The Calculation of Two-Dimensional Convolutions by Polynomial Transforms and the W Transforms

Zhou Liuding

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The Calculation of Two-Dimensional Convolutions by Polynomial Transforms and the W Transforms

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- The Calculation of Two-Dimensional Convolutions by Polynomial Transforms and the W Transforms
- Acta Electronica Sinica Issue 2, (1994)
- 作者机构：
  
  重庆大学计算机系
- 作者简介：
- 基金信息：
- DOI：
  CLC： TP391.41
- Published：1994
- 稿件说明：
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[1]周六丁.用多项式变换及W变换计算二维卷积[J].电子学报,1994(02):40-46.

Zhou Liuding. The Calculation of Two-Dimensional Convolutions by Polynomial Transforms and the W Transforms[J]. Acta Electronica Sinica, 1994, (2).
[1]周六丁.用多项式变换及W变换计算二维卷积[J].电子学报,1994(02):40-46. DOI：

Zhou Liuding. The Calculation of Two-Dimensional Convolutions by Polynomial Transforms and the W Transforms[J]. Acta Electronica Sinica, 1994, (2). DOI：

摘要

本文先给出了一种用Ｗ变换计算模（Ｚ

Ｎ

＋１）多项式积的新算法。然后将它与多项式变换结合用于计算Ｎ×Ｎ（Ｎ＝２

ｔ

）二维复值圆卷积。这种结合法完成上述卷积仅需２Ｎ２·（ｌｏｇ＿２Ｎ＋３／２）次实乘及１０·Ｎ

２

·ｌｏｇ＿２Ｎ＋Ｎ

２

次实加．该乘法量仅为常规多项式变换法的一半。

Abstract

First

We demonstrate a new algorithm for polynomial product modulo（Z￣N +1）implemented by the W transforms.Next

we combine this new algorithm with polynomial transforms to calculate N×N（N=2￣t）complex-valued convolutions.This combining approach only needs 2N￣2·（log

N +3/2） real multiplication counts and 10N￣2·log

N+10 real addition counts to calculate above convolutions.

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