Signals and systems electrical engineering miscellaneous
- Consider the following statements regarding a linear discrete-time system
H(z) = z² + 1 (z + 0.5)(z - 0.5)
1. The system is stable.
2. The initial value h(0) of the impulse response is – 4.
3. The steady-state output is zero for a sinusoidal discrete-time input of frequency equal to onefourth the sampling frequency? Which of these statements are correct? \
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NA
Correct Option: C
NA
- The system described by the difference equation
y(n)– 2y (n– 1) + y(n– 2) = x(n) – x (n– 1) has y(n) = 0 and n ≤ 0.
If x(n) = δ(n), then y(2) will be
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Y(n) – 2y(n – 1) + y(n – 2) = x(n) – x(n – 1)
For n = 0,
y(0) – 2y(– 1) + y(– 2) = x(0) – x(– 1)
∴ y(0) = x(0) – x(– 1)
∴ y(n) = 0 for n < 0
For n = 1,
y(1) = – 2y(0) + y(– 1) = x(1) – x(0)
∴ y(1) = x(1) – x(0) + 2x(0) – 2x(– 1)
= x(1) + x(0) – 2x(– 1)
For n = 2,
y(2) = x(2) – x(1) + 2y(1) – y(0)
= x(2) – x(1) + 2x(1) + 2x(0) – 4x(– 1) – x(0) + x(– 1)
= x(2) + x(1) + x(0) – 3x(– 1)
= d(2) + d(1) + d(0) – 3d(– 1)Correct Option: C
Y(n) – 2y(n – 1) + y(n – 2) = x(n) – x(n – 1)
For n = 0,
y(0) – 2y(– 1) + y(– 2) = x(0) – x(– 1)
∴ y(0) = x(0) – x(– 1)
∴ y(n) = 0 for n < 0
For n = 1,
y(1) = – 2y(0) + y(– 1) = x(1) – x(0)
∴ y(1) = x(1) – x(0) + 2x(0) – 2x(– 1)
= x(1) + x(0) – 2x(– 1)
For n = 2,
y(2) = x(2) – x(1) + 2y(1) – y(0)
= x(2) – x(1) + 2x(1) + 2x(0) – 4x(– 1) – x(0) + x(– 1)
= x(2) + x(1) + x(0) – 3x(– 1)
= d(2) + d(1) + d(0) – 3d(– 1)
- The signal having the Fourier transform
X(ejΩ) = 1 - 1 e-jΩ 3 1 - 1 e-jΩ - 1 e-2jΩ 4 8
will be
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Correct Option: A
- The signal having the Fourier transform
X(ejΩ) = 
1, π/4 ≤|Ω|< 3π/4 0 0 ≤|Ω| < 3π/4, 3π/4 ≤|Ω ≤ π
will be
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Correct Option: A
- Determine-time Fourier Transform for the signal
x[n] = sin 
π n 
will be. 2
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Correct Option: D
