Here is Signal Wave Explorer, using FFT, to model 3 pulses thru a LPF. On right side of the plots is a dotted vertical line, the Nyquist frequency. In the Mag/Phase that is the mirroring frequency, indeed shown here.

Shown below these 8 plots is screenshot with just InputWaveform, Magnitude plots, and OutputWaveform. Examine the OutputWaveform carefully, particularly the 3rd output pulse, and you'll see that final decay to zero amplitude. The first 2 pulses are not allowed enough time to decay to zero amplitude.

Thus we have used the FFT to fully capture the transient behavior.

[![enter image description here][1]][1]


And now without the Phase plots. In the InputSpectrum, you see the sin(x)/x components of the squarewave, with amplitudes decaying as 1/Harmonic#. The tool --SWE--- simply multiplies this InputSpectrum with the SystemSpectrum, producing the OutputSpectrum; magnitudes are multiplied; phases are added. Then OutputSpectrum undergoes InverseFFT, to produce the OutputWave.

[![enter image description here][2]][2]


  [1]: https://i.sstatic.net/1q9yH.png
  [2]: https://i.sstatic.net/4ZVM5.png