A specific radar system can be implemented more easily using the frequency modulated continuous wave comparing with the pulse Doppler radar. It also has the advantage of LPI (low probability of interception) because of the low power and wide bandwidth characteristics. These radars are usually used to cover the short range area and to obtain the high resolution measurements of the target range and velocity information. The transmitted waveform is used in the mixer to demodulate the received echo signal and the resulting beat signal can be obtained. This beat signal is analyzed using the FFT method for the purpose of clutter removal, detection of a target, extraction of velocity and range information, etc. However, for the case of short signal acquisition time, this FFT method can cause the serious leakage effect which disables the detection of weaker echo signals masked by strong side lobes of the clutter. Therefore, in this paper, the weighting window method is analyzed to suppress the strong side lobes while maintaining the proper main lobe width. Also, the results of FFT beat spectrum analysis are shown under various environments.