Tuning into spatial frequency space: Satellite and space debris detection in the ZTF alert stream

A significant challenge in the study of transient astrophysical phenomena is the identification of bogus events, among which human-made satellites and debris in Earth orbit remain major contaminants. Existing pipelines effectively identify satellite trails but can miss more complex signatures, such as collections of satellite glints. In the Rubin Observatory era, the scale of operations will increase tenfold compared to its precursor, the Zwicky Transient Facility (ZTF), requiring improvements in classification purity, data compression for informative alerts, and pipeline speed. We explore the use of the 2D Fast Fourier Transform (FFT) on difference images as a tool to enhance machine learning models for satellite detection. Using the ALeRCE single-stamp classifier as a baseline, we adapt its architecture to incorporate a cutout of the FFT of the difference image alongside the standard ZTF image triplet (science, reference, and difference stamps). We evaluate several stamp sizes and resolutions, focusing on regimes where data compression is critical due to alert size limits and real-time constraints. Incorporating the FFT significantly improves satellite classification, especially in the smallest field-of-view model (16 arcsec), where accuracy increases from 72.0\pm2.9% to 87.8\pm1.3%. This demonstrates the FFT's value in compressing and capturing extended satellite features. However, the FFT alone does not match the full-context performance of the 63 arcsec (95.9\pm1.3%) or multiscale (90.6\pm0.8%) models, highlighting the complementary role of spatial context. We show how FFTs can be leveraged to cull satellite and debris signatures from alert streams in current and future time-domain surveys.