The correlation coefficient is one measure of how well two signals can be resolved. The effect of record length on the correlation of complex exponentials is examined. For two decaying exponentials of complex frequencies s1 = σ1 + jω j and s2 = σ2+ jω 2,with σ2 > σ1, it is shown that a finite time record length Δ may be considered as though it were infinite, provided Δ > 2/|σ1|. This is also the condition for near-orthogonalization of a set of complex exponentials, with small error.
ASJC Scopus subject areas
- Electrical and Electronic Engineering