. x[n] = 0.5^n × u[n]
EXPLANATION

Using partial fractions or standard Z-transform tables: X(z) = z/(z-0.5) corresponds to x[n] = 0.5^n × u[n] where u[n] is the unit step function. The ROC |z| > 0.5 confirms a causal right-sided sequence.

Test
The energy of a signal x[n] = {1, 2, -1, 0} is:
A 4
B 6
C 5
D 3
Correct Answer:  B. 6
EXPLANATION

Energy = 1² + 2² + (-1)² + 0² = 1 + 4 + 1 + 0 = 6.

Test
An even signal x(t) has Fourier transform X(f). What can be said about X(f)?
A X(f) is purely imaginary
B X(f) is real and even
C X(f) is complex
D X(f) is purely real but odd
Correct Answer:  B. X(f) is real and even
EXPLANATION

For an even signal, the Fourier transform is real and even: X(-f) = X(f) and X*(f) = X(f).

Test
The Z-transform of x[n] = (1/2)^n u[n] is:
A z/(z - 0.5), |z| > 0.5
B 1/(1 - 0.5z^(-1)), |z| > 0.5
C z/(z - 2), |z| > 2
D 0.5z/(z - 1), |z| > 1
Correct Answer:  A. z/(z - 0.5), |z| > 0.5
EXPLANATION

X(z) = Σ(1/2)^n z^(-n) = z/(z - 1/2) = z/(z - 0.5) with ROC |z| > 0.5.

Test
A causal LTI system has impulse response h(t) = e^(-3t)u(t). Is this system stable?
A Yes, because the impulse response is absolutely integrable
B No, because the pole is at s = 3
C No, because the ROC doesn't include the jω axis
D Yes, but only for t > 0
Correct Answer:  A. Yes, because the impulse response is absolutely integrable
EXPLANATION

∫₀^∞ e^(-3t) dt = 1/3 < ∞. For stability, BIBO condition requires absolute integrability, which is satisfied.

Test
Which property of the Fourier transform states that multiplication in time domain equals convolution in frequency domain?
A Linearity
B Modulation theorem
C Parseval's theorem
D Time-shifting property
Correct Answer:  B. Modulation theorem
EXPLANATION

The modulation theorem (or frequency convolution property) states that x(t)×y(t) ↔ X(f)*Y(f).

Test
A continuous-time signal x(t) = 5sin(100πt) is sampled at 150 Hz. What is the Nyquist frequency required to avoid aliasing?
A 50 Hz
B 100 Hz
C 150 Hz
D 200 Hz
Correct Answer:  B. 100 Hz
EXPLANATION

The maximum frequency in the signal is 50 Hz (from 100π = 2πf). Nyquist frequency = 2 × 50 = 100 Hz.

Test
A system with transfer function H(s) = (s+2)/(s²+3s+2) has poles at:
A s = -1, -2
B s = 1, 2
C s = -1 ± j
D s = 2, -3
Correct Answer:  A. s = -1, -2
EXPLANATION

Denominator s²+3s+2 = (s+1)(s+2) = 0, giving poles at s = -1 and s = -2.

Test
The convolution of two signals each of length 5 using linear convolution yields an output of length:
A 5
B 9
C 10
D 25
Correct Answer:  B. 9
EXPLANATION

Linear convolution of signals of length M and N produces output of length M+N-1 = 5+5-1 = 9.

Test
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