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An algebraic approach to a calculus of functional differences : fixed differences and integrals / [by] Bruce J. MacLennan.

by: MacLennan, Bruce J.

Publication date: 1987-09

Topics: AUTOMATIC SPEECH RECOGNITION., SPEECH PERCEPTION., SPEECH PROCESSING SYSTEMS., VOICE.

Publisher: Monterey, California : Naval Postgraduate School

Collection: navalpostgraduateschoollibrary; fedlink; americana

Contributor: Naval Postgraduate School, Dudley Knox Library

Language: English

Title from cover

"Prepared for: Chief of Naval Research"--Cover

"September 1987"--Cover

"NPS-52-87-041"--Cover

DTIC Identifiers: Functional differences, Fixed differences, PE61153N

Includes bibliographical references (p. 27-28)

Technical report; 1987

This document introduces a notion of functional differences in which the difference of a function f with respect to a function h is that function g that describes how the value of f changes when its argument is altered by h: f(h(x) = g(f(x)). The author introduces the inverse operation of functional integration and derive useful properties of both operations. The result is a calculus that facilitates derivation and reasoning about recursive programs. This is illustrated in a number of simple examples. The present report uses algebraic methods to establish preliminary results pertaining to fixed differences, that is, functional differences that do not depend on the value of the argument x. Keywords: Theorems; Integrals

aq/aq cc:91160 03/27/97

kmc/kmc 11/4/09