Q320 : The Meaning of Modulated Frequency Spectrum

Question
What is the meaning of the modulated frequency spectrum in FFTSES? What about the un-modulated frequency spectrum?

---

Answer
The un-modulated response generated by HIFREQ is a measure of the characteristics of the system that is independent of any input signal. Knowing the un-modulated response, you can deduce the time-domain response of the system when it is subject to any transient input signal. As such, it is a very important and useful quantity.

The modulated frequency-domain response gives the actual response of the system at a given frequency when a specific transient input signal is used. It can be difficult to provide a physical interpretation of this quantity, although various integrals of this quantity can be meaningful (giving the energy density in the fields, for instance).

Conceptually, we could try and see how this could be measured. If we were to bring an electric field meter to a specific observation point and attempt to measure the frequency-domain field, what would we measure? To measure the frequency-domain field, our meter would have to have a very narrow frequency filter built into it. We would then tune that filter to the desired frequency, and carry out the measurement. What would be the measurement result? If the frequency filter is very narrow, the answer would be the modulated spectrum as computed by HIFREQ/FFTSES for that frequency. If the filter is not very narrow, the answer would be an average of the modulated spectrum (an integral!) for the frequency range that passes through the filter.

---