A sinusoidal detector with adaptive thresholding CFAR (constant‐false‐alarm‐rate) processor operating in noise of changing statistics is analyzed for some very general situations. The detector contains FFT and a cell‐averaging processor, which can be easily implemented for real time applications, such as in pulse doppler radar. For signals in stationary noise in particular, the second‐order statistics of the FFT‐based periodogram of the windowed data are derived. In the AWGN case, this detector possesses the desired CFAR characteristics. For Gaussian colored noise, the detector performance is derived analytically with certain reasonable approximations. It is shown from some numerical examples that in this case the variation of the false alarm probability with respect to the unknown sinusoidal frequency and noise spectrum is not significant, which reveals the property of robustness. Moreover, the detection probability is satisfactory for most cases.