Effect of Record Length on the Correlation of Complex Exponentials

Joshua Nebat; Donald D. Weiner; Tapan K. Sarkar; Vijay K. Jain

doi:10.1109/TAP.1982.1142782

Effect of Record Length on the Correlation of Complex Exponentials

Joshua Nebat, Donald D. Weiner, Tapan K. Sarkar, Vijay K. Jain

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

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 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.

Original language	English (US)
Pages (from-to)	267-272
Number of pages	6
Journal	IEEE Transactions on Antennas and Propagation
Volume	30
Issue number	2
DOIs	https://doi.org/10.1109/TAP.1982.1142782
State	Published - Mar 1982
Externally published	Yes

ASJC Scopus subject areas

Electrical and Electronic Engineering

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10.1109/TAP.1982.1142782

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AU - Sarkar, Tapan K.

AU - Jain, Vijay K.

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AB - 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.

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Effect of Record Length on the Correlation of Complex Exponentials

Abstract

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