Nonlinearly bandlimited signals

In this paper, we study the inverse scattering problem for a class of signals that have a compactly
supported reflection coefficient. The problem boils down to the solution of the
Gelfand–Levitan–Marchenko (GLM) integral equations with a kernel that is bandlimited. By adopting a
sampling theory approach to the associated Hankel operators in the Bernstein spaces, a constructive
proof of existence of a solution of the GLM equations is obtained under various restrictions on the
nonlinear impulse response (NIR). The formalism developed in this article also lends itself well to
numerical computations yielding algorithms that are shown to have algebraic rates of convergence. In
particular, the use Whittaker–Kotelnikov–Shannon sampling series yields an algorithm that converges
as ##IMG## [http://ej.iop.org/images/1751-8121/52/10/105202/aab01c4ieqn001.gif] whereas the use of
Helms and Thomas (HT) version of the sampling expansion yields an algorithm that converg...

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