Efficient computation of discrete polynomial transforms

Maurice F. Aburdene; Xie Jin; R. J. Kozick

Efficient computation of discrete polynomial transforms

Maurice F. Aburdene
, Xie Jin
, R. J. Kozick

Bucknell University

Research output: Contribution to journal › Article › peer-review

Abstract

This letter presents a new recursive method for computing discrete polynomial transforms. The method is shown for forward and inverse transforms of the Hermite, binomial, and Laguerre transforms. The recursive flow diagrams require only 2 additions, 2( +1) memory units, and +1multipliers for the +1-point Hermite and binomial transforms. The recursive flow diagram for the +1-point Laguerre transform requires 2 additions, 2( +1) memory units, and 2( +1) multipliers. The transform computation time for all of these transforms is ( )

Original language	American English
Journal	Default journal
Volume	10
State	Published - Oct 1 2003

Keywords

Binomial transform
discrete polynomial transform
flow diagram
Hermite transform
Laguerre transform
signal processing algorithms

Disciplines

Mathematics

Cite this

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title = "Efficient computation of discrete polynomial transforms",

abstract = " This letter presents a new recursive method for computing discrete polynomial transforms. The method is shown for forward and inverse transforms of the Hermite, binomial, and Laguerre transforms. The recursive flow diagrams require only 2 additions, 2( +1) memory units, and +1multipliers for the +1-point Hermite and binomial transforms. The recursive flow diagram for the +1-point Laguerre transform requires 2 additions, 2( +1) memory units, and 2( +1) multipliers. The transform computation time for all of these transforms is ( )",

keywords = "Binomial transform, discrete polynomial transform, flow diagram, Hermite transform, Laguerre transform, signal processing algorithms",

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AU - Aburdene, Maurice F.

AU - Jin, Xie

AU - Kozick, R. J.

PY - 2003/10/1

Y1 - 2003/10/1

N2 - This letter presents a new recursive method for computing discrete polynomial transforms. The method is shown for forward and inverse transforms of the Hermite, binomial, and Laguerre transforms. The recursive flow diagrams require only 2 additions, 2( +1) memory units, and +1multipliers for the +1-point Hermite and binomial transforms. The recursive flow diagram for the +1-point Laguerre transform requires 2 additions, 2( +1) memory units, and 2( +1) multipliers. The transform computation time for all of these transforms is ( )

AB - This letter presents a new recursive method for computing discrete polynomial transforms. The method is shown for forward and inverse transforms of the Hermite, binomial, and Laguerre transforms. The recursive flow diagrams require only 2 additions, 2( +1) memory units, and +1multipliers for the +1-point Hermite and binomial transforms. The recursive flow diagram for the +1-point Laguerre transform requires 2 additions, 2( +1) memory units, and 2( +1) multipliers. The transform computation time for all of these transforms is ( )

KW - Binomial transform

KW - discrete polynomial transform

KW - flow diagram

KW - Hermite transform

KW - Laguerre transform

KW - signal processing algorithms

UR - https://digitalcommons.bucknell.edu/fac_journ/407

M3 - Article

VL - 10

JO - Default journal

JF - Default journal

ER -

Efficient computation of discrete polynomial transforms

Abstract

Keywords

Disciplines

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