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A circuit theory model is derived for coherent radar, communication, sonar and antenna systems. The model involves linear time invariant operators and hence can be thought of as cascaded filters. The model provides insight for such systems not previously available, and it provides a unified approach to the analysis of all the above systems. The analysis is concerned with continuously distributed target fields and point targets, perturbed by both additive noise and random phase errors. The model in general consists of two filters, a pre-filter and a post-filter. For radar, sonar, and antenna systems the input is the reflectivity of the target field to be sensed. For the radar and sonar case the impulse response of the pre-filter is the transmitted pulse while for antenna systems the impulse response is the current distribution. For communications, radar, and sonar the post-filter is the receiver while for antennas the post-filter is a combination of the receiver and the receiving antenna. Additive receiver noise is accounted for at the input of the post-filter. Lack of perfect coherence or phase errors can be due to many causes, e.g., atmosphere or ocean inhomogeneities. To account for the various sources of phase errors, one must consider both the pre-filter and post-filter as random parameter systems and include a multiplicative error at the input of the post-filter. This also accounts for fading. Optimum detection has been considered extensively in the literature; in this report we emphasize two other related criteria, namely resolution and mean-square error.