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A note on exact discrete Fourier transforms

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1 Author(s)
C. Rader ; MIT, Lincoln Laboratory, Lexington, MA, USA

It is proved that the z transform of a sequence of data values cannot be exactly computed using a binary number representation for values of z on the unit circle, except z =±1, z = ±j. It is also proved that the discrete Fourier transform (DFT) of a sequence of data values cannot be evaluated with rational numbers.

Published in:

IEEE Transactions on Audio and Electroacoustics  (Volume:21 ,  Issue: 6 )