A rapidly scanning directionally sensitive three-velocity-component laser Doppler velocimeter (RSLDV) has been designed. It permits scans through three-dimensional flows to obtain space-time velocity information and almost "instantaneous" velocity profiles vital to understanding such flows. A flexible optical system allows for easy variation of the fringe spacing as well as the location and size of the measurement volume. Several optical techniques to maintain coincidence between the horizontal, U and W, and vertical, V, probe volumes were investigated. A lens, used like a prism, and two plane mirrors for the out of plane scanning laser beam maintains good coincidence between the probe volumes, while maintaining some flexibility. Moving fringe patterns in the horizontal and vertical planes are produced by two solid state Bragg cells. The Doppler frequency is independent of the position of the receiving optics, and only one photomultiplier tube (PMT) is needed to receive the signals for all three velocity components. A data acquisition, control and processing system has also been designed for use with the RSLDV. The PMT signal and location of the measurement volume are recorded simultaneously by two transient recorders. The system provides storage for up to 1.25 gigabytes (6 secs.) of LDV data, with permanent storage onto optical disk. A 20 MFLOP array processor provides for fast computation of velocity information. The Pisarenko harmonic decomposition (PHD) and fast Fourier transform (FFT) algorithms, with various interpolation techniques, were investigated for processing low signal-to-noise ratio signals for use with the RSLDV. The PHD algorithm was found to be unsuitable for use with processing RSLDV signals, however, the algorithm does provide superior frequency estimation for some frequency ratios at SNR levels above 30 dB, which are typical quality signals required for frequency counters. The FFT with zero-padding and log parabolic fit provides frequency estimates with RMS error below 1 % for signals with SNR above -5 dB. To obtain frequency estimates for signals with SNR below -5 dB, the FFT with zero-padding and parabolic lit must be used, signals with SNR down to -18 dB can be processed with this technique. / Master of Science / incomplete_metadata