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 if the transmitter and receiver are rapidly accelerating with respect to one another, for example, as in interplanetary and space communications. We assume that both the frequency and the drift are unknown. We also assume that the signal is weak compared with 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. In this paper, we show how to compute these accumulations for many shifts in an efficient manner using a variant of the fast Fourier transform (FFT). Computing time is proportional to LlogL, where L is the length of the time series. Computational results are presented.