Spectral shaping of Gaussian white noise for synthetic axion signal generation in microwave cavity haloscopes
Microwave cavity haloscopes search for dark-matter axions through the weak electromagnetic field generated by axion-photon conversion in a static magnetic field. Realistic synthetic signals are essential for end-to-end calibration of the receiver, validation of the analysis pipeline, measurement of signal recovery efficiency, and blind-injection studies. Here, we present a general method for producing stochastic synthetic axion waveforms by shaping Gaussian white noise in the frequency domain. The target axion power spectral density is imposed directly on the Fourier coefficients, and arbitrarily long continuous time streams are generated efficiently using an overlap-save implementation. The method reproduces both the ensemble-averaged spectral line shape and the time-domain fluctuations expected for a classical axion field, while providing direct control of the total injected power. Because the spectral model enters only through a replaceable transfer function, the routine can accommodate the Standard Halo Model as well as nonstandard velocity distributions and narrow substructure.