Almost unique specification of discrete finite length signal: From its end point and Fourier transform magnitude
Lei Xu, Pingfan Yan, Tong Chang · 1987
In this paper, the reconstruction of discrete signal with finite time duration from its end point and Fourier Transform (FT) magnitude is considered. Based on one result of [1] that a class of discrete signal can be reconstructed from its FT magnitude and one end sample point, with the help of Measure Theory, furtherly we point out that a correspondence between RN+1space and discrete signals with duration of N+1 points can be set up, and the signals that can't be reconstructed from its end point and FT magnitude correspond to a subset of RN+1with measure zero. In other words, discrete signal with finite time duration can almost be uniquely reconstructed from its end point and FT magnitude.