My understanding is that when dealing with discrete finite sequences, convolution done thru FFT is circular. To obtain linear convolution, one would pad the input with zeros up some appropriate length. Then take FFT of two padded sequences, element-by-element multiplication, then IFFT.
For very long signal, to do Linear convolution, one might use the Overlap-Add (OLA) method, which breaks the long signal into segments of equal length, then do the linear convolution as above and sum all the overlapping section together to get the final output.
My question is that isn't that when one breaks a long signal into parts and to use FFT on it later, one should apply a Hann window to minimize Gibbs phenomena due to discontinuities that might occur at two end points ?? So far all the documents about OLA that I come across has not shown use of Hann window in conjuction with OLA. I wonder if it's somehow not needed or all the OLA document just want to illustrate one idea clearly, so as not to confuse reader with addition of Hann window. I understand that if we use both OLA and Hann, it will be more complicated. Please enlighten. Thank you.