It was found that, as a by-product of its uniform performance over all signal waveform classes, the first-order model derived in the preceding section was broadly limited to mildly nonlinear system operation as the signal bandwidth goes beyond a few megahertz. We can however enlarge the operating range of the model if we could make some assumptions about either the system structure or the excitation signal waveform class.
The signal, 
, 
used previously to extract the kernel has the particular feature that it stimulates both the short-term memory (in-band memory) and long-term memory (low-frequency memory) effects. This is possible because the frequency of the alternating envelope component 
is swept over the pass-band to sense the in-band dynamics and thanks to the system nonlinearity, a beat frequency ( ? 0 = ( ? x + ? 0)- ? x) is created that excites the long-term dynamics. However, since the alternating component is kept small 
, the sensing process therefore assumes that the system dynamic is fully controlled by the envelope time average 
, which of course is likely to be untrue as the system saturates and the signal bandwidth is large.
Now if we assume that the system has negligible long-term dynamics, then it is not necessary to use a sensing signal that stimulates this dynamics. Doing so we gain more freedom to choose a sensing signal that stimulates more effectively the remaining dynamics; that is, the short-term one. A...
TABLE OF CONTENTS 
