  Microwave cavity haloscopes are among the most sensitive direct detection
experiments searching for dark matter axions via their coupling to photons.
When the power of the expected microwave signal due to axion-photon conversion
is on the order of $10^{-24}$~W, having the ability to validate the detector
response and analysis procedure by injecting realistic synthetic axion signals
becomes helpful. Here we present a method based on frequency hopping spread
spectrum for synthesizing axion signals in a microwave cavity haloscope
experiment. It allows us to generate a narrow and asymmetric shape in frequency
space that mimics an axion's spectral distribution, which is derived from a
Maxwell-Boltzmann distribution. In addition, we show that the synthetic axion's
power can be calibrated with reference to the system noise. Compared to the
synthetic axion injection in HAYSTAC phase I, we demonstrated synthetic signal
injection with a more realistic lineshape and calibrated power.
