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where <math>T</math> is the sampling interval.
Now the Laplace transform of the sampled signal (discrete time) is called [[Star_Transform]] and is given by :
<math> \begin{array}{l l l l l l}
L\{x^{*}(k)\} & = & X^{*}(s) & = & \int_0^{\infty}{\sum_{k=0}^{\infty}{x(t).\delta(t-kT)} e^{-st}dt} \\
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