I am using DFT with windows. The way I understand how a window makes the DFT "look" better, is that multiplication in time domain is convolution in frequency domain. Therefore a window with following FT (Hann window), will suppress the side lobes found in a signal FT (second picture) :
But I dont understand how are the values |F($\omega$)| related to suppressing the signals side lobes ... e.g. Tukey window plotted as |F($\omega$)|
How is the width and the pace of decreasing sidelobes (of the above plot) related to getting rid of sidelobes of signals FT ? Is there any intuitive way to explain ?