DefinitionA Laplace transform of impulses which will be discussed later: The Dirac delta functions are idealized impulse like expressions. A Dirac delta function, also known as a unit impulse function, is a generalized function that is zero everywhere except at zero, with an integral (area under the curve) of one. The Laplace transform of the durn is L{δ(t−a)}=e−as. This describes the property and application of systems with impulses actions in control theory and signal processing. So Long story short here is an example: Our first ideal Impulse is Dirac delta function δ(t) the Laplace transform L{δ(t)}=1. L{δ(t−2)}=e−2s (3)
