Accurate estimation of second-order turbulence statistics using pulsed Doppler lidar has been a challenge for a long time, mainly due to the negative influence of probe volume averaging. The present study aims to investigate a novel approach to extracting first- and second-order turbulence statistics directly from the average Doppler spectra in the frequency domain. The main hypothesis is that averaging Doppler spectra over 10-minute intervals can mitigate the influence of probe volume averaging and random noise in velocity retrievals, thereby improving estimates of velocity variance. To achieve this, we develop a new analytical model for the time-averaged Doppler spectrum, beginning with a theoretical formulation based on the beat signal within the interrogation window. The model is applied to 10-minute averaged Doppler spectra collected by a pulsed lidar system pointing toward a sonic anemometer mounted on a meteorological mast in front of a Vestas V52 wind turbine at the DTU Risø campus in Denmark. Validation results demonstrate that the Doppler spectra model, when fitted to 400 ns nominal pulse durations, closely matches sonic anemometer measurements in both mean radial velocities and standard deviations. This agreement is quantified by the least orthogonal square fit slopes of 0.978 for the mean velocities and 0.967 for the standard deviations. In comparison to the conventional time-domain approach, which accounts for only 70.6 % of the standard deviation, the proposed spectral method captures 96.7 %, corresponding to an 88.7 % reduction in estimation loss. However, this model does not accurately estimate variances using the short pulse (200 ns) of the instrument. Despite this limitation for the short pulse, the proposed method is an important step towards better turbulence estimation from pulsed Doppler lidars.