I was reading this thread: How to get Instantaneous Magnitude for a Instantaneous Frequency From FFT?
I have basically the same question, but I'm curious about more detail about the Hann window kernel. ederwander said that once you know the frequency offset from the nearest bin then the instantaneous magnitude is a the Hann kernel of your offset times FFT length, times magnitude of the bin you're offset for.
Where the Hann window kernel $W(k) = 0.5 (\operatorname{sinc}(k(M/N)) / (1 - (k(M/N))^2)$
I'm just not sure why that kernel evaluated at offset*N gives the proper scaling factor for adjusting the magnitude. I couldn't even find any other information on the Hann kernel or how it is derived.
Thanks!!