基于欠采样的频率测量方法

A method of frequency measurement based on sub-nyquist sampling

奈奎斯特采样定理限制采样率必须大于输入信号频率的2倍以上,因而对高频信号进行精密测量需要花费昂贵成本来得到适合的高采样率,本文提出一种欠采样的频率测量算法,也就是用不符合采样定律的特定低采样率对高频信号进行采集,采用互相关算法对采集所得的数据进行处理,最终实现了对高频信号的精密测量。试验结果得出:应用该算法采样能得到较逼真的波形,对于5MHz以上的高频信号,频率信息仍能精准的保留。运用该方法测量10MHz的信号,频率测量精度可达10?12量级。

The Nyquist sampling theorem astricts that the sample rate must be at least twice than the import frequency. So precision measurement of high frequency signal must cost highly to match suitable high sample rate. In this paper we present a frequency measurement algorithm based on Sub-nyquist sampling. That is, sample the high frequency signal with specifically low sample rate, which is not accord with Nyquist sampling theorem, and process the acquired data using the Cross-correlation theorem. Finally we successfully complete the precision Measurement for high frequency signal. We can conclude from experiment that with this method we can get lively waveform. For high frequency signal which is higher then 5 MHz, the frequency information still can be reserved. And use this method to measure signals of 10MHz, the measuring accuracy can reach to 10^-12 or over.