離散Walsh-Haar變換的快速算法
Fast Algorithm of Discrete Walsh-Haar Transformation
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摘要: Walsh-Haar函數(shù)系是一種具有良好的全局/局部性質(zhì)的函數(shù)系，與其對應(yīng)的離散變換是一種正交變換，有著廣闊的應(yīng)用前景。該文給出了離散Walsh-Haar變換及其逆變換的定義，并運(yùn)用二分技術(shù)得到了離散Walsh-Haar變換的快速算法。文中的設(shè)計(jì)思想和方法可用于研究其它序的離散Walsh-Haar變換和其它的正交變換的快速算法。
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關(guān)鍵詞:
- Walsh-Haar矩陣;離散Walsh-Haar變換;二分技術(shù);快速算法
Abstract: Walsh-Haar function system is a new kind of function systems that has good global/local property. Discrete Walsh-Haar transformation is an orthogonal transformation that can be widely used in signal processing. In this paper, a new type of transformation,discrete Walsh-Haar transformation, is proposed, and the fast algorithm of discrete Walsh-Haar transformation is studied based on the dichotomous technique. The idea and method used to design the fast algorithm in this paper can be used to study the fast algorithms of other order discrete Walsh-Haar transformations and other discrete orthogonal transformations. -
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