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Time-frequency analysis with eight-figure kernel

Time-Frequency (TF) analyses have been widely used to analyze some nonstationary signals like speech and biological signals. Cohen's class TF distribution has a high resolution in time and frequency and becomes a powerful tool for nonstationary signal analysis. In order to apply the TF analysis using a novel kernel to biological signals, the authors investigated a higher resolution kernel for the ultrasound Doppler signal. The authors would like to apply the TF analysis to blood flow signal analysis. They measured the ultrasound Doppler signal which was obtained in olive oil with a steel ball moving to and fro in the continuous ultrasound. The movement of the steel ball was controlled by various functions. The authors used three kinds of kernel: (1) the Wigner distribution, (2) the Choi-Williams distribution (ED), and (3) the authors' new kernel (named eight figure-kernel), that has high resolution. The results show that the demodulation accuracy with the authors' new kernel is higher and the negative components are smaller than the ED, which makes the cross-term small.