A novel x-ray phase contrast imaging technique based on coded apertures was recently developed at University College London. This technique removes most limitations of previous phase contrast methods and provides image improvements comparable to those obtained with synchrotron radiation with conventional x-ray sources. Unlike other phase contrast approaches, the technique does not impose restrictive wavelength and/or angular filtering on the beam emitted by the source, meaning that the beam can be exploited in full thus minimizing exposure times. As a consequence, the method provides, for the first time, a concrete opportunity to transfer x-ray phase contrast imaging into real medical applications. This paper discusses the image formation principles, analyses the shape and nature of the phase contrast profiles obtained and draws a significant conclusion on the role of convolution integrals in the acquisition of phase contrast patterns, applicable also to other phase contrast imaging approaches.