Time-frequency analysis of a noisy ultrasound Doppler signal with a 2nd figure eight kernel

Nonstationary ultrasound Doppler signals, those are changing with time and frequency simultaneously, are widely observed in biological and speech signals. A Cohen´s class time-frequency (TF) analysis can analyze nonstationary signals with high resolution in time and frequency at a same time. A time-frequency distribution (TFD) is largely affected by a kernel function. Thus, there is sometimes a case where auto-terms (those are signal components) are covered by cross-terms (those are spurious components). In order to apply TFDs to a nonstationary and nonlinear Doppler ultrasound signals, experimental data were obtained by moving a steel ball to and fro by continuously irradiating it with ultrasound in olive oil. The movement of the steel ball was controlled by various functions. To analyze these signals, four kernels were used: (1) a Wigner kernel, (2) a Choi-Williams kernel, (3) a figure eight kernel, and (4) a 2nd figure eight kernel. Using our 2nd figure eight kernel, the demodulation accuracy was improved even with noise.