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Phase calculation using resized FFT spectrum(time spectrum), is there noise benefits?

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Terminator3

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Hello all!
What if we do the following:
1. get complex spectrum of a signal using 1024 pt FFT. Now we can get ArcTan(A/B), but we do not.
2. store recent 16 spectrums (so we get two images with size 16x1024)
3. apply Gaussian blur with kernel 16x16 to both images, now we can get smoothed values of complex spectrum Asmt Bsmt i=0..1023
4. get ArcTan(Asmt/Bsmt) of smoothed spectrum.
5. each new spectrum produces "sliding" gaussian window..
Can we do phase measurements of slowly changing frequencies better this way? I think the result ArcTan(Asmt/Bsmt) can be better, than smoothing result of ArcTan(a/b).
 

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