This thesis explores the dealiasing methods of the Doppler spectrum for the case of a fast-scanning weather radar with the possibility of being used in the development of future weather radars. From the literature, log-periodic sampling which is a type of non-uniform sampling is adapted for Doppler dealiasing. The sampling parameters of log-periodic are optimized to provide superior point Doppler dealiasing performance by orders of magnitude. To extend the dealiasing to weather targets with a wider spectrum, the log-periodic sampling is embedded into a ’Periodic Non-Uniform Non-Coherent Burst (PNU-NCB)’ structure. Additionally, the unique structure of PNU-NCB enables it to be used readily for fast-scanning radars as a multi-burst processing scheme. Furthermore, an Iterative Adaptive Approach (IAA) algorithm is used in combination with PNU-NCB to suppress the effect of noise and enable the estimation of Doppler moments for wider Doppler targets. The final performance of the designed waveform after processing yields the dealiasing and estimation of moments for even extended Doppler targets with extremely good performance. By using, the optimized PNU-NCB coupled with IAA, it is possible to accurately estimate the Doppler moments unambiguously for targets smaller than 0.1 times the uniform sampling Nyquist window. For higher target spectral width, the estimation of the spectral moments is comparable to the performance in the uniform sampling case with the added benefit of resolving ambiguities. Further performance improvements to the performance can be achieved by exploring the future recommendations provided.