What could be the arguments of using fractional Fourier transform instead of multiscale wavelet for data analysis ?
Optimization of the good time-frequency domain parameter? good in the sens of best time-frequency domains that minimize spectral entropy of the data. But often, best entropy is achieved in a full 100% frequency domain.
Due to the physic world behavior, particle-path is locally described by fractional Fourier in N-slit problem context. Usefull for describing binary brownian data or differential binary brownian data ? ( sign(cumsum(randn(n,1))) or abs(diff(sign(cumsum(randn(n,1))))) )
Wavelet could be thinking as just a fast and efficient dyadic scheme of a particular sparse fractional transform ?
Continuous transformation from time to frequency: What would be the purpose of this transformation? Maybe to bring up patterns?
I really appreciate any strong argument about advantage of fractional Fourier Transform in comparison to wavelet.
(Our universe choosed fractional transform coding scheme for particles, there must be a reason of efficiency somewhere...)