Parametric TFR via windowed 2-order polynomial frequency modulated atoms

A novel parametric time-frequency representation called FM²let transform, which uses the dilated and translated windowed 2-order polynomial frequency modulated atoms (FM²lets), is proposed. The Fourier transform, short-time Fourier transform (including Gabor transform), wavelet transform, and chirplet transform are reformulated in one framework of FM²let transform accordingly. By FM²let transform, both the signal´s time-invariant and time-varying spectral contents can be compactly characterized. The superiority of the proposed method to some existing time-frequency distributions (TFDs) is demonstrated using a bat sonar signal.