We present a method to accurately model and generate Gaussian bandpass noise, with the primary goal of facilitating Built-In Self Test (BIST) in digital receivers in wireless communications systems. The algorithm outlined in this paper allows for complete BIST of the receiver, from the Intermediate Frequency (IF) to the output data stream. We focus on implementational details which are of most interest to contemporary wireless communications systems, namely on providing solutions for the following system attributes: (1) all-digital software radio receivers; (2) fixed-point implementation; (3) hardware implementations; (4) applications for BIST in satellite, cellular, mobile, and low-power applications. While the problem of generating bandpass Gaussian noise is related to generation of Additive White Gaussian Noise (AWGN), it is shown that to generate bandpass Gaussian noise samples for all-digital receivers it is necessary to generate non-white correlated noise. As an additional complication, fixed-point representation of this noise must address dynamic range considerations to avoid saturation and underflow. We present a method by which bandpass Gaussian noise can be generated and incorporated with ease within BIST circuits in contemporary receivers while conforming to any low-power, fixed-point, and small form-factor constraints that apply to the receiver as a whole.