The LCL filter design procedure presented here is similar to that presented in references [1] and [2]. Here, the procedure is presented in a step-by-step way and the simulation file is freely available on http://busarello.prof.ufsc.br/
[1] Teodorescu, R. ; Liserre, M. ; Rodriguez, P. . Grid Converters for Photovoltaic and Wind Power Systems. 2011, Wiley.
The DFT and FFT are used mainly to obtain the amplitude of a harmonic component from a periodic signal containing several harmonics. For instance, it is desired to know the 180 Hz harmonic amplitude from a signal. Then, the DFT and FFT are the best choices to do that.