The main inconvenience of the Volterra series is that being a Taylor series expansion it inherits the latter's poor convergence properties. Hence, it requires a large number of terms to characterize applications that posses a saturating behavior (for example, n ? 5 may be required for a power amplifier modeling). Also in certain cases the series is not convergent in a portion of the input signal space, so that the kernels cannot be drawn.
In fact, the extraction of higher-order kernels ( n ? 2) and the evaluation of associated multidimensional integrals tend to be practically and computationally very ineffective, so that only the zeroth, the first- and eventually the second-order terms can be considered as viable components for modern communication circuit modeling. This problem was considered by Asdente et al. [30] and pursued by Filicori et al. [31] for large-signal electron device modeling. Applying their approach to the complex-envelope functional defined above, the idea is rather than carrying directly the Taylor expansion of the functional 
as in (3.9) to consider the expansion of a modified functional 
, where ? 0( t) is a carefully selected approximation of the system response. If the approximation ? 0( t) is conveniently selected, then the modified Volterra series is likely to converge very quickly at the first or second order. The main issue then rests on the selection of the system response approximation ? 0( t
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