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The relatively cheap computation promised by the advent of advanced large-scale integrated (LSI) devices has made it possible to consider the use of complex joint parameter estimators in many signal processing applications. In certain cases however the performance of such an estimator is limited by the lack of "observability" of the signal generating process, where observability in this context implies the ability to discern all possible variations in the parameters contributing to a signal of interest. This concept is pursued by defining parameter observability and developing a mathematical test for it. It is then shown that the uniqueness of joint maximum likelilhood parameter estimates is directly related to the observability of tke signal generating process. With this background the observabiity of several typical signal generating structures is examined.