Turbulent velocity spectra, as measured by a scanning pulsed wind lidar (WindCube), are analyzed. The relationship between ordinary velocity spectra and lidar derived spectra is mathematically very complex, and deployment of the three-dimensional spectral velocity tensor is necessary. The resulting scanning lidar spectra depend on beam angles, line-of-sight averaging, sampling rate, and the full three-dimensional structure of the turbulence being measured, in a convoluted way. The model captures the attenuation and redistribution of the spectral energy at high and low wave numbers very well. The model and measured spectra are in good agreement at two analyzed heights for the u and w components of the velocity field. An interference phenomenon is observed, both in the model and the measurements, when the diameter of the scanning circle divided by the mean wind speed is a multiple of the time between the beam measurements. For the v spectrum, the model and the measurements agree well at both heights, except at very low wave numbers, k1 <0.005 m−1. In this region, where the spectral tensor model has not been verified, the model overestimates the spectral energy measured by the lidar. The theoretical understanding of the shape of turbulent velocity spectra measured by scanning pulsed wind lidar is given a firm foundation.