Signals and systems electrical engineering miscellaneous
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If L[f(t)] = 2(s + 2) , then ƒ(0+) and ƒ(∞) are given by s² + 2s + 5
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2(s + 1) = 2(s + 1) = 2 s + 1 (s² + 2s + 5) (s² + 1)² + 5 (s + 1)² + 4
This is standard Laplace Transform for the functionL| exp (– at) cos ωt | = (s + a) (s + a)² + ω²
where a = 1, ω = 2
Hence ƒ(t) = 2e– t cos 2t
ƒ(0) = ƒ(0+) = 2e– 0 cos 2 × 0 = 2
ƒ(∞) = 2e– ∞ t = 0Correct Option: B
2(s + 1) = 2(s + 1) = 2 s + 1 (s² + 2s + 5) (s² + 1)² + 5 (s + 1)² + 4
This is standard Laplace Transform for the functionL| exp (– at) cos ωt | = (s + a) (s + a)² + ω²
where a = 1, ω = 2
Hence ƒ(t) = 2e– t cos 2t
ƒ(0) = ƒ(0+) = 2e– 0 cos 2 × 0 = 2
ƒ(∞) = 2e– ∞ t = 0
- The unit impulse response of a linear time invariant system is unit step function u(t). For t > 0, the response of the system to an excitation e– at u(t), a > 0 will be
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Given: h(t) = u(t)
x(t) = e–at u(t)∴ Y(s) = X(s) H(s) = 1 . 1 = 1 1 - 1 (s + a) s a s s + a
y(t) = 1/a (1 – e– at) u(t)Correct Option: B
Given: h(t) = u(t)
x(t) = e–at u(t)∴ Y(s) = X(s) H(s) = 1 . 1 = 1 1 - 1 (s + a) s a s s + a
y(t) = 1/a (1 – e– at) u(t)
- Given the transform pair
Determine the laplace transform Y(s) of the given time signal in question and choose correct option. y(t) = x(t – 2)
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Correct Option: A