Optimization of the Processing Time of Cross-Correlation Spectra for Frequency Measurements of Noisy Signals

Abstract

Accurate frequency measurement plays an important role in many industrial and robotic systems. However, different influences from the application’s environment cause signal noises, which complicate frequency measurement. In rough environments, small signals are intensively disturbed by noises. Thus, even negative Signal-to-Noise Ratios (SNR) are possible in practice. Thus, frequency measuring methods, which can be used for low SNR signals, are in great demand. In previous work, the method of cross-correlation spectrum has been developed as an alternative to Fast Fourier-Transformation or Continuous Wavelet Transformation. It is able to determine the frequencies of a signal under strong noise and is not affected by Heisenberg’s uncertainty principle. However, in its current version, its creation is computationally very intensive. Thus, its application to real-time operations is limited. In this article, a new way to create the cross-correlation spectrum is presented. It is capable of reducing the calculation time by 89% without significant accuracy loss. In simulations, it achieves an average deviation of less than 0.1% on sinusoidal signals with an SNR of −14 dB and a signal length of 2000 data points. When applied to “self-mixing”-interferometry signals, the method can reach a normalized root-mean-square error of 0.21% with the aid of an estimation method and an averaging algorithm. Therefore, further research of the method is recommended.