I am a researcher in the field of cochlear implants, in which sounds are transformed into a series of discrete electrical pulses (amplitude $x$ at each unit time) that are output from electrodes in the device to stimulate the auditory nerve. I am interested in comparing the frequency spectrum of stimulation output across electrodes, but am not convinced that such a measure is theoretically meaningful. Specifically, the problem is that the amplitude applied to each pulse is on an interval scale, i.e. sometimes stimulation is off (zero amplitude) and otherwise the amplitude ranges in integer steps between the lowest amplitude the listener can hear ($T$) and the loudest amplitude they can comfortably stand ($C$). The distance between $0$ and $T$ isn't meaningful because $T$ is different for every channel, which I think invalidates comparisons of the spectrum across channels. Is there a way to perform some kind of spectral analysis on interval data like I have here?
Restated, is there a meaningful interpretation of $\hat{f}(x_1)$, $\hat{f}(x_2)$ when compared to one another under the conditions:
$x_1\in 0 \cup [T_1,C_1]$, $x_2 \in 0 \cup [T_2,C_2]$,
$T_1\ne T_2$, $C_1 \ne C_2$,
$T_1,T_2,C_1,C_2 \in Z^+$