連續(xù)小波變換的一種快速算法
A FAST ALGORITHM OF CONTINUOUS WAVELET TRANSFORMS
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摘要: 連續(xù)小波變換(CWT)由于其優(yōu)良的特性,在信號(hào)處理的許多領(lǐng)域得到了應(yīng)用。但是CWT在實(shí)現(xiàn)時(shí)有很大的計(jì)算量,針對(duì)此問題,本文提出了一種利用離散小波變換(DWT)實(shí)現(xiàn)CWT的快速算法。通過理論分析,本文得出了該算法所需的兩個(gè)濾波器f(n)和g(n)的構(gòu)造方法和整個(gè)快速算法的組織方式,并利用一個(gè)技巧對(duì)小波系數(shù)的尺度間隔進(jìn)行了細(xì)化。最后對(duì)算法的計(jì)算復(fù)雜度進(jìn)行了簡(jiǎn)略的定性分析。
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關(guān)鍵詞:
- 小波變換; 連續(xù)小波變換; 快速算法
Abstract: Continuous wavelet transforms (CWT) have lots of applications in the field of signal processing due to its unique characteristics. Their realization, however, request considerable computation. Therefore, a fast algorithm is provided to combat this contradiction. This algorithm is realized by organizing some computing cells which are built by two filters f(n) and g(n). In this paper, some practicable methods are discussed to construct these filters. Moreover, the structure of the whole fast algorithm, along with a method to refine the scale interval of wavelet coefficients, is also presented. -
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