Feature Selection by Filtering
The problem is that the following statement- "So now for the spectrum between 0 to 100 MHz the vector s⃗ l contains amplitudes for 20000 frequencies (D=20000)"- is faulty.

A signal that lasts $5\mu s$ is captured at 4 GS/s.  That is a total of 5e-6 * 4e9 = 20000 samples.  The Nyquist frequency is half the sample rate, or 2 GHz.  They take the Fourier transform of the samples ($F(w,l)$).  At this point, assuming the samples are real (as opposed to complex), there are 20000 frequency bins representing -2 GHz to +2 GHz.  The negative frequency information is redundant since it mirrors the positive frequencies.  I believe that when they said "We then remove from F(ω,l) its DC component and the redundant part of the spectrum" they were talking about getting rid of the 0 Hz and negative frequency information.

That would leave you with 9999 frequency bins representing 200 kHz to 2 GHz.  To make life easier, though, let's bring back the DC bin and say that we have 10000 frequency bins representing 0 Hz to 2 GHz.

Hopefully it is clear now why "So now for the spectrum between 0 to 100 MHz the vector s⃗ l contains amplitudes for 20000 frequencies (D=20000)" is faulty.  There are 10000 bins and they represent 0 to 2 GHz, not 0 to 100 MHz.  They now bandpass the signal down to 4 MHz bandwidth.  $(4e6 / 2e9) * 10000 = 20$ frequency bins.  I believe they get 40 dimensions from those 20 bins by counting both the amplitude and phase of the bins as features, $20 * 2 = 40$.