On the Eigenvectors of the Matrix That Performs the Discrete Finite Fourier Transform
TELEDYNE GEOTECH ALEXANDRIA VA ALEXANDRIA LABS
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The discrete finite Fourier transform can be regarded as a matrix operation, since each element of one member of the pair is a linear combination of all the elements of the other member. A remarkably simple relation between a periodic function of a discrete variable and its discrete finite Fourier transform, namely that the absolute values of their expansion coefficients in these eigenvectors are the same, has been demonstrated. A canonical form for such functions with respect to the finite Fourier transform is suggested in which the transform can be done by inspection.
- Theoretical Mathematics