This paper proposes an exact direct method to determine all parameters including an envelope peak of the white-light interferogram. A novel mathematical technique, the weighted integral method (WIM), is applied that starts from the characteristic differential equation of the target signal, interferogram in this paper, to obtain the algebraic relation among the finite-interval weighted integrals (observations) of the signal and the waveform parameters (unknowns). We implemented this method using FFT and examined through various numerical simulations. The results show the method is able to localize the envelope peak very accurately even if it is not included in the observed interval. The performance comparisons reveal the superiority of the proposed algorithm over conventional algorithms in all terms of accuracy, efficiency, and estimation range.