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Instantaneous frequency estimation by using the Wigner distribution and linear interpolation

机译：使用Wigner分布和线性插值的瞬时频率估计

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摘要

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.
机译：本文考虑了使用具有自适应窗口长度的Wigner分布（WD）进行瞬时频率（IF）估计的非参数算法。该算法产生接近最佳的偏差到方差的折衷，这意味着估计的均方误差几乎最小。因此，自适应窗口长度的特征在于所考虑的瞬间的小偏差。然后，根据WD浓度属性，可以将IF估计假定为该窗口内的线性函数。代替在此间隔内的其他点进行非参数IF估计，可以执行线性IF插值。内插段的长度基于自适应窗口长度来确定。以此方式在插值引起的误差和计算复杂度之间进行权衡。此修改可以节省大量计算费用，而无需增加总体MSE。理论分析已通过四个合成信号的数值示例和统计研究得到证实。此处介绍的方法可以直接方式概括为非线性插值和更高阶的时频表示。

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