Improving performance of doppler ultrasound spectral estimation using a truncated autocorrelation function

Abstract

A fundamental problem in Doppler Ultrasound blood flow measurements is the computation of the signal instantaneous frequency, which is generated when the signal is acquired. It is proportional to the flow velocity. The Cohen class of Time Frequency Distributions (TFD) has efficiently determined a very close estimation of the instantaneous frequency for quasi-stationary signals such as arterial blood flow. Nevertheless, the computation of each of the distributions has an O(N3) complexity, where N is the sample length. This imposes a great limitation specially when working with real-time systems. Previous works have proposed simplified expressions with more or less the same order of complexity. In this work a study is conducted to observe the response of different distributions when truncating the TFD's autocorrelation function. It also studies the relationship with the precision obtained in the frequency estimation when considering particular distribution kernels (e.g. Choi Williams, Bessel and Born Jordan). It considers the signal SNR and sample length in order to define a truncation procedure that introduces a minimum RMS error. A real Doppler Ultrasound signal taken from the Carotid artery is used for the performance evaluation.