Identification of cubically nonlinear systems excited by bandpass inputs

Identification of cubically nonlinear systems excited by bandpass inputs using discrete-time samples of the input and output signals is investigated. When excited by a bandpass signal, a nonlinear system may generate an output signal which occupies multiple frequency bands. Therefore, although the input signal can be bandpass sampled without causing aliasing by following the well known bandpass sampling theorem, the output signal must obey more sophisticated bandpass sampling criteria to avoid aliasing. Specifically, when a cubically nonlinear system is excited by a bandpass input signal whose highest frequency is larger than three times its bandwidth, a proper bandpass sampling frequency without causing aliasing in the sampled output signal must be at least 18 times the bandwidth of the input signal. First, a method for identifying the cubically nonlinear system using properly bandpass sampled data is developed. Then, a novel method is proposed, which allows identification of the cubically nonlinear system using data sampled at about twice the bandwidth of the input signal, even though aliasing exists in the sampled output under these circumstances. Compared to conventional methods, the proposed methods have the advantage of requiring a lower sampling rate. This makes the proposed methods highly appreciated in situations where high-speed sampling is unattainable.