  In this paper, we study the problem of transient signal analysis. A
signal-dependent algorithm is proposed which sequentially identifies the
countable sets of decay rates and expansion coefficients present in a given
signal. We qualitatively compare our method to existing techniques such as
orthogonal exponential transforms generated from orthogonal polynomial classes.
The presented algorithm has immediate utility to signal processing applications
wherein the decay rates and expansion coefficients associated with a transient
signal convey information. We also provide a functional interpretation of our
parameter extraction method via signal approximation using monomials over the
unit interval from the perspective of biorthogonal constraint satisfaction.
