Decomposing aliased output of quadratically nonlinear systems

A practical methodology for obtaining a meaningful output power spectrum from undersampled output data of a quadratically nonlinear system is presented in this paper. In the case of output signal being undersampled, the power spectrum calculated directly from the output data samples is aliased and does not represent the true characteristics of the output. By using the discrete frequency-domain Volterra series representation of a quadratically nonlinear system, we show that the aliased output can be decomposed into a true output and an alias. The true output power spectrum then can be reconstructed from the aliased output by using a nonlinear system identification scheme. Furthermore, various coherence spectra are proposed to quantify the degree of aliasing in the output data. They can serve as indication on whether the output data are aliased or not.