1
$\begingroup$

The eigenvalues of the discrete fourier transform are $\{1, -1, i, -i\}$ in approximately equal proportions.

https://en.wikipedia.org/wiki/Discrete_Fourier_transform#Eigenvalues_and_eigenvectors

Is there a generalization of this transform where the eigenvalues are other roots of unity?

$\endgroup$

1 Answer 1

2
$\begingroup$

The Fractional Fourier transform (and see here for details in the non-discrete case).

$\endgroup$
1
  • $\begingroup$ From what I can understand, the fractional fourier transform is just a power of the usual fourier transform. How could it have more than 4 distinct eigenvalues? $\endgroup$
    – Yi Liu
    Mar 2, 2016 at 22:56

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.