Signal processing

111. 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

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

Detailed

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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

class="screen-reader-text">The trigonometric Fourier series of an even function does not have the

113. 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] =

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{-4 – j5, 1 + j2, 4} The conjugate antisymmetric part of the sequence is

114. 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″]

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f(t), the Laplace transform of $$\int\limits_0^t {f\left( \tau \right)} d\tau $$ is" class="read-more button" href="https://exam.pscnotes.com/mcq/given-that-fs-is-the-one-sided-laplace-transform-of-ft-the-laplace-transform-of-intlimits_0t-fleft-tau-right-dtau-is/#more-42881">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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