  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.
