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In this work, we propose a new method of computing the Karhunen-Lo\`{e}veTransform (KLT) applied to complex voltage data for the detection and noiselevel reduction in astronomical signals. We compared this method with thestandard KLT techniques based on the Toeplitz correlation matrix and weconducted a performance analysis for the detection and extraction ofastrophysical and artificial signals via Monte Carlo simulations. We appliedour novel method to a real data study-case: the Voyager 1 telemetry signal. Weevaluated the KLT performance in an astrophysical context: our techniqueprovides a remarkable improvement in computation time and Monte-Carlosimulations show significant reconstruction results for signal-to-noise ratio(SNR) down to -10 dB and comparable results with standard signal detectiontechniques. The application to artificial signals, such as the Voyager 1 data,shows a notable gain in SNR after the KLT.

Performance analysis of the Karhunen-Lo\`{e}ve Transform for artificial and astrophysical transmissions: denoising and detection