Method of estimation of frequency variation relying on estimation of shift of spectral peaks

Abstract

Problem of estimation of variated frequency of components of polyharmonic signals has been arose. Three-dimensional time-frequency representation of signals is usually used to resolve this problem. But simple and reliable method of instantaneous frequency tracking is needed. Frequency tracking method based on estimation of shifts of peaks of spectrogram has been proposed in this paper. It is assumed that shift of spectral peaks of components of signal is proportional to variation of fundamental frequency. Logarithmic scaling of time-frequency representation is used to make spectral peaks equidistant. Temporal dependence of shift of spectral maximums is obtained using correlation of windowed spectrum at the first frame and spectrum of signal in the current window. Then obtained track is translated in linear scale. Proposed method does not estimate values of instantaneous frequency or central frequency of signal component but estimates its variation. Advantage of the method is that it can estimate frequency track even if range of frequency variation and its central value are known roughly or unknown at all. Multiple components do not interfere to estimate fundamental frequency variation. Reduction of bandwidth is recommended to increase accuracy of frequency track estimation, but analysis of time-frequency representation containing a few components is also possible. Dependency of performance of analysis of synthetic signals using the method on various signal to noise ratios under different conditions was estimated. Applicability of the method for vibrational diagnosing of rotary equipment was checked out using spectral interference method.

Keywords

• instantaneous frequency
• wavelets
• spectrogram
• correlation function
• frequency tracking
• frequency estimation
• fundamental frequency