Image blur in digital imaging systems results from both the spatial spreading of quanta representing the image in the detector system and from the integration of quanta over the finite detector element width. Linear-systems theory has often been used to describe these blurring mechanisms as a convolution, implying the existence of a corresponding modulation transfer function (MTF) in the spatial-frequency domain. This also implies that the resulting noise- power spectrum (NPS) is modified by the square of the blurring MTF. This deterministic approach correctly describes the effect of each blurring mechanism on the overall system MTF, but does not correctly describe image noise characteristics. This is because the convolution is a deterministic calculation, and neglects the statistical properties of the image quanta. Rabbani et al. developed an expression for the NPS following a stochastic spreading mechanism that correctly accounts for these statistical properties. Use of their results requires a modification in how we should interpret the convolution theorem. We suggest the use of a `stochastic' convolution operator, that uses the Rabbani equation for the NPS rather than the deterministic result. This approach unifies the description of both image blur and image noise into a single linear-systems framework. This method is then used to develop expressions for the signal, NPS, DQE, and pixel SNR for a hypothetical digital detector design that includes the effects of conversion to secondary quanta, stochastic spreading of the secondary quanta, and a finite detector-element width.