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Efficient detection of a CW signal with a linear frequency drift

An efficient method is presented for the detection of a continuous wave (CW) signal with a frequency drift that is linear in time. Signals of this type occur in transmissions between any two locations that are accelerating relative to one another, e.g., transmissions from the Voyager spacecraft. We assume that both the frequency and the drift are unknown. We also assume that the signal is weak compared to the Gaussian noise. The signal is partitioned into subsequences whose discrete Fourier transforms provide a sequence of instantaneous spectra at equal time intervals. These spectra are then accumulated with a shift that is proportional to time. When the shift is equal to the frequency drift, the signal to noise ratio increases and detection occurs. Here, we show how to compute these accumulations for many shifts in an efficient manner using a variety of Fast Fourier Transformations (FFT). Computing time is proportional to L log L where L is the length of the time series.