Flow acceleration with Lagrangian description is crucial to understanding particle movements in turbulent jet flows or dissipation statistics in isotropic turbulence. Laser Doppler anemometry is regarded as a suitable experimental tool for measuring flow acceleration, because scattering particles generate trajectories in the measurement volume, which process gives rise to flow acceleration at a fixed measuring point with the Lagrangian description. The most useful algorithm for processing Doppler signals is either the quadrature demodulation technique (QDT) or the iterative parametric method (alternatively, the minimization of least squares, LSM) as in the literature. In the present study, another algorithm using the Wigner-Ville transform (W-V) is introduced to give more accurate estimation of flow acceleration than the QDT or the LSM. Five signal-processing algorithms, including the QDT, the LSM, the MC (maximization of correlation), and the W-V, were compared with each other in experiments with an impinging air jet flow with a cylindrical rod and a round free-air jet flow. Mean flow acceleration distribution in the streamwise direction was mainly investigated. Processing speeds for the above-mentioned signal-processing algorithms were checked to find the best algorithm, which has best performance with short processing time. Although QDT was found to be an accurate algorithm with short processing time, it has limited applications to flows with large acceleration and high SNR. The MC was also found to be a good algorithm with moderate processing speed, which can be useful in flows with low SNR because the MC is an iterative parametric method. The W-V gave the most accurate values for flow acceleration; however, the processing time for this method was the slowest among the signal-processing algorithms.