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This paper presents a new idea to detect a continuous-wave (CW) burst with unknown frequency using the discrete Fourier transform. Given a CW burst of certain length, an obvious detection scheme would be to compute the DFT power over the whole burst and in the given frequency bins that cover the total frequency uncertainty range. This may result in poor performance when the CW frequency is not exactly in one of the DFT bins. The new scheme divides the CW burst into L sub-bursts and computes the summation of the DFT power in each sub-burst. With very little increase on the DFT computation complexity, the overall detection performance can he greatly improved. The analysis employs a unified approach to derive the expressions of probabilities of false alarm and miss detection for both the conventional and the new schemes over the additive white Gaussian noise (AWGN) channel. Simulations are done for both the AWGN channel and the satellite fading channel.