arXiv:2610.09161v1 Announce Type: new Abstract: The computational cost of Whittle maximum-likelihood parametric spectrum estimation (PSE) for short-dwell weather-radar Doppler moment retrieval is addressed. PSE can reduce finite-sample bias, especially for short coherent processing intervals and broad spectra, but repeated likelihood evaluations make direct use expensive. A fast implementation of the finite-sample Gaussian Doppler model is introduced by writing the likelihood in terms of closed-form autocorrelation lags and synthesizing the model spectrum and analytic derivatives by fast Fourier transforms (FFTs) on the same N-point grid as the periodogram. The estimator is extended to jointly estimate total power, normalized mean Doppler frequency, and normalized spectral width. Monte Carlo simulations with 1000 noise realizations show that the fast PSE keeps the accuracy advantage of the original PSE, while objective-level timing confirms the reduction from dense lag-to-frequency synthesis to FFT-based evaluation.