Performance analysis of the Karhunen–Loève Transform for artificial and astrophysical transmissions: denoizing and detection

Abstract

In this work, we propose a new method of computing the Karhunen-Loève Transform (KLT) applied to complex voltage data for the detection and noise level reduction in astronomical signals. We compared this method with the standard KLT techniques based on the Toeplitz correlation matrix and we conducted a performance analysis for the detection and extraction of astrophysical and artificial signals via Monte Carlo (MC) simulations. We applied our novel method to a real data study-case: the Voyager 1 telemetry signal. We evaluated the KLT performance in an astrophysical context: our technique provides a remarkable improvement in computation time and MC simulations show significant reconstruction results for signal-to-noise ratio (SNR) down to −10 dB and comparable results with standard signal detection techniques. The application to artificial signals, such as the Voyager 1 data, shows a notable gain in SNR after the KLT.