Computation of Discrete W Transform with Arbitrary Length Using Clenshaw’s Recurrence Formula

LING Qi; SHU Hua-zhong; LI Song-yi; LUO Li-min

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Computation of Discrete W Transform with Arbitrary Length Using Clenshaw’s Recurrence Formula

更新时间：2025-07-16

- Computation of Discrete W Transform with Arbitrary Length Using Clenshaw’s Recurrence Formula
- Acta Electronica Sinica Vol. 35, Issue 10, Pages: 1949-1953(2007)
- 作者机构：
  
  东南大学影像科学与技术实验室,江苏,南京,210096
- 作者简介：
- 基金信息：
- DOI：
  CLC： TP301
- Published：2007
- 稿件说明：
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LING Qi, SHU Hua-zhong, LI Song-yi, et al. Computation of Discrete W Transform with Arbitrary Length Using Clenshaw’s Recurrence Formula[J]. Acta Electronica Sinica, 2007, 35(10): 1949-1953.
DOI：

LING Qi, SHU Hua-zhong, LI Song-yi, et al. Computation of Discrete W Transform with Arbitrary Length Using Clenshaw’s Recurrence Formula[J]. Acta Electronica Sinica, 2007, 35(10): 1949-1953. DOI：

摘要

离散W变换(DWT)在数字信号和图像处理领域有着广泛的应用.由于其涉及的计算的复杂性

众多学者提出了诸多DWT的快速算法来降低计算复杂度和硬件复杂度.本文针对任意长度的序列提出一种新的计算DWT的递归方法.我们利用Clenshaw 递归关系式推导了一种可以有效计算II型

III型和IV型DWT系数的递归算法.结果表明

该算法不仅结构简单

而且非常适合采用VLSI来并行实现.

Abstract

The Discrete W Transforms (DWT) have been widely used in the field of digital signal and image processing.Due to its high computational complexity

many fast algorithms for computing the DWT have been reported in the literature to improve the computational speed and hardware complexity.In this paper

a recursive algorithm for computing the DWT is proposed.By using Clenshaw’s recurrence formula

we derive an efficient method for computing the type-II

-III

and -IV DWT of sequences with general length.The results indicate that the proposed algorithms achieve a simple computational structure which is particularly suitable for parallel VLSI realization.

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