Number theoretic transforms of periodic structures and their applications
Said Boussakta, Ali Yeon Md Shakaff, Farhi Marir, A.G.J. Holt · IEE Proceedings G (Electronic Circuits and Systems) · 1988
The properties of the Fermat number transforms of periodic data are investigated and it is shown they have regular structures with many zero-valued elements. Expressions are derived for the maximum number of nonzero elements related to the data row and column periods. Examples are given and applications suggested for image compression and data storage. It is also shown that the effects of defects as small as a single pixel in the image data produce effects upon the FNT, completely altering its regular structure. Applications for this result are suggested to the detection of errors in maskmaking for integrated circuit design and defect detection in industrial inspection.