Frequency Measurement Method of Signals with Low Signal-to-Noise-Ratio Using Cross-Correlation

Machines

Jigou Liu¹  Yang Liu¹  Ralph Kennel² 

[1] ChenYang Technologies GmbH & Co. KG, 85464 Finsing, Germany;Institute for Electrical Drive Systems and Power Electronics, Technical University of Munich, 80333 Munich, Germany;

关键词: cross-correlation;    frequency measurement;    low SNR;    Fast-Fourier Transformation (FFT);    continuous wavelet transformation;    self-mixing interferometry;   

DOI  :  10.3390/machines9060123

来源: DOAJ

【 摘 要 】

Precise frequency measurement plays an essential role in many industrial and robotic systems. However, different effects in the application’s environment cause signal noises, which make frequency measurement more difficult. In small signals or rough environments, even negative Signal-to-Noise Ratios (SNRs) are possible. Thus, frequency measuring methods, which are suited for low SNR signals, are in great demand. While denoising methods such as autocorrelation do not suffice for small signal with low SNR, frequency measurement methods such as Fast-Fourier Transformation or Continuous Wavelet Transformation suffer from Heisenberg’s uncertainty principle, which makes simultaneous high frequency and time resolutions impossible. In this paper, the cross-correlation spectrum is presented as a new frequency measuring method. It can be used in any frequency domain, and provides greater denoising than autocorrelation. Furthermore, frequency and time resolutions are independent from one another, and can be set separately by the user. In simulations, it achieves an average deviation of less than 0.1% on sinusoidal signals with a SNR of −10 dB and a signal length of 1000 data points. When applied to “self-mixing”-interferometry signals, the method can reach a normalized root-mean square error of 0.2% with the aid of an estimation method and an averaging algorithm. Therefore, further research of the method is recommended.

【 授权许可】

Unknown