System and method for characterizing a Gaussian pulse in a signal. The
system includes a computer operable to receive the signal, determine a set
of estimated parameters for the Gaussian pulse using a "zoom-in" approach,
permute the estimated parameter set to generate one or more permuted
parameter sets, where the estimated and permuted parameter sets each
represent a corresponding waveform, generate closed form inner products
between the received signal and each waveform, generate linear equations
from the inner products, each linear equation being a function of a
respective one of the parameter sets and corresponding parameter variables
for the Gaussian pulse, and determine values for the parameter variables
by solving the linear equations. The determined parameters characterize
the Gaussian pulse. If there are N parameters to determine and M
permutations generated, where M is greater than or equal to N, M+1 linear
equations are solved to overdetermine the N parameters.
