How is Linear Canonical Transform a generalization of Fractional Fourier Transform? I have studied that Fourier transform changes the domain of a signal from time to frequency, and in that way it is a 90 degree shift. When it comes to Fractional Fourier Transform a generalization of Fourier Transform, the resulting transform can lie anywhere between time and frequency domain depending on parameter 'alpha'.

My question is how in the same way Linear Canonical Transform is a generalization of Fractional Fourier Transform.Its physical interpretation in terms of signal processing.
Can any body help?
The linear canonical transforms are all area preserving, orientation preserving, linear transforms on the time-frequency plane. The fractional Fourier transforms are a subset, namely the rotations. Both sets form (Lie-)groups under composition, and the rotations are a subgroup.