A theory of acoustic emission is presented based on a Green's function type of formalism. Sources are represented by stress drop tensors and conditions derived from which the source can be considered small in terms of wavelength and distance to the transducer. These "pseudopoint" sources are examined over a restricted frequency bandwidth, called the "informative bandwidth". Such a bandlimited system may be des~ribed by a transfer function matrix type of formalism, facilitating the analysis and reducing the inverse probelm--where the source is not known a priori--to a deconvolution operation. Due to the tensor nature of the source, multiple transducer measurements (generally six) are necessary to reconstruct the source stress drop. The difficulty of using spectral techniques for data analysis in the presence of multiple sources is discussed. In addition, the strong directionality of the signal with respect to source type and orientation is illustrated by calculating the acoustic emission signals generated by loop expansion of slip and climb (prismatic collapse) type dislocations.