Abstract
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.
Highlights
This study presents a new method based on cross-correlation to measure the frequencies of low Signalto-Noise Ratios (SNRs) signals with high accuracy
The fact from the Fourier analysis, that a signal can be approximated with a linear combination of trigonometric functions, one can assume that the frequencies of a test signal y(t) can be identified by determining values of the frequency fN, which result in the largest amplitude of the cross-correlation function φxy (τ )
The parameter Z (see Equation (16)) should be set to the signal period length of φx f w y (k); The cross-correlation spectrum’s value K ( f w ) for the current frequency f w is determined by identifying the amplitude of the cross-correlation function φx f w y (k)
Summary
Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. Methods which can measure frequencies of low SNR signals are in great demand [9]. In the case of small signals with low SNR, autocorrelation is not suited to denoise the signal while preserving frequency information (see Chapter 3). This study presents a new method based on cross-correlation to measure the frequencies of low SNR signals with high accuracy. The rest of the paper is organized as follows: Section 2 describes cross-correlation and its relevant characteristics as fundamentals It presents the new signal processing method, its working principle, as well as its characteristics and benefits.
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
