Effect of Fast Fourier Transform Windows on Event Reconstruction for Project 8

The Project 8 Experiment is pioneering the Cyclotron Radiation Emission Spectroscopy (CRES) technique to achieve sensitivity of 40 meV/c^2 to the neutrino mass. In the experiment, electrons emitted from tritium beta decay are placed in an external magnetic field, thereby releasing cyclotron radiation with frequency inversely proportional to their energy. The neutrino mass can be probed by reconstructing the electrons' energy spectrum near its endpoint. In Project 8's standard data processing pipeline, the data is split into narrow time slices and the frequencies are extracted using Fast Fourier Transforms (FFTs). However, FFTs of real signals are prone to spectral leakage, a phenomenon in which power is spread across multiple frequency bins. As the frequency changes, the magnitude of the leakage varies across time slices, which can cause difficulties for event reconstruction. FFT windowing functions emerge as possible remedies to the leakage by attenuating the signal at the edges of each time slice. We present a thorough study into the use of FFT windows by analyzing frequency resolution and track reconstruction in both a toy model and high-fidelity simulations. The resulting work can guide Project 8's signal processing procedures and contribute to the collaboration's efforts to measure the neutrino mass.