Ultrasound in Med. & Biol. Vot. 16, No. 5, pp. 511-518, 1990 0301-5629/90 $3.00 + .00 Printed in the U.S.A. © 1990 Pergamon Press plc OOriginal Contribution ii ON THE BEHAVIOR OF INSTANTANEOUS FREQUENCY ESTIMATORS IMPLEMENTED ON DOPPLER FLOW IMAGERS A. NOWICKI,* J. REID,* P. C. PEDERSEN, § A. W. SCHMIDT ¢ and H. OUNG* *Institute of Fundamental Technological Research PAN, 00049 Warsaw, Poland *Biomedical Engineering and Science Institute, Drexel University, Philadelphia, PA 19104 ~Department of Electrical Engineering, Worcester Polytechnic Institute, Worcester, MA 01609 (Received 3 February 1989; in final form 11 January 1990) Abstract--Analytical and experimental results have been used to examine the behavior of the "autocorrelator" or instantaneous frequency detector (IFD) applied to color-coded Doppler flow mapping. Two effects were studied. The first was the influence of noise, as modified by a stationary echo canceler, on the Doppler frequency detector. Our theoretical considerations predict that uncorrelated input noise signals become partially correlated after cancellation, and bias the response to flow signals. This effect was confirmed by experiment. The canceler introduces a constant negative bias into the denominator of the algorithm implemented by the estimator, thus changing the indicated frequency. The second phenomenon, examined through processing computer simulated Doppler signals added to real noise, is related to the possible ambiguity, called aliasing, of measurements of the mean frequency for wide-band Doppler spectra. We show that aliasing cannot be observed with these spectra unless the signal is first processed by a canceler. Thus, regions of apparent reversed flow direction on two-di- mensional flow images of turbulence must usually be due to real reversal of the flow direction. Key Words: Ultrasound, Doppler flow imaging, Color Doppler, Doppler spectra, Frequency estimation. INTRODUCTION Acoustic measurements of blood flow velocity are based on the Doppler effect. Perhaps the most diffi- cult aspect of these measurements is the accurate de- termination of the Doppler frequency shift in a noisy environment. This noise arises from acoustic sources (clutter) and from electronic sources. Since acoustic clutter of high amplitude affects the mean Doppler frequency estimation, circuits (or digital algorithms) called stationary echo cancelers that remove the clut- ter signals precede the estimator. In general, these cancelers subtract successive pulse trains from each other. Since the electronic noise is also modified by such cancelers, a realistic assessment of estimator per- formance must include these effects. In addition, estimator performance, with or without the cancelers, may also be influenced by wideband Doppler signals. The presence of a high- frequency Doppler spectrum is usually evident by aliasing, or the sudden appearance of a velocity re- versal in the image. This interpretation is straightfor- ward for narrow-band signals but, for complex car- diac flows within the sometimes large sensitive vol- ume of cardiac imagers, has to be modified for the effects of simultaneously occurring high and low fre- quencies in the spectrum presented to the frequency estimator. Numerous techniques for estimation of the Doppler shift have been suggested. In continuous- wave (CW) Doppler frequency processing, a dedi- cated fast Fourier transform (FFT) or time-compres- sion spectrum analysis are the most promising tech- niques and indeed the most commonly used ones today. In multigate Doppler systems, however, time domain rather than frequency domain processing is used. This choice is based on the available technol- ogy, and on cost effectiveness. A multichannel FFT performed in real time requires a great deal of hard- ware and engineering development, which increases the overall cost of the equipment. Moreover, as was pointed out by Barber et al. (1985), the sensitivity of time domain processing may be better than that of frequency domain processing. THE NOISE BIASING EFFECT ON THE DOPPLER DETECTOR OUTPUT Range-gated mean frequency detection in the time domain is based upon processing the I and Q 511