High frequency signal reconstruction based on compressive sensing and equivalent-time sampling

Ning JING; Dingyi YAO; Zhibin WANG; Minjuan ZHANG; Rui ZHANG

doi:10.37188/OPE.20223010.1240

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High frequency signal reconstruction based on compressive sensing and equivalent-time sampling

Information Sciences | 更新时间：2022-06-21

- High frequency signal reconstruction based on compressive sensing and equivalent-time sampling
- Optics and Precision Engineering Vol. 30, Issue 10, Pages: 1240-1245(2022)
- 作者机构：
  
  1.中北大学信息与通信工程学院，山西太原 030051
  2.山西省光电信息与仪器工程技术研究中心，山西太原 030051
  3.中北大学前沿交叉科学研究院，山西太原 030051
- 作者简介：
- 基金信息：
- DOI：10.37188/OPE.20223010.1240
  CLC： TH73
- Received：29 December 2021，
  
  Revised：26 January 2022，
  
  Published：25 May 2022
- 稿件说明：
移动端阅览
景宁,姚鼎一,王志斌等.等效时间采样压缩感知高频信号重建[J].光学精密工程,2022,30(10):1240-1245.

JING Ning,YAO Dingyi,WANG Zhibin,et al.High frequency signal reconstruction based on compressive sensing and equivalent-time sampling[J].Optics and Precision Engineering,2022,30(10):1240-1245.
景宁,姚鼎一,王志斌等.等效时间采样压缩感知高频信号重建[J].光学精密工程,2022,30(10):1240-1245. DOI： 10.37188/OPE.20223010.1240.

JING Ning,YAO Dingyi,WANG Zhibin,et al.High frequency signal reconstruction based on compressive sensing and equivalent-time sampling[J].Optics and Precision Engineering,2022,30(10):1240-1245. DOI： 10.37188/OPE.20223010.1240.

摘要

为在欠采样率条件下实现高频信号的测量与恢复，本文使用自研国产皮秒级等效时间采样光取样示波器对频率10~100 GHz的简谐波信号进行采集和恢复。该示波器中，分别采用粗、细两级延迟进位产生延迟分辨率5 ps、动态范围10 μs的触发序列，驱动高带宽取样器对信号进行取样，取样信号通过50 kHz 模数转换器输出得到测量值，即每间隔20 μs增加5 ps延迟的方式对高频信号进行一次取样，压缩比约为10

，实际采样率远低于奈奎斯特定理限制。根据压缩感知原理，通过傅里叶变换及等效时间采样构成测量矩阵，构成该信号测量过程的稀疏化表示，并求解L1范数最小化问题，恢复得到被测信号波形。结果表明，最高可实现100 GHz的高频信号均方根误差小于5×10

-5

的欠采样恢复，拓展了该类型示波器测量的动态范围。

Abstract

A simple harmonic wave with frequency 10–100 GHz is collected by a domestic equivalence time optical sampling oscilloscope to measure and recover high-frequency signals in undersampling situations. There is a trigger sequence with a 5 ps delay resolution and 10 μs dynamic range in the oscilloscope. The trigger sequence， generated by two steps of coarse and fine delayers， is used to drive the high band-wide sampler， and the sampling value is output by an ADC with a frequency of 50 kHz. In this advancement， the high-frequency signal is sampled with an increasing 5 ps delay every 20 μs. The compress ratio is approximately 10

， and the sampling rate is far below the Nyquist law. With compressive sensing theory， the measurement matrix is constructed by Fourier translation and equivalence time sampling sequence and sparsify the signal measurement process. The measurement signal is reconstructed by solving an L1-norm minimum problem. The results demonstrate that the signal with a frequency of 100 GHz can be undersampled and reconstructed with a mean square error below 5×10

， implying that the dynastic range of the sampling oscilloscope should be expanded.

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