Cramer-Rao bounds for wavelet transform-based instantaneous frequency estimates

Authors:
R.A. Scheper;A. Teolis
Affiliations:
Naval Res. Lab., Washington, DC, USA;-
Venue:
IEEE Transactions on Signal Processing
Year:
2003

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Abstract

We use an asymptotic integral approximation of a wavelet transform as a model for the estimation of instantaneous frequency (IF). Our approach allows the calculation of the Cramer-Rao bound for the IF variance at each time directly, without the need for explicit phase parameterization. This is in contrast to other approaches where the Cramer-Rao bounds rely on a preliminary decomposition of the IF with respect to a (usually polynomial) basis. Attention is confined to the Morlet wavelet transform of single-component signals corrupted with additive Gaussian noise. Potential computationally and statistically efficient IF extraction algorithms suggested by the analysis are also discussed.