基于FFT超声波传输时间测量的误差分析

为精确测量高斯白噪声背景下超声波的传输时间，不仅要考虑传统相位差测量中的高斯噪声误差，还要考虑A／D量化误差所带来的影响。应用误差理论，推导了正弦信号A／D量化误差，并得到了总误差均方根公式，进而得出传输时间误差的计算公式。为了避免电路和传感器的干扰，采用传输距离不同的同源双路正弦发送信号。理论和仿真结果均表明：在超声波信号频率为40kHz、信噪比为25dB、采样点数为2048、A／D位数为11位、采样率为200kHz的情况下，传输时间的测量误差小于10DS；在超声波信号频率未知时，而其他条件相同的情况下，FFT相位差频率校正法也能很好地估计超声波传输时间。该方案的实现为实际工程应用提供了依据。

Error Analysis of Measurement for Ultrasonic Wave Transmission Time Based on FFT

To estimate the ultrasonic transmission time accurately under the background of white Gaussian noise, in addition to considering the error caused by Gaussian noise considered in traditional phase difference measurement, the influence of A/D quantizing error was needed to be considered. Using error theory, the sine signal A/D quantizing error was deduced, and the root mean square （RMS） formula of total error was presented, and then the calculation formulation of transmission time error was attained. To avoid the interference of circuit and sensors, the double homologous sine sending signals with different transmission distance was employed. Theory and simulation results indicated that when signal frequency was 40 kHz, signal noise ratio（SNR） was 25 dB, sampling points were 2 048, A/D bits were 11 bits and the sampling rate was 200 kHz, the final measurement time error was less than 10 ns. When signal frequency was unknown and the other conditions were identical, ultrasonic transmission time can be exactly estimated by the method of phase difference frequency correction based on fast fourier transform （FFT）. The realization of the program provides a basis for practical applications.