Editing Fractional Fourier transform (section)

===Generalizations===
The Fourier transform is essentially [[bosonic]]; it works because it is consistent with the superposition principle and related interference patterns.  There is also a [[fermionic]] Fourier transform.<ref name = "xyz">{{cite journal |last= De Bie |first= Hendrik |date= 1 September 2008 |title= Fourier transform and related integral transforms in superspace |journal= Journal of Mathematical Analysis and Applications |volume= 345 |issue= 1 |pages= 147–164 |doi= 10.1016/j.jmaa.2008.03.047 |arxiv= 0805.1918 |bibcode= 2008JMAA..345..147D |s2cid= 17066592 }}</ref> These have been generalized into a [[supersymmetric]] FRFT, and a supersymmetric [[Radon transform]].<ref name = "xyz" />  There is also a fractional Radon transform, a [[time–frequency analysis|symplectic]] FRFT, and a symplectic [[wavelet transform]].<ref>{{cite journal |surname1= Fan |given1= Hong-yi |surname2= Hu |given2= Li-yun |title= Optical transformation from chirplet to fractional Fourier transformation kernel |date= 2009 |journal= Journal of Modern Optics |volume= 56 |issue= 11 |pages= 1227–1229 |doi= 10.1080/09500340903033690 |arxiv= 0902.1800 |bibcode= 2009JMOp...56.1227F |s2cid= 118463188 }}</ref>  Because [[quantum circuit]]s are based on [[unitary operation]]s, they are useful for computing [[integral transform]]s as the latter are unitary operators on a [[function space]].  A quantum circuit has been designed which implements the FRFT.<ref>{{cite journal |last1= Klappenecker |first1= Andreas |last2= Roetteler |first2=  Martin |date= January 2002 |title= Engineering Functional Quantum Algorithms |journal= Physical Review A |volume= 67 |issue= 1 |pages= 010302 |doi= 10.1103/PhysRevA.67.010302 |arxiv= quant-ph/0208130 |s2cid= 14501861 }}</ref>