Signals and Systems - ECE Questions and Answers

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-j sgn (f) x X(f)

j2pf x e^jptf X(f)

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Which of the following is/are not a property/properties power spectral density function Sx(ω)?

Sx(ω) is real function of ω

Sx(ω) is a even function of ω

Sx(ω) is non-positive function of ωSx(ω) ≤ 0 for all ω

All of the above

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A casual LTI system is described by the difference equation
2y[n] = ay[n - 2] - 2x[n] + βx[n -1]
The system is stable only if

|a| = 2 |β| < 2

|a| > 2 |β| > 2

|a| < 2 any value of β

|β| < 2, any value of a

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Which of the following can be impulse response of a casual system?

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An excitation is applied to a system at t = T and the response in zero for -∞ < t < T. This system is

non casual

stable

casual

unstable

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For the wave i = I₀ + I_1m sin ωt + I_3m sin 3ωt, the rms value is

I = (I²₀ + I²_1m + I²_3m)^0.5

I = 0.707 (I²₀ + I²_₁m + I²_3m)^0.5

none of these

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The Laplace transform of sin ∝t is

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The signumm function written as [sgn(t)] is defined as

sgn(t) = - 1 for t < 0, = 0 for t = 0 and = 1 for t > 0

sgn(t) = 1 for t < 0, = 0 for t = 0 and = - 1 for t > 0

sgn(t) = 0 for t < 0, = 1 for t = 0 and = 0 for t > 0

sgn(t) = 0 for t < 0, = 1 for t³ 0

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Fourier transform of the unit step function (i.e., u(t) = 1 for t ≥ 0 and u(t) = 0 for t < 0) is

pδ (ω)