finv=involute(f); finv=involute(f,dim);
involute(f) will return the involution of f.
involute(f,dim) will return the involution of f along dimension dim. This can for instance be used to calculate the 2D involution:
f=involute(f,1); f=involute(f,2);
The involution finv of f is given by:
finv(l+1)=conj(f(mod(-l,L)+1));
for \(l=0,\ldots,L-1\).
The relation between conjugation, Fourier transformation and involution is expressed by:
conj(dft(f)) == dft(involute(f))
for all signals f. The inverse discrete Fourier transform can be expressed by:
idft(f) == conj(involute(dft(f)));