KEYWORDS: Transform theory, Fourier transforms, Control systems, Signal processing, Computer engineering, Image processing, Imaging systems, Electronic imaging, Current controlled current source, Binary data
This paper describes the 2-D reversible integer discrete Fourier transform (RiDFT), which is based on the concept
of the paired representation of the 2-D signal or image. The Fourier transform is split into a minimum set of
short transforms. By means of the paired transform, the 2-D signal is represented as a set of 1-D signals which
carry the spectral information of the signal at disjoint sets of frequency-points. The paired transform-based
2-D DFT involves a few operations of multiplication that can be approximated by integer transforms. Such
one-point transforms with one control bit are applied for calculating the 2-D DFT. 24 real multiplications and
24 control bits are required to perform the 8x8-point RiDFT, and 264 real multiplications and 168 control bits
for the 16 x 16-point 2-D RiDFT of real inputs. The computational complexity of the proposed 2-D RiDFTs is
comparative with the complexity of the fast 2-D DFT.
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