Signal processing methods commonly used in engineering practice, such as Fourier transform, short time Fourier transform, wavelet transform, second generation wavelet transform, and multiwavelet transform, lay the foundation for operating monitoring and fault diagnosis of key equipments. To profoundly understand their common problems, an intensive and systematic research on the physical nature and key techniques of these signal processing methods is conducted. It is found in the research that their transform principle is inner product transform. The purpose of the principle is to search the components contained in the signal, which are the most relevant or similar to the “basis function”. The key point lies in the construction and selection of basis functions matching fault feature waveforms, so as to achieve condition monitoring and fault diagnosis. The principle is validated by simulations and engineering cases, which sufficiently proves its accuracy and reliability. Furthermore, some conclusions from the experimental results supplement and improve the inner product principle.