The ill-posedness of the extrapolation problem in the presence of noise is considered. A stable algorithm is constructed by solving a Fredholm equation based on a regularization method. The algorithm appears relatively robust, since the noise eta /sub delta /(t) is taken as a function in L/sup 2/(-T,T)(T<0) such that the error energy integral mod eta /sub delta /(t) mod /sup 2/dt>or= delta /sup 2/, where integration is from -T to T, and the constructed extrapolation uniformly converges to the desired signal over (- infinity , + infinity ) as delta to 0. An estimate for the error energy of the constructed extrapolation over (- infinity , + infinity ) and for the absolute error between the constructed extrapolation and the desired signal over (- infinity , + infinity ) are presented.
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机译：考虑到存在噪声时外推问题的不适定性。通过基于正则化方法求解Fredholm方程构造稳定的算法。该算法显得相对健壮，因为将噪声eta / sub delta /（t）作为函数作为L / sup 2 /（-T，T）（T <0）的函数，使得误差能量积分模η/ sub delta /（t）mod / sup 2 / dt> or = delta / sup 2 /，其中积分是从-T到T，并且所构造的外推均匀地收敛为期望的信号，其增量为（-infinity，+ infinity），增量为0给出了对（-无穷大，+无穷大）的构造外推的误差能量的估计，以及对（-无穷大，+无穷大）的期望信号之间的绝对误差的估计。
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