Laplace Transform Convergence

Cuthbert Nyack
The Laplace Transform F(s) of f(t) is defined as
The above integral does not converge for functions that increase faster than exponential and these functions do not have a Laplace Transform. For many functions f(t) the integral and hence the Laplace transform only converges for some range of s. For thr Fourier transform to exist, the region of convergence must include the imaginary axis.
Some examples of functions and the region of convergence of the above integral are given below:-

Return to main page
Return to page index
Copyright 1996 Cuthbert A. Nyack.