A spline function approximation approach for measuring the Doppler spectral peak frequency in a laser Doppler velocimeter system is presented. The processor is designed for signal bursts with mean Doppler shift frequencies up to 100 MHz, input turbulence up to 20%, and photon counts as low as 300. The frequency-domain processor uses a bank of digital bandpass filters for the capture of the energy spectrum of each signal burst. The average values of the filter output energies, as a function of normalized frequency, are modeled as deterministic spline functions which are linearly weighted to evaluate the spectral peak location associated with the Doppler shift. The weighting coefficients are chosen to minimize the mean square error. Performance evaluation by simulation yields average errors in estimating mean Doppler frequencies within 0.5% for poor signal-to-noise conditions associated with a low photon count of 300 photons/burst.