This paper describes the near-infrared detector system noise generator (NG) that we wrote for the James Webb Space Telescope (JWST) Near Infrared Spectrograph (NIRSpec). NG simulates many important noise components including; (1) white "read noise," (2) residual bias drifts, (3) pink $1/f$ noise, (4) alternating column noise, and (5) picture frame noise. By adjusting the input parameters, NG can simulate noise for Teledyne's H1RG, H2RG, and H4RG detectors with and without Teledyne's SIDECAR ASIC IR array controller. NG can be used as a starting point for simulating astronomical scenes by adding dark current, scattered light, and astronomical sources into the results from NG. NG is written in Python-3.4. The source code is freely available for download from http://jwst.nasa.gov/publications.html.
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