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Anisotropic Instantaneous Frequency Estimator

We present a novel transform, called anisotropic chirplet transform, for the time-frequency analysis of overlapping signals. This transform is motivated by a desire to characterize micro-Doppler signals from the continuous wave radars, especially a challenging topic for instantaneous frequency (IF) estimation in high noise environments. By combining the instantaneous rotating angle with the anisotropic operator, an optimal time-frequency-varying window width is achieved to directionally compensate for the energy of each component. In addition, the chirplet ridge detection algorithm based on the anisotropic chirplet transform is further proposed to extract chirplet ridges in noisy signals. The proposed method is applied to analyze overlapping multicomponent signals with a high noise, which demonstrates its effectiveness in the simulated examples and application data sets.