The fringe-imaging Fabry-Perot (FIFP) interferometer and fringe-imaging Mach-Zehnder (FIMZ) interferometer as frequency discriminator for incoherent molecular Doppler wind lidar are proposed, analyzed and compared theoretically respectively. Using ZEMAX software, the FIFP interferometer and FIMZ interferometer are designed and simulated respectively. Compared with Fabry-Perot interferometer (FPI), Mach-Zehnder interferometer (MZI) produces equidistant linear parallel fringes instead of circular rings. The record of the MZI fringe pattern is noticeably easier than that of the FPI and can be performed with a cylindrical lens and focused on a linear CCD array rather than a complex circle to line interferometer optical (CLIO) system. According to the U.S. standard atmospheric model, the transmission, signal-to-noise ratio (SNR), sensitivity and wind error for FIFP and FIMZ systems are simulated respectively. The results show that, the MZI sensitivity is lower than that of FPI, however, the MZI offers 4 times higher transmission, resulting to about 1.4 times smaller wind error in the line-of-sight (LOS) velocity component than that of FIFP. In addition, the MZI can be designed with a compensated field to accept sources of appreciable dimensions without significant performance reduction, which will provide an effective technique for Doppler wind lidar to improve the accuracy of wind velocity measurement by using MZI as frequency discriminator.