由相位重建信号的唯一性判据

The novel criterion of uniqueness for signal reconstruction from phase

从信号的傅立叶变换的相位或幅度重建信号引起了人们很大的兴趣,M.H.Hayes和A.VOppenheim于1980年提出了唯一重建信号的一系列条件,以后又有许多人在该领域作了进一步的研究。对于有限长实信号序列,要从其相位唯一的重建(相差一比例因子),对序列的Z变换多项式的零点作了一定的限制,而判定Z变换的零点是很困难的。本文提出了一种判定一个由信号序列组成的矩阵的奇异性来确定从相位重建信号的唯性的充要条件,对于多维有限实序列作了同样的讨论。显然这种方法是方便易行的。

The signal reconstruction form its Fourier transform phase or magni-tude, due to its applications in the areas of speech processing, geophysical signalprocessing and image processing and so on,has arouseaa great interest.Monson H. Haces and A.v.Oppenheim gave some conditions to reconstruct signal from its phase or magnitude uniquely in 1980. For uniquely reconstructing some restrictionsmust be imposed on the distribution of zeros of z transform of the finite sequen-ces. It is difficult to determine the uniqueness of the reconstruction or whetherthe phase and the finite sequences have an unique mapping or not because oftroublesome of finding the zeros of the polynomials. In this paper we give a novelpproach to determine the uniqueness of the singnal reconstruction from phase bydetermining the rank of the matrix which is formed per the finite sequences. Onlycimple matrix operations are needed so it is convenient and feasible.