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中文摘要：
机械故障诊断广泛使用的方法是对动态信号进行傅里叶变换、短时傅里叶变换、小波变换以及第二代小波变换。指出这些变换的本质是采用不同的基函数与信号进行内积变换．从动态信号中提取和基函数最相似的故障特征。运用三角基函数、Gabor基函数、离散基函数、谐波基函数、Laplace基函数、Hermitian基函数、第二代小波基函数等，有效地提取出发电机组松动、齿轮箱冲击摩擦、高压缸蒸汽激振、机车轮对滚动轴承损伤等故障特征。采用合理的基函数或多重基函数（多小波）对动态信号进行内积变换，可有效地提取故障特征，进行正确的故障诊断。
英文摘要：
Fourier transform, short time Fourier transform, wavelet transform and second generation wavelet transform are widely used for mechanical fault diagnosis. In this paper, it is revealed that the essence of these transforms is inner product transform for signals with various basis functions, from which fault feature being the most similar to basis function can be extracted from dynamic signals. A lot of basis functions such as trigonometric basis, Gabor basis, discrete basis, harmonic basis, Laplace basis, Hermitian basis, second generation wavelet basis, etc. have been adopted for fault feature extraction. Looseness fault feature of a turbo-generator, impulse friction symptom of gearbox, failure feature of high-pressure turbine excited by steam, and bearing defect of electric locomotive were extracted successfully. Provided that adopt reasonable basis functions or multi-bases （multiwavelet） for inner product transform of dynamic signals, effective fault features and correct fault diagnosis can be obtained.
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