Abstract: A new method of the original signal reconstruction from phase function of the spectrum is presented in this paper. The amplitude and time-delay of the components of the original signal, and the magnitude of the spectrum can be obtained from the pha.se function. The iterative operations of the new method are converged fastly, so that the number of operations is reduced greatly comparing with the previous methods. By using the complex exponential expansion method, the above technique is expanded to the case in which the time-delay does not be integer number times of sample duration exactly, and the accurate estimations of the time-delay of original signal components are further obtained. At last, the experimental results of computer simulation are giving in this paper.