超声信号拉盖尔模型及在渡越时间测量中的应用

Laguerre model of ultrasonic signal and its application in ToF measurement

超声信号建模是利用脉冲信号进行渡越时间(ToF)测量中的关键技术之一。针对传统经验模型的局限性,提出基于拉盖尔(Laguerre)函数的超声信号建模方法。首先分析Laguerre函数的时域和拉氏域特征,然后将超声信号建模与确定Laguerre谱归属为同一问题。通过泰勒级数展开和拉格朗日插值,从理论上证明双指数模型和混合指数模型是Laguerre模型特殊形式,并通过仿真验证了此结论。对实测数据分析表明,Laguerre模型拟合误差小于0.1%,ToF测量结果相对偏差小于10-6。

Ultrasonic signal modeling is one of the most crucial techniques in time of flight （ToF） measurement with pulse signal. Aiming at the limitation of traditional experiential models, a novel ultrasonic signal modeling method based on Laguerre function is proposed. The characteristics of Laguerre function in time domain and Laplace domain are analyzed, and the ultrasonic signal modeling and Laguerre lems. The hybrid and dual exponential models are theoretically Taylor series expansion and Lagrange analysis results of experimental data deviation of ToF measurement result interpolation, and show that the fitting error is less than 10-6. spectrum estimating are confirmed as homologous prob- proved to be the specific forms of Laguerre model with conclusion is verified with numerical simulation. The of Laguerre model is less than O. 1% , and the relative