The linearity,time shifting,time scaling,and time inversion properties of FMmlet transform are proved,and the frequency shifting property of one of the subspaces of FMmlet transform,namely the chirplet transform is presented.Moreover,it is proved that in the process of FMm let based atomic signal decomposition,the residual signals decay exponentially.
The subspaces of FMmlet transform are investigated. It is shown that some of the existing transforms like the Fourier transform, short-time Fourier transform, Gabor transform, wavelet transform, chirplet transform, the mean of signal, and the FM-1let transform, and the butterfly subspace are all special cases of FMmlet transform. Therefore the FMmlet transform is more flexible for delineating both the linear and nonlinear time-varying structures of a signal.
