利用哈尔变换分析机械振动冲击信号

TO ANALYZE THE MECHANICAL VIBRATION-SHOCK SIGNALS BY HAAR TRANSFORM

本文首先介绍了哈尔变换的数学基础：哈尔函数和哈尔级数及其特点；接着介绍哈尔交换及其逆变换和快速算法（ＦＨＴ＆ＩＦＨＴ）的实现；最后在波谱分析方面与傅里叶变换作了比较，指出了在分析机械振动冲击信号时，哈尔交换更能突出信号特征，更易识别。

Firstly, the paper introduces the mathmatical basis of Haar Transform, i. e. Haar functions, Haar series and their characteristics. And then illustrates Haar Transform, Inverse Haar Transform and their fast algorithms (FHT & IFHT), as well as computation programs. It Points out that Haar Transform is much fitter for real-time on-line machinery monitoring system because of its higher transformation speed than Fourier Transform. Finally, by comparison with Fourier Transform on wave-spectrum analysis with several kinds of common signals. It concludes that Haar Transform is more suitable for analyzing mechanical vibration--shock signals owing to the advantages of faster transformation, higher sensitivity to pulse signals and good signal restoring ability.