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The Laplace transform of unit impulse function δ(t) is
1. 1
2. \(\frac{1}{s}\)
3. s
4. 0

1 Answer

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by (238k points)
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Best answer
Correct Answer - Option 1 : 1

Concept:

The Laplace transform of an impulse response is 1, i.e.

δ (t) ↔ 1

Notes: 

Some common Laplace transforms are:

f(t)

F(s)

ROC

δ (t)

1

All s

u(t)

\(\frac{1}{s}\)

Re (s) > 0

t

\(\frac{1}{{{s^2}}}\)

Re (s) > 0

tn

\(\frac{{n!}}{{{s^{n + 1}}}}\)

Re (s) > 0

e-at

\(\frac{1}{{s + a}}\)

Re (s) > -a

t e-at

\(\frac{1}{{{{\left( {s + a} \right)}^2}}}\)

Re (s) > -a

tn e-at

\(\frac{{n!}}{{{{\left( {s + a} \right)}^n}}}\)

Re (s) > -a

sin at

\(\frac{a}{{{s^2} + {a^2}}}\)

Re (s) > 0

cos at

\(\frac{s}{{{s^2} + {a^2}}}\)

Re (s) > 0

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