  We propose a numerical method to spline-interpolate discrete signals and then
apply the integral transforms to the corresponding analytical spline functions.
This represents a robust and computationally efficient technique for estimating
the Laplace transform for noisy data. We revisited a Meijer-G symbolic approach
to compute the Laplace transform and alternative approaches to extend canonical
observed time-series. A discrete quantization scheme provides the foundation
for rapid and reliable estimation of the inverse Laplace transform. We derive
theoretic estimates for the inverse Laplace transform of analytic functions and
demonstrate empirical results validating the algorithmic performance using
observed and simulated data. We also introduce a generalization of the Laplace
transform in higher dimensional space-time. We tested the discrete LT algorithm
on data sampled from analytic functions with known exact Laplace transforms.
The validation of the discrete ILT involves using complex functions with known
analytic ILTs.
