Adaptive instantaneous frequency estimation based on time-frequency distributions with derivative approximation

A new method for nonparametric and adaptive instantaneous frequency (IF) estimation of monocomponent signals based on time-frequency distributions (TFDs) is presented. This method uses an estimate of the IF second-order derivative to approximate the width of the TFD observation window associated with the estimation least mean squared error (MSE), which was previously derived in a closed-form expression. The derivative estimate is obtained in two steps. First, a preliminary TFD is computed and its local maxima are used as a rough estimate of the IF trajectory. Thence, the continuous wavelet transform (CWT) is introduced for calculations of high-order derivatives. The proposed method is evaluated and compared with state-of-the-art algorithms based on the intersection of confidence intervals (ICI) rule. Numerical results demonstrate that the proposed method achieves a significant improvement in estimation accuracy.