An averaged time-frequency distribution for noisy signals analysis

A time-frequency approach for improved instantaneous frequency estimation of a noisy signal has been proposed. This approach is based on a time-frequency distribution obtained by averaging the L-spectrograms. The spectrogram with lower values of parameter L produces large bias and low variance, while higher L decreases bias and increases the variance of instantaneous frequency estimation. In order to provide low mean square error of the instantaneous frequency estimation, the averaged L-spectrogram based distribution is proposed leading to the better bias-variance compromise. The proposed approach has been tested on a noisy synthetic signal for with different values of signal to noise ratio.