Detecting recursive and nonrecursive filters using chaos.

Filtering a chaotic signal through a recursive [or infinite impulse response (IIR)] filter has been shown to increase the dimension of chaos under certain conditions. Filtering with a nonrecursive [or finite impulse response (FIR)] filter should not increase dimension, but it has been shown that if the FIR filter has a long tail, measurements of actual signals may appear to show a dimension increase. I simulate IIR and FIR filters that correspond to naturally occurring resonant objects, and I show that using dimension measurements, I can distinguish the filter type. These measurements could be used to detect resonances using radar, sonar, or laser signals, or to determine if a resonance is due to an IIR or an FIR filter.