The goals of the work described here were the development of a method of selection of spectral estimation for use with pulsed Doppler ultrasonic blood flow instruments, and the use of this method to select an estimator and its implementation in a form suitable for real-time applications. A study of estimation accuracy of the mean frequency and bandwidth using a number of spectral estimators was carried out. Fourier based, parametric, and, minimum variance estimators were considered. A Doppler signal simulator was developed to allow the accuracy tests required. A method of selection of spectral estimators based on the accuracy of estimation of decisive signal parameters, under the constraint of low computational complexity has been proposed. This novel cost/benefit criterion, allows the possibility of weighting appropriate to estimator (mean frequency and bandwidth) and signal frequency importance (across the range of signal characteristics). For parametric spectral estimators, this criterion may also be used to select model order, leading to lower orders than FPE, AIC and CAT criteria. Its use led to the selection of a 4t' order modified covariance parametric method. A new version of the modified covariance method for spectral estimation of real signals was developed. This was created with a view to the parallel partitioning of the algorithm for parallel implementation on a transputer-based system, using OCCAM. A number of parallel topologies were implemented. Their performance was evaluated considering estimation of a single, and a sequence of Doppler signal segments, revealing the feasibility of these parallel implementations to be achieved in real-time