Improved procedures for estimating amplitudes and phases of harmonics with application to vibration analysis

Abstract

In this paper, we propose two procedures for accurate amplitude and phase estimation of multifrequency signals in rotating machinery. The first method reduces the amplitude attenuation and phase shift caused by the "nonflat" top of the main lobe of the window. The second procedure is able to reduce not only the leakage effects due to windowing but also the distortion that appears when the rotation frequency changes slowly. This second method uses an additional sensor, giving one pulse per revolution, to transform the input (asynchronous) signal into a synchronous signal having a fixed number of samples per revolution. The performance and effectiveness of both procedures are illustrated by means of simulation examples.

A Scale Factor-Based Interpolated DFT for Chatter Frequency Estimation

“…Most of these techniques are based on the discrete Fourier transform (DFT) for their low computational burden and feasibility for real-time applications [6]- [8]. However, when performing the DFT, the observation interval must be an exact integer multiple of the period of the signal.…”

Frequency estimation of the weighted real tones or resolved multiple tones by iterative interpolation DFT algorithm

“…Frequency-domain algorithms are based on the windowed discrete Fourier transform (DFT), as implemented by the fast Fourier transform (FFT), and are commonly preferred in consideration of their simple implementation and low computational burden. However, due to the FFT picket fence effect (PFE) and spectral leakage effect (SLE), significant bias would be introduced into the estimates of frequency, amplitude, and in particular, phase, if the sample frame is not an integer multiple of signal period [2,3]. Previous studies have shown that the maximum estimation error for the amplitude of a single sinusoid is up to −3.92 dB for the rectangle window and −1.42 dB for the Hanning window [4].…”

Estimation of multi-frequency signal parameters by frequency domain non-linear least squares

“…. ; N À 1Þ spectral samples when processing a signal sequence of length MN ordered from 0 to MN À 1: Following the simple idea that selecting a shorter window that has a broader spectral mainlobe could reduce the spectrum granularity effect, a procedure is presented to estimate the window length for a given limit of amplitude error [7], however, the estimated phase is very coarse. As for periodic signals, a rough algorithm is proposed to modify the actual sampled sequence to be an ideal sample sequence that is synchronised with the original periodic signal [8].…”