Fundamental component extraction using window DFT

I am dealing with phasor estimation (fundamental component extraction primarily), and i am using sliding window DFT (which happens to be very popular for phasor estimation). Now at nominal frequency (50 or 60 Hz) i get the exact amplitude and phase, but when frequency deviates from the nominal, magnitude attenuation (and several other undesirable phenomenon) take place due to spectral leakage. To reduce leakage the samples of the original time-domain signal are weighted by windows other than the default rectangular window. The phasor estimation equation looks like this, , where X is the fundamental component of the signal, represents the time-domain signal of which i need the fundamental component, represents any window function, G is given by and N is the number of samples chosen to compute one phasor sample. Now at off-nominal frequencies even though the phasor is estimated, there is an attenuation in the fundamental component (different due to different windows). For example blackman window has a different effect on off-nominal magnitude than say the hamming window. Is there any way i can get the analytical solution for the magnitude attenuation caused by these windows to my desired component for any window taken. Any help would be appreciated.