Abstract: Fast wavelet transform is an important problem faced by digital signal processing, this paper studies the parallel wavelet algorithm, how to reduce the convolution operation in wavelet transform scale, improve the parallel efficiency of wavelet transform, in order to achieve fast parallel calculation of wavelet transform. By FFT polynomial calculation, this paper eliminates the communication process of parallel computing synchronization, reduces the number of multiplication. On the thought of the algorithm is analyzed, it is indicated that the new algorithm in case of short data segments can reduce the multiplication operation of 50%~75%；tested on two different MPSoc platform, its results demonstrate the advantage and validity of the algorithm. The parallel wavelet transform algorithm based on polynomial FFT is a kind of stable and efficient parallel algorithm.

Key words: signal processing, fast Fourier Transform, wavelet transform, multi-core embedded real-time platform, parallel computing

摘要： 快速小波变换是数字信号处理面临的一个重要问题，针对并行小波算法展开研究，缩减小波变换中卷积运算的规模，提高小波变换过程中的并行效能，以实现小波变换的快速并行计算。通过FFT矩阵代入计算，消去了并行计算过程中的同步通信，降低了乘法运算次数。对算法思想进行了理论分析，说明新算法在短小数据分段情况下能够减少50%~75%的乘法操作；通过搭建两种不同平台进行了对比测试，证明了算法的先进性与有效性。基于FFT矩阵的并行小波变换算法是一种稳定有效的经典小波并行算法。

关键词: 信号处理, 快速傅里叶变换, 小波变换, 多核嵌入式系统, 并行计算