Time Shifting in Fourier Transform – Translation Property :: Danielitte

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Laplace Transform

Time Shifting / Translation

Time shifting describes how delaying a signal in time affects its Laplace transform. It's essential in systems with delay.

Time shifting in Laplace Transform.

Formula:

\[ \mathcal{L}\{u(t - a)f(t - a)\} = e^{-as}F(s) \]

\[ u(t) = \begin{cases} 0 & t < 0 \\ 1 & t > 0 \end{cases} \]

Applications:

Modeling systems with input/output delay.
Used in unit step functions and switching circuits.
Helpful in impulse/step response analysis.