Diagnosis Using the Formal Theory of a Signal-Processing System

Abstract
Many signal-processing systems can be viewed as transforming their input signals into a representation of the real-world scenario from which the signals originated. Such systems usually have parameters whose settings are selected on the basis of the class of expected input scenarios. Finding the appropriate parameter settings for a class of input scenarios usually involves testing the system against typical and/or important input scenarios from that class. Whenever the system output does not match the input scenario, the parameter settings responsible for the fault are identified. The system user can then adjust the system parameters to ensure correct system behavior for such scenarios. The diagnostic process of identifying the parameters responsible for system faults is generally difficult because the signal-processing system carries out a complicated mathematical transformation involving a multistage algorithm that generates an enormous amount of intermediate data. A new approach to the diagnosis of such systems is developed. The approach is based on the availability of an abstract and possibly qualitative description of the input scenario and the use of an alternative system model derived from the underlying mathematical theory that explicitly represents the phenomena responsible for any incorrect processing. This approach to diagnosis models a system as a combination of processes that transform the user-specified abstract description of the input scenario into the system output. Whenever the correct answer is obtained at the system output, each process reduces to an identity transformation at the level of abstraction of the system output.

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