Spectral Absorption Pattern Detection and Estimation. I. Analytical Techniques

Abstract

Spectroscopic techniques have been widely employed in the middle infrared and other regions of the electromagnetic spectrum for the identification and concentration measurement of atmospheric constituents. A principal consideration in such applications is the discrimination of target gas effects from a whole background of interference effects, especially from other known or unknown gases that are present. The primary results presented in this paper concern the development of a unified theory and optimum signal processing techniques that specifically address this problem. Both active and passive, narrowband (laser), and broadband systems are treated simultaneously by adopting a vector space formalism whereby Euclidian coordinates represent appropriate spectral samples. Linear hypothesis testing and LMS estimation theory are then applied in order to derive mathematical expressions for optimum linear weights under various constraints. Both single and multiple targets are considered and a systematic approach to linear weight design is developed.