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Find unilateral Laplace transform for the following signals, $ x(t)=u(t) $
1 Answer
written 22 months ago by |
Solution:
$ X(S)=\int_0^{\infty} \mathrm{x}(\mathrm{t}) \mathrm{e}^{-\mathrm{st}} \mathrm{dt}\\ $
$ =\int_0^{\infty} \mathrm{u}(\mathrm{t}) \mathrm{e}^{-\mathrm{st}} \mathrm{dt}\\ $
$ \int_0^{\infty} 1 e^{-s t} d t=\left[\frac{e^{-s t}}{-s}\right]_0^{\infty}\\ $
$ =\left[\frac{e^{-s t}}{-s}\right]_0^{\infty}=\frac{1}{s}\\ $