A new zoom algorithm and its use in frequency estimation

Abstract

This paper presents a novel zoom transform algorithm for a more reliable frequency estimation. In fact, in many signal processing problems exact determination of the frequency of a signal is of paramount importance. Some techniques derived from the Fast Fourier Transform (FFT), just pad the signal with enough zeros in order to better sample its Discrete-Time Fourier Transform. The proposed algorithm is based on the FFT and avoids the problems observed in the standard heuristic approaches. The analytic formulation of the novel approach is presented and illustrated by means of simulations over short-time based signals. The presented examples demonstrate that the method gives rise to precise and deterministic results.

Amplitude and frequency estimator for aperiodic multi-frequency noisy vibration signals of a tram gearbox

“…Finally, the MSE is mapped as a function of the variable . Special attention is paid to the CRLB [3][4][5][6], [27,28] and [34,35]. It represents the lower limit for the MSE of estimators.…”

“…The short signal segment is generated from the original signal by a simple decimation, which reduces the maximal bandwidth around a selectable centre frequency. Both CZT and ZFFT achieve an improvement in frequency estimation, but are limited in terms of frequency resolution and they can only calculate a small portion of the entire spectrum around the centre frequency [27,28].…”

“…These are, e.g. the Cramer-Rao lower bound (CRLB) [3][4][5][6], [27,28] and [34,35], which represents the lower limit for the MSE of an estimator and the spline interpolation of at least two spectral lines. In chapter 4, the estimator is applied to real vibration signals of a tram gearbox to evaluate its performance in practice.…”

A Novel Spectral Zoom Method based on Zolotarev Polynomials

“…The lower the value of k the higher is the value of the center frequency. This feature is similar to, so-called, "zoom" technique [16], [17], where a desired frequency band is selected by a filter bank and consequentially zoomed in. Therefore, the proposed technique has been named "DZT zoom".…”