| m07 - The Laplace Transform |

| | The **Laplace** **transform** can be thought of as a generalization of the Fourier **transform** in order to include a larger class of functions, to allow the use of complex variable theory, to solve initial value differential equations, and to give a tool for input-output description of linear systems. |

| | This definition is often called the bilateral **Laplace** **transform** to distinguish it from the unilateral **transform** (ULT) which is defined with zero as the lower limit of the forward **transform** integral (Equation 1). |

| | It does not reduce to the Fourier **transform** for signals that exist for negative time, but if the negative time part of a signal can be neglected, the unilateral **transform** will converge for a much larger class of function that the bilateral **transform** will. |

| cnx.org /content/m13876/latest (479 words) |