Environmental Engineering Reference
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the second-order Volterra circuit is dominated by the interpolation error
To estimate this error, the input of the second-order Volterra
circuit is derived with the step sizes
T
and respectively. The order
of interpolation is determined from the normalized mean square error
(NMSE) [67]
where
and
are the response of the circuit with the
step sizes of
T
and
respectively. In order to compute
and
and
are
needed. The relationship
and
can be employed to reduce computational cost.
6.3.4 Simulation Window
When a simulation window is employed it is assumed that the data
series sampled by the window is periodic. The rate of convergence of the
interpolating Fourier series depends upon the boundary condition of the
data series. It was shown in [67, 68] that a large error will exist if the
data series is discontinuous at the boundary, known as Gibb effect. The
error will be further increased if the derivatives of the function are also
discontinuous [69]. To minimize the error due to the discontinuity of the
function value at the boundary, the window should be chosen such that
the input of Volterra circuits is periodic with respect to the simulation
window. For circuits with only one sinusoidal input, the window size that
is the same as the period of the sinusoidal input meets this requirement
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