一种离散小波变换的快速分解和重构算法

通过对实序列的快速傅里叶变换算法的推导及Mallat算法原理的分析，根据离散小波变换（DWT）算法结构特征，提出了一种离散小波变换的快速分解和重构算法；给出了相应的算法步骤，从数学理论上对该算法进行了论证。结果表明与原有的快速小波算法（Mallat算法）相比，可显著减少信号与滤波器长度N较大（大于16）时小波变换的实乘次数（分解仅为（5log2N 7)N次，重构仅为4N（1 log2N)次）提高了运算速度，且该算法有着良好的并行性，易于数字信号处理器（DSP）的快速实现。

Fast decomposition and reconstruction algorithm on discrete wavelet transform

On the basis of analyzing the principle of Mallat algorithm and deriving the real signal FFT algorithm, according to Discrete Wavelet Transform (DWT) structure, the paper proposes a fast decomposition and reconstruction algorithm for DWT; and the related algorithm procedures are given. The mathematical theories demonstrate that compared with conventional fast wavelet algorithm Mallat algorithm under long signal and filter (the length N >16), the proposed algorithm can significantly reduce the real multiplication times of DWT ((5log 2 N +7) N times only for decomposition and 4 N (1+log 2 N ) times only for reconstruction) and efficiently improve the work speed. Meantime, the algorithm is easily implemented by digital signal processing (DSP) because of its good parallel property.