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What is the best argument of fractional Fourier transform over multiscale wavelet in data analysis purpose.

  • Optimization of the good time-frequency domain parameter ? "Good" will be, find the %time-%fq domain that minimize spectral entropy of the data.

  • Real physic world behavior, since particle-path is locally describe by fractional Fourier in N-slit problem context ?

  • Wavelet is just a fast log2 implementation of fractFt ?

  • Continuous transformation from time to frequency... But for what purpose ?

I take any strong argument of fracFt over wavelet

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    $\begingroup$ Please don't overuse abbreviations. $\endgroup$ – YCor Feb 14 at 13:41
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Performance of wavelet, fractional Fourier and fractional cosine transform in image compression compares these techniques. Wavelets perform better at lower compression ratios, whereas the fractional Fourier transform provides good results at higher compression ratios.

Here is an example at compression ratio 10:1, where wavelet clearly gives better results than the fractional Fourier transform.

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  • $\begingroup$ Yes, I often notify that wavelet perform better than fractional Transform in various signal processing fields ! I argue that because signal are brownian motion (frequencies decrease in $\frac{1}{x}$), thus log-scale power spectrum is constant ! So naturally well fitted for dyadic wavelet quantification. In fact, even for fractional brownian signal, wavelet perform better than all classes of fractional transform at same bitrate. At high compression level, it's not so clear that the opposite is true. I seek for a more "philosophical" way to use fractional transform or a strong reason/property $\endgroup$ – sharl Feb 14 at 14:33

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