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Moon (2000) discussed the reconstruction of samples of signal from samples of its integral on bandlimited spaces with applicable background. But we often meet non-bandlimited spaces and irregular sampling. In this paper, we study the reconstruction of signals on some non-bandlimited spaces - time-warped band-limited spaces and spline subspaces. We obtain an iterative algorithm in a kind of non-band-limited spaces - time-warped bandlimited spaces. This algorithm is easy to practice in application so that overcome some difficulties in reconstructing some non-band-limited signals from irregular sampling set.