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

In this paper, 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 Cramér–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 Cramér–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 briefly discussed.