In-time non-iterative fast-algorithm for support constrained deconvolution

It has been shown, in the kernel splitting method for support constrained deconvolution recently presented, that the restored signal can be obtained from an infinite series of time-functions. In the present work it is proved that the series is finite when the convolution kernel is left-time-limited. Each function of the series is itself a series built from delayed replicas of the convolved signal multiplied by weighted and delayed rectangular windows. The non-overlapping time-regions of the windows are first located and then by zero trivial multiplication are not computed. Then an in-time non-iterative fast algorithm is deduced. Finally the input recovery of a linear system whose transfer function vanishes at several points is investigated both with a noise-free or a noisy output signal. In these conditions where inverse filtering fails, the present algorithm works well.