  In this work, we propose a new method of computing the Karhunen-Lo\`{e}ve
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 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 Monte-Carlo
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.
