Instantaneous Frequency, Mean Frequency, and Variance of Mean Frequency Estimators for Ultrasonic Blood Velocity Doppler Signals

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Abstract
The relationship between the instantaneous frequency and the mean frequency of ultrasonic Doppler signals in blood velocity measurements is discussed. The probability distribution density for the instantaneous frequency is calculated. The time interval histogram (TIH), which has been used to characterize the Doppler signal, is found to be an approximation of this probability density. The probability density will also describe the output of phase-lock loop analysis of the Doppler signal. The variance of mean frequency estimators is calculated, and the implication of this for practical estimators is discussed. The effect of hard limiting of the signal on the estimator performance is also discussed.