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In its most general form, a signature is a unique or distinguishing measurement, pattern, or collection of data that identifies a phenomenon (object, action, or behavior) of interest. The discovery of signatures is an important aspect of a wide range of disciplines from basic science to national security for the rapid and efficient detection and/or prediction of phenomena. Current practice in signature discovery is typically accomplished by asking domain experts to characterize and/or model individual phenomena to identify what might compose a useful signature. What is lacking is an approach that can be applied across a broad spectrum of domains and information sources to efficiently and robustly construct candidate signatures, validate their reliability, measure their quality, and overcome the challenge of detection - all in the face of dynamic conditions, measurement obfuscation, and noisy data environments. Our research has focused on the identification of common elements of signature discovery across application domains and the synthesis of those elements into a systematic process for more robust and efficient signature development. In this way, a systematic signature discovery process lays the groundwork for leveraging knowledge obtained from signatures to a particular domain or problem area, and, more generally, to problems outside that domain. This paper presents the initial results of this research by discussing a mathematical framework for representing signatures and placing that framework in the context of a systematic signature discovery process. Additionally, the basic steps of this process are described with details about the methods available to support the different stages of signature discovery, development, and deployment.