Is there a generalization for the discrete fourier transform whereby eigenvalues are other roots of unity?

Question

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

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

dls · Accepted Answer · 2016-02-12 02:24:44Z

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answered Feb 12, 2016 at 2:24

dls

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$\begingroup$ 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
Commented Mar 2, 2016 at 22:56

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