Title :
A note on exact discrete Fourier transforms
Author_Institution :
MIT, Lincoln Laboratory, Lexington, MA, USA
fDate :
12/1/1973 12:00:00 AM
Abstract :
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.
Keywords :
Arithmetic; Discrete Fourier transforms; Discrete transforms;
Journal_Title :
Audio and Electroacoustics, IEEE Transactions on
DOI :
10.1109/TAU.1973.1162518
