Almost unique specification of discrete finite length signal: From its end point and Fourier transform magnitude

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 R
^N+1
space 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 R
^N+1
with measure zero. In other words, discrete signal with finite time duration can almost be uniquely reconstructed from its end point and FT magnitude.