Introduction. The problem of recovery of a finite support signal from a given set of smnples and the Fourier transform (F. T.) magnitude is considered. The problem is dealt with from an extrapolation point of view. That is, in a manner similar to the bandlirnited extrapolation problem and its extensions using a weighted frequency domain norm. Should one decide to set the weight function exactly equal to the given magnitude, it would give a resulting estimate with magnitude that resembles, but does not equal, the general shape of the weight function. Therefore, this would not be a phase retrieval technique. In order to get an exact match to the given magnitude, one must devise a scheme to accomplish this. An algorithm is presented here which is designed to satisfy the constraints of the given time samples at each iteration (extrapolation) and, in the limit, match the Fourier transform magnitude. P, ecent work has shown that for one and two dimensional finite support sequences, the Fourier transform magnitude and one boundary time or object domain sample is enough to determine certain signals uniquely [I]. The proposed scheme in [I] depends on a ~,ery crucial constrain which could very easily be broken in the presence of noise in the Iu1own edge-sample or in the F. T. magnitude. In this paper the motivation to find a tradeoff between the amount of available data and the necessary signal-to-noise ratio for successful recovery leads us to consider the case where a variable set of time samples is available. It is expected that an increase in the number of samples available will result in more accurate recovery of the true signal. The general philosophy of this paper is that we always seek signal ~ using all a priori information whether or not this information uniquely determines the signal of interest.