Abstract
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 <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s_ {1} = \sigma_{1} + j\omega_{1}</tex> and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s_ {2} = \sigma_{2} + j\omega_{2}</tex> with <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\sigma_{2} > \sigma_{1}</tex> , it is shown that a finite time record length <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\Delta</tex> may be considered as though it were infinite, provided <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\Delta > 2/ |\sigma_{1}|</tex> . This is also the condition for near-orthogonalization of a set of complex exponentials, with small error.
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