Complex composite spectra of Unified Complex Hadamard transform for logic functions

Author

Rahardja, Susanto ; Falkowski, Bogdan J.

Author_Institution

PT SRIKAYA MITRAMAKMUR, Indonesia

Volume

47

Issue

11

fYear

2000

fDate

11/1/2000 12:00:00 AM

Firstpage

1291

Lastpage

1297

Abstract

A method to evaluate the Unified Complex Hadamard spectra of AND, OR, and XOR for Boolean functions, directly from the spectra of the functions, is presented. The results are given using a general coding scheme, and different possible codings of Boolean functions are also discussed. A new definition of the convolution operation called complex convolution is derived. Different properties of such a convolution are presented. A theorem giving final formulas for the composite Unified Complex Hadamard spectra of Boolean functions is stated in terms of the complex convolution. Efficient representations of the spectra in the form of decision diagrams are presented. An application of Unified Complex Hadamard Transform in image watermarking is also discussed.

Keywords

Boolean functions; Hadamard transforms; convolution; decision diagrams; logic design; Boolean function; Unified Complex Hadamard transform; complex composite spectra; complex convolution; decision diagram; image watermarking; logic design; logic function; Application software; Arithmetic; Boolean functions; Circuit testing; Convolution; Gaussian processes; Logic design; Logic functions; Standards publication; Watermarking;

fLanguage

English

Journal_Title

Circuits and Systems II: Analog and Digital Signal Processing, IEEE Transactions on

Publisher

ieee

ISSN

1057-7130

Type

jour

DOI

10.1109/82.885135

Filename

885135