Numerical simulations have been performed to investigate various spectral estimators used in LDV signal processing. In order to simulate a particle arrival time statistics known as the doubly stochastic poisson process, an autoregressive vector model was adopted to construct a primary velocity field. The conditional Poisson process with a random rate parameter was generated through the rescaling time process using the mean value function. The direct transform based on random sampling sequences and the standard periodogram using periodically resampled data by the sample and hold interpolation were applied to obtain power spectral density functions. For low turbulent intensity flows, the direct transform with a constant Poisson intensity is in good agreement with the theoretical spectrum. The periodogram using the sample and hold sequences is better than the direct transform in the view of the stability and the weighting of the velocity bias for high data density flows. The high Reynolds stress and high fluctuation of the transverse velocity component affects the velocity bias which increases the distortion of spectral components in the direct transform.