Question What is the physical interpretation of the computation results of HIFREQ and how do they relate to the time-domain results (transients) computed with FFTSES.
Answer The results produced by HIFREQ always have a direct physical interpretation. Every individual HIFREQ run is for a single frequency only. (You can specify several frequencies in the same input file, but basically the program will run several times, once for each frequency.) When a system is energized in the time-domain with a pure sine wave at a given frequency, the time-domain potentials and electric fields will also be sinusoidal. The magnitude of the results produced by HIFREQ for that frequency will give the amplitude of the sinusoidal time-domain potentials and electric fields, and its phase will define how much they are shifted in time with respect to the energization signal.
When you are considering a transient signal, the signal is spread out continuously over a wide range of frequencies. Each individual frequency generates a sinusoidal response as described above, and the sum of those responses gives the transient potentials or electric fields. The results computed by HIFREQ at any given frequency therefore still have the meaning described above (i.e., in the case where the energization is a pure sine wave), only now it is more difficult to relate the computed amplitude to the strength of the energization as defined in FFTSES.
In the inverse operation in FFTSES, the program multiplies the results computed by HIFREQ at a given frequency by the strength of the frequency spectrum for that frequency (this gives the modulated response) and sums the results over all frequencies to give the time-domain results. At this step, the process becomes somewhat counter-intuitive.
The strength of the frequency spectrum of the current discharge for a typical lightning stroke at any given frequency is usually much smaller than the maximum value of the stroke in the time-domain. The reason for this is the inverse relationship that exists between the time behavior and the frequency behavior of a signal: fast signals are spread out over a large range of frequencies; slow signals require only a small range of low frequencies. Because a fast signal such as lightning is spread out over many frequencies, the contribution of the signal at any given frequency is usually very small. Nevertheless, when all the contributions are added, the full time-domain signal emerges.