Photon counting detector (PCD) x-ray imaging systems have seen increasing use in the past decade in applications such as low-dose radiography and tomography. A cascaded systems analysis model has been developed to describe the signal and noise transfer characteristics for such systems in a manner that accounts for unique PCD functionality (such as an application of a threshold) and explicitly considers the distribution of quanta through each stage. This model was used to predict the mean signal, modulation transfer function (MTF), noise-power spectrum (NPS), and detective quantum efficiency (DQE) of a silicon-strip PCD system, and these predictions were compared to measurements across a range of exposure conditions and thresholds. Further, the model was used to investigate the impact of design parameters such as detector thickness and pulse height amplification as well as unique PCD performance effects such as charge sharing and additive noise with respect to threshold. The development of an analytical model for prediction of such metrics provides a framework for understanding the complex imaging performance characteristics of PCD systems - especially important in the early development of new radiographic and tomographic applications - and a guide to task-based performance optimization.