Linear Optimum Filtering for Axion Dark Matter Search

The Haloscope At Yale Sensitive To Axion CDM (HAYSTAC) Experiment is a microwave cavity search for cold dark matter (CDM) axions in the galactic halo. It attempts to detect a resonant photon signal produced by axion conversion in a magnetic field, the detection of which would provide useful insights on the nature of dark matter. Thus, the data acquisition from this experiment necessitates efficient filtering out of noise and other interfering signals, along with minimal scan times.

In this project, we present the theory and applications of linear optimum filters, namely the Wiener-Hopf and matched filters that minimize the mean-squared-error between processed and desired signals on MATLAB. By injecting random noise into an initially known signal, we present filtering techniques that allow us to perform the following three things: first, obtaining the best linear estimate of the desired signal d(n) from noisy data x(n); second, predicting a signal d(n+m) for m>0 from data x(n); and lastly, carrying out an a posteriori estimation of d(n+m) for m<0 from data x(n). By incorporating principles of optimization theory, this project helps speed up data analysis during the operation of the HAYSTAC experiment.