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

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3 Author(s)
Lei Xu ; Tsinghua University, Beijing, China ; Pingfan Yan ; Tong Chang

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.

Published in:

Acoustics, Speech, and Signal Processing, IEEE International Conference on ICASSP '87.  (Volume:12 )

Date of Conference:

6-9 April 1987