Smoothed power spectrum estimate applied for analysis of the Doppler signal from blood flow

A simple method for the improvement of the definition of the instantaneous spectrum estimate of Doppler signal is proposed. A short review of the stochastical properties of FFT spectrum estimates is presented. This review allowed us to develop a concept of the 'estimation noise' as an interpretation of the stochastic uncertainty of the estimation. This, in turn, permitted us to propose a method of adaptive filtering of spectral estimation to minimise the effects of the 'estimation noise'. Proposed filtering in the frequency domain corresponds to a procedure known as smoothing of the estimate. Two different smoothing procedures are presented: classical, linear smoothing and nonlinear, homomorphic smoothing. The performances of the smoothed spectrum estimate are theoretically and experimentally studied, showing that their effectiveness depends mostly on the shape of the Doppler spectrum. Although smoothing always reduces the spectral resolution, the important limitation of the variance of estimation can be achieved without meaningful deterioration of the resolution in our application. Thus, the proposed procedures may sensibly improve the accuracy of the relationship between the shape of the spectrum and the flow parameters. As a result, more exact determination of flow characteristics such as stability or maximum velocity, even in cases of low signal-to-noise power ratio, should be possible.