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Synchronous averaging is commonly known as time synchronous averaging (TSA) but is applicable to many independent variable domains that demonstrate periodic signals of interest. An alternative domain of example is the spatial domain. The common use of the synchronous averaging technique is the attenuation of both non-coherent components and the non-synchronous components to negligible levels. A common rule of thumb is that the amount of attenuation is related to the reciprocal of √N where N is the number of averages. This rule is highly representative for the non-coherent components but is not representative for the non-synchronous terms. This paper lays down a synchronous averaging theory in a one dimension domain for both the synchronous components and the non-synchronous components, with some interesting results. The paper is of interest to anyone who uses the synchronous averaging process.