Performance of short-time spectral parametric methods for reducing the variance of the Doppler ultrasound mean instantaneous frequency estimation

To achieve an accurate estimation of the instantaneous turbulent velocity fluctuations downstream of prosthetic heart valves in vivo, the variability of the spectral method used to measure the mean frequency shift of the Doppler signal (i.e. the Doppler velocity) should be minimised. This paper investigates the performance of various short-time spectral parametric methods such as the short-time Fourier transform, autoregressive modelling based on two different approaches, autoregressive moving average modelling based on the Steiglitz-McBride method, and Prony's spectral method. A simulated Doppler signal was used to evaluate the performance of the above mentioned spectral methods and Gaussian noise was added to obtain a set of signals with various signal-to-noise ratios. Two different parameters were used to evaluate the performance of each method in terms of variability and accurate matching of the theoretical Doppler mean instantaneous frequency variation within the cardiac cycle. Results show that autoregressive modelling outperforms the other investigated spectral techniques for window lengths varying between 1 and 10 ms. Among the autoregressive algorithms implemented, it is shown that the maximum entropy method based on a block data processing technique gives the best results for a signal-to-noise ratio of 20 dB. However, at 10 and 0 dB, the Levinson-Durbin algorithm surpasses the performance of the maximum entropy method. It is expected that the intrinsic variance of the spectral methods can be an important source of error for the estimation of the turbulence intensity. The range of this error varies from 0.38% to 24% depending on the parameters of the spectral method and the signal-to-noise ratio.