Signal processing

11. Input x(t) and output y(t) of an LTI system are related by the differential equation y”(t) – y'(t) – 6y(t) = x(t). If the system is neither causal nor stable, the impulse response h(t) of the system is

$${1 over 5}{e^{3t}}uleft( { - t} ight) + {1 over 5}{e^{ - 2t}}uleft( { - t} ight)$$
$$ - {1 over 5}{e^{3t}}uleft( { - t} ight) + {1 over 5}{e^{ - 2t}}uleft( { - t} ight)$$
$${1 over 5}{e^{3t}}uleft( { - t} ight) - {1 over 5}{e^{ - 2t}}uleft( t ight)$$
$$ - {1 over 5}{e^{3t}}uleft( { - t} ight) - {1 over 5}{e^{ - 2t}}uleft( t ight)$$

Detailed SolutionInput x(t) and output y(t) of an LTI system are related by the differential equation y”(t) – y'(t) – 6y(t) = x(t). If the system is neither causal nor stable, the impulse response h(t) of the system is

12. The trigonometric Fourier series of an even function does not have the

Dc term
Cosine terms
Sine terms
Odd harmonic terms

Detailed SolutionThe trigonometric Fourier series of an even function does not have the

13. Consider the sequence x[n] = {-4 – j5, 1 + j2, 4} The conjugate antisymmetric part of the sequence is

{-4 - j2.5, j2, 4 - j2.5}
{-j2.5, 1, j2.5}
{-j5, j2, 0}
{-4, 1, 4}

Detailed SolutionConsider the sequence x[n] = {-4 – j5, 1 + j2, 4} The conjugate antisymmetric part of the sequence is

14. Given that F(s) is the one-sided Laplace transform of f(t), the Laplace transform of $$\int\limits_0^t {f\left( \tau \right)} d\tau $$ is

”sF(s)
”$${1
”$$intlimits_0^s
”$${1
$$” correct=”option4″]

Detailed SolutionGiven that F(s) is the one-sided Laplace transform of f(t), the Laplace transform of $$\int\limits_0^t {f\left( \tau \right)} d\tau $$ is

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