Hartley transforms over Finite Fields

A general framework is presented for constructing transforms in the field of the input which have a convolution-like property. The construction is carried out over finite fields, but is shown to be valid over the real and complex fields as well. It is shown that these basefield transforms can be viewed as “projections” of the discrete Fourier transform (DFT) and that they exist for all lengths N for which the DFT is defined. The convolution property of the basefield transforms is derived and a condition for such transforms to have the self-inverse property is given. Also, fast algorithms for these basefield transforms are developed, showing gains when compared to computations using the FFT. Application of the methodology to Hartley transforms over R leads to a simple derivation of fast algorithms for computing real Hartley transforms


Published in:
IEEE Transactions on Information Theory, 39, 5, 1628-1638
Year:
1993
Publisher:
Institute of Electrical and Electronics Engineers
ISSN:
0018-9448
Keywords:
Laboratories:




 Record created 2005-04-18, last modified 2018-03-17

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