89,141 research outputs found
Data-driven inference on optimal input-output properties of polynomial systems with focus on nonlinearity measures
In the context of dynamical systems, nonlinearity measures quantify the
strength of nonlinearity by means of the distance of their input-output
behaviour to a set of linear input-output mappings. In this paper, we establish
a framework to determine nonlinearity measures and other optimal input-output
properties for nonlinear polynomial systems without explicitly identifying a
model but from a finite number of input-state measurements which are subject to
noise. To this end, we deduce from data for the unidentified ground-truth
system three possible set-membership representations, compare their accuracy,
and prove that they are asymptotically consistent with respect to the amount of
samples. Moreover, we leverage these representations to compute guaranteed
upper bounds on nonlinearity measures and the corresponding optimal linear
approximation model via semi-definite programming. Furthermore, we extend the
established framework to determine optimal input-output properties described by
time domain hard integral quadratic constraints
Frequency-Domain Analysis of Linear Time-Periodic Systems
In this paper, we study convergence of truncated representations of the frequency-response operator of a linear time-periodic system. The frequency-response operator is frequently called the harmonic transfer function. We introduce the concepts of input, output, and skew roll-off. These concepts are related to the decay rates of elements in the harmonic transfer function. A system with high input and output roll-off may be well approximated by a low-dimensional matrix function. A system with high skew roll-off may be represented by an operator with only few diagonals. Furthermore, the roll-off rates are shown to be determined by certain properties of Taylor and Fourier expansions of the periodic systems. Finally, we clarify the connections between the different methods for computing the harmonic transfer function that are suggested in the literature
Canonical time-frequency, time-scale, and frequency-scale representations of time-varying channels
Mobile communication channels are often modeled as linear time-varying
filters or, equivalently, as time-frequency integral operators with finite
support in time and frequency. Such a characterization inherently assumes the
signals are narrowband and may not be appropriate for wideband signals. In this
paper time-scale characterizations are examined that are useful in wideband
time-varying channels, for which a time-scale integral operator is physically
justifiable. A review of these time-frequency and time-scale characterizations
is presented. Both the time-frequency and time-scale integral operators have a
two-dimensional discrete characterization which motivates the design of
time-frequency or time-scale rake receivers. These receivers have taps for both
time and frequency (or time and scale) shifts of the transmitted signal. A
general theory of these characterizations which generates, as specific cases,
the discrete time-frequency and time-scale models is presented here. The
interpretation of these models, namely, that they can be seen to arise from
processing assumptions on the transmit and receive waveforms is discussed. Out
of this discussion a third model arises: a frequency-scale continuous channel
model with an associated discrete frequency-scale characterization.Comment: To appear in Communications in Information and Systems - special
issue in honor of Thomas Kailath's seventieth birthda
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