Instantaneous frequency estimation by using the Wigner distribution and linear interpolation

Nonparametric algorithm for the instantaneous frequency (IF) estimation, by using the Wigner distribution (WD) with an adaptive window length, is considered in the paper. This algorithm produces a bias-to-variance trade-off close to optimal, meaning almost minimal mean squared error (MSE) of the estimation. Thus, the adaptive window length is characterized by a small bias at the considered instant. Then, according to the WD concentration property, the IF estimate can be assumed as a linear function within this window. Instead of nonparametric IF estimation in other points within this interval the linear IF interpolation can be performed. Length of the interpolation segment is determined based on the adaptive window length. It is done in such a way to produce a trade-off between the interpolation caused error and calculational complexity. This modification can produce a significant calculation savings, without increasing the overall MSE. Theoretical analysis has been confirmed on numerical examples and statistical study with four synthetic signals. The approach presented here can be generalized in a straightforward manner to nonlinear interpolations and higher order time-frequency representations. (C) 2002 Elsevier Science B.V. All rights reserved.