Instantaneous frequency tracking of a sinusoidally frequency-modulated signal with low modulation index: application to laser measurements in acoustics

  • Authors:

  • V. Valeau;J.-C. Valière;C. Mellet

  • Affiliations:

  • Laboratoire d'Acoustique de I'Université du Maine, UMR-CNRS 6613, Av. O Messiaen, 72085 Le Mans, Cedex 9, France;Laboratoire d'Acoustique de I'Université du Maine, UMR-CNRS 6613, Av. O Messiaen, 72085 Le Mans, Cedex 9, France;Laboratoire d'Acoustique de I'Université du Maine, UMR-CNRS 6613, Av. O Messiaen, 72085 Le Mans, Cedex 9, France

  • Venue:
  • Signal Processing
  • Year:
  • 2004

Quantified Score

Hi-index 0.08

Visualization

Abstract

In this paper, the problem of the instantaneous frequency (IF) estimation of sinusoidally frequency-modulated signals has been addressed, especially when small modulation indices are involved. Such a problem is encountered when laser-Doppler velocity measurements are carried out in acoustics. The amplitude and phase of the sine-wave IF law are then the searched parameters. A new time-frequency transform, specifically designed for tracking sine wave IF variations has been developed, using as a starting point the formalism of the Polynomial Wigner-Ville distributions. The computation of this transform, quick and simple, followed by an amplitude and phase estimation of the IF law, is the so-called Time-Frequency Synchronous Detector (TFSD). After a derivation of the Cramer-Rao bounds for the estimation of the searched parameters, the performances of the detector are studied and compared to those of the Cross Wigner-Ville based estimator (CWV) and those of a parametric estimator based on the maximum likelihood (ML). For moderate SNR, the TFSD represents a better compromise in terms of bias. variance and computational time than the CWV. The ML performances are slightly better for synthesized signals than those of the time-frequency methods, but the latter provide significantly better estimates for experimental signals.