Interpolation DFT (discrete Fourier transform) is the most widely applied and deeply studied approach in spectrum correction methods. A lot of interpolation algorithms were proposed in past decades, which can be divided into amplitude-spectrum-based algorithms and complex-spectrum-based algorithms. Anti-noise performance is one of the most important indexes for evaluating an algorithm in the practical engineering applications. On the review of the theory and the development in recent years of interpolation methods, the principles and characteristics of different algorithms were briefly introduced. In addition, the anti-noise performance of algorithms was investigated through computer simulations. The problem of incorrect polarity estimation was particularly analyzed. At last, the deficiency and problems in the current interpolation approaches were pointed out, and the future developments and prospects of interpolation algorithms were discussed.