On the output of nonlinear systems excited by discrete prolate spheroidal sequences

The discrete prolate spheroidal sequences (DPSSs) - a set of optimally bandlimited sequences with unique properties - are important to applications in both science and engineering. In this work, properties of nonlinear system response due to DPSS excitation are reported. In particular, this output is shown to be approximately orthogonal after passing through a nonlinear, multiple-input multiple-output system with memory under quite general conditions. This work quantifies these conditions in terms of constraints upon the higher-order generalized transfer functions characterizing the Volterra expansion of a MIMO system, the Volterra order of the system, and the DPSS bandwidth parameter W and time-bandwidth parameter NW. The approximate system output orthogonality allows multiple input, multiple-output parameter identification of edge structure in interconnected nonlinear systems using simultaneous, DPSS excitation. This narrowband method of system identification is particularly appealing when compared to classical broadband system excitation in sensitive, neural engineering applications involving electrical stimulation of multiple brain regions. Through the comparison of inner-product and kernel-based narrowband detectors, the utility of this work is demonstrated when identifying narrowband system response of a third-order Volterra system from noisy observations.