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Doppler lidar (DL) applications with a focus on turbulence measurements sometimes require measurement settings with a relatively small number of accumulated pulses per ray in order to achieve high sampling rates. Low pulse accumulation comes at the cost of the accuracy of radial velocity estimates and increases the probability of outliers, also referred to as "bad" estimates. Careful noise filtering is therefore the first important step in the data processing chain from raw data to the retrieved turbulence variable. It is shown that commonly applied filtering techniques have weaknesses in distinguishing between "good" and "bad" estimates with the sensitivity needed for a turbulence retrieval. For that reason, new ways of noise filtering have been explored, taking into account that the DL background noise can differ from generally assumed white noise. It is shown that the introduction of a new coordinate frame for a graphical representation of DL radial velocities from conical scans offers a different perspective onto the data when compared to the well-known velocity-azimuth-display (VAD) and thus opens up new possibilities for data analysis and filtering. This new way of displaying DL radial velocities builds on the use of a phase-space perspective. Following the mathematical formalism used to explain a harmonic oscillator, the VAD's sinusoidal representation of the DL radial velocities is transformed into a circular arrangement. Using this kind of representation of DL measurements, "bad" estimates can be identified in two different ways. Either in a direct way, by singular point detection in subsets of radial velocity data grouped in circular rings, or indirectly, by localizing circular rings with mostly "good" radial velocity estimates by means of the autocorrelation function. The improved performance of the new filter techniques compared to conventional approaches is demonstrated, both through a direct comparison of unfiltered with filtered data sets, and through a comparison of retrieved turbulence variables with independent measurements. [ABSTRACT FROM AUTHOR]