Line2->line3. Use Fourier convolution theorem. Not here delta function is defined as 1 at zero, 0 all others. It's different with the continuous Dirac Delta distribution.
Line3->Line4. Use the property of the comb function with other function. See like http://www-rohan.sdsu.edu/~jiracek/DAGSAW/4.2.html
Note there is a * missing in (4.2.6).
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