锯齿调频连续波建模与数值仿真

锯齿调频连续波由于测距精度高,在测距系统中有着广泛的应用.为了描述锯齿调频连续波多个调频周期中的频率和相位变化及跨越调频周期时的不连续性,结合具有一定周期性和不连续性的模数函数,推导了锯齿调频连续波的频率和相位的数学表达式,并进行建模及仿真.通过对频率与相位的微积分关系的推导解析地验证了数学表达式的正确性.数值仿真结果也表明:频率和相位的数学表达式满足微积分的关系,是频率与相位的正确的表达式,能够描述锯齿波调频在跨越调频周期时的不连续性.提出的锯齿调频连续波的多调频周期频率与相位表达式可为进一步研究锯齿调频连续波测距过程提供基础.

Modeling and numerical simulation of sawtooth FMCW

Sawtooth FMCW is widely used in ranging systems because of the high ranging precision. Combining features of modulo function, which is periodic and discontinuous, the analytical expressions of frequency and phase of sawtooth FMCW were deduced to express them in multi-FM-period, and the discontinuousness at boundary between FM periods. The mathematics modeling and simulations were realized. The correctness of analytical expressions was proven analytically by deduction of differential and integral relationships between frequency and phase. The result of numerical simulation also shows that frequency and phase expressions have relationships of differential and integral, which are the corrective expressions for frequency and phase. And the expressions could correctly describe the discontinuousness of sawtooth FMCW at boundary between FM periods. The expressions for frequency and phase of Sawtooth FMCW in multi-FM-period can serve as a base for further research of ranging process involving sawtooth FMCW.