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The signal to noise ratio efficiency $\epsilon_{\rm SNR}$ in axion darkmatter searches has been estimated using large-statistic simulation datareflecting the background information and the expected axion signal powerobtained from a real experiment. This usually requires a lot of computing timeeven with the assistance of powerful computing resources. Employing aSavitzky-Golay filter for background subtraction, in this work, we estimated afully analytical $\epsilon_{\rm SNR}$ without relying on large-statisticsimulation data, but only with an arbitrary axion mass and the relevant signalshape information. Hence, our work can provide $\epsilon_{\rm SNR}$ usingminimal computing time and resources prior to the acquisition of experimentaldata, without the detailed information that has to be obtained from realexperiments. Axion haloscope searches have been observing the coincidence thatthe frequency independent scale factor $\xi$ is approximately consistent withthe $\epsilon_{\rm SNR}$. This was confirmed analytically in this work, whenthe window length of the Savitzky-Golay filter is reasonably wide enough, i.e.,at least 5 times the signal window.

Analytical estimation of the signal to noise ratio efficiency in axion dark matter searches using a Savitzky-Golay filter