Microstructural heterogeneities in cardiac tissue, such as embedded connective tissue secondary to fibrosis, may lead to complex patterns of electrical activation that are reflected in the fractionation of extracellularly recorded electrograms. The decomposition of such electrograms into non-fractionated components is expected to provide additional information to allow a more precise classification of the microstructural properties adjacent to a given recording site. For the sake of this, an analytic signal model is introduced in this study that is capable of reliably identifying extracellular waveforms associated with sites of initiating, free-running, and terminating or colliding activation wavefronts. Using this signal model as a template, a procedure is developed for the automatic decomposition of complex fractionated electrograms into non-fractionated components. The decomposition method has been validated using electrograms obtained from one- and two-dimensional computer simulations in which all relevant intracellular and extracellular quantities are accessible at a very high spatiotemporal resolution and can be manipulated in a controlled manner. Fractionated electrograms were generated in these models by incorporating microstructural obstacles that mimicked inlays of connective tissue. Using this signal model, fractionated electrograms emerging from microstructural heterogeneities in the submillimeter range with latencies between components down to 0.6 ms can be decomposed.