PROPERTIES AND WAYS OF CALCULATION OF MULTIPOLARITY GENERALIZED WALSH TRANSFORMS

被引：20

作者：

FALKOWSKI, BJ

机构：

[1] Electrical and Electronic Engineering, Nanyang Technological University

来源：

IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS II-ANALOG AND DIGITAL SIGNAL PROCESSING | 1994年 / 41卷 / 06期

关键词：

D O I：

10.1109/82.300195

中图分类号：

TM [电工技术]; TN [电子技术、通信技术];

学科分类号：

0808 ; 0809 ;

摘要：

A new formulation of the Multi-Polarity Generalized Walsh Transform has been introduced. The formulation allows a uniform representation of Boolean functions by a set of orthogonal and generalized Walsh spectral coefficients. Forward and inverse transformation kernels and the method of recursive generation of transform matrices by using Kronecker products of elementary matrices have been given. Mutual relations among transform matrices and spectra for arbitrary polarities have been investigated. Fast Forward and Inverse Generalized Walsh Transforms have been developed. An algorithm to calculate the Generalized Walsh transform from a cube array specification of incompletely specified Boolean functions has been shown. The transforms algorithm makes use of the properties of an array of disjoint cubes and allows the determination of the spectral coefficients in an independent way. The computer implementation drastically reduces the required time of computation by allowing calculation of only chosen coefficients in specified polarity. The entire spectrum-if required-can be computed incrementally for groups of coefficients.

引用

页码：380 / 391

页数：12

共 24 条

[1]

AGAIAN SS, 1985, LECTURE MATH, V1168

[2]

[Anonymous], 1990, WALSH SERIES INTRO D

[3]

BEAUCHAMPS KG, 1984, APPLICATIONS WALSH R

[4]

BRAYTON R, 1984, LOGIC MINIMIZATION A

[5]

CHRESTENSON HE, 1955, PAC J MATH, V5, P17

[6]

ELLIOT DF, 1982, FAST TRANSFORMS ALGO

[7] EFFECTIVE COMPUTER METHODS FOR THE CALCULATION OF RADEMACHER-WALSH SPECTRUM FOR COMPLETELY AND INCOMPLETELY SPECIFIED BOOLEAN FUNCTIONS [J].

FALKOWSKI, BJ ;

SCHAFER, I ;

PERKOWSKI, MA .

IEEE TRANSACTIONS ON COMPUTER-AIDED DESIGN OF INTEGRATED CIRCUITS AND SYSTEMS, 1992, 11 (10) :1207-1226

[8]

FALKOWSKI BJ, 1993, 26TH P IEEE INT S CI, P1694

[9]

FALKOWSKI BJ, 1990, 23RD P IEEE INT S CI, P2913

[10]

FALKOWSKI BJ, 1992, 25TH P IEEE INT S CI, P137

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