Can I use more than one Window on an FFT? I was wondering if it is possible to take a signal and run it through an FFT multiple times with a range of different windows, and then combine/average the results to get a more accurate Signal analysis than just one window. For example, could i run my signal through a Hamming window to predict the component frequencies and then run a copy of the signal through a Flat Top window to get better amplitude predictions. combine the two data sets with some math and achieve a more accurate overall picture.
Are there any major flaws in this method? Are there better methods?
That makes little sense; the FFT (which is just an implementation of the DFT) is a linear operation; summing/weightedly averaging the same signal windowed with different windows is mathematically identical to just windowing with the summed/weightedly averaged window to begin with. It's literally the same.
So, what you really want is to design / choose a window that's appropriate for your use case instead!