Wavelet Anti-aliasing Single Sub-band Reconstruction Algorithm And Its Application In Bearing Fault Feature Extraction

Fourier transform has been very successfully applied in signal processing,however, it is always defined either in the whole time domain or in the wholefrequency domain, so the signal feature of some certain period of time or some certainblock of spectrum can not be described by it, meaning that the Fourier transform is notcapable of time-frequency analyzing. The advent of wavelet analysis has brought us anadaptive way of processing signal in both time and frequency domain. No matter whatfrequencies the signal is consist of, wavelet analysis can process it in an adaptive way.At the mean time, the thought of wavelet multi-resolution analysis has put forward anew way to process signals. Mallat algorithm plays a great role in industrial application,which is as important as FFT to Fourier transform. At present, the study of waveletanalysis is still hot, and many new methods and new theories are being proposed. Withso many excellent characteristics, wavelet theory has been widely used intime-frequency analysis and in industrial applications.Firstly, this paper introduced the basic theory and the main characteristics ofwavelet analysis, such like time-frequency localization, multi-resolution analysis,sigularity detection and so on. Then this paper systematically introduced the thought ofmulti-resolution analysis, including wavelet multi-resolution analysis and singularvalue decomposition. Because of the great importance of Mallat algorithm, this papermainly introduced wavelet Mallat algorithm and wavelet packet Mallat algorithm.Because the great importance of the single sub-band reconstruction algorithm infrequency feature extraction, this paper made a deep research on this algorithm, andafter repeatedly analyzing, this paper found that there is serious frequency aliasingexisting in the Mallat algorithm, which is rooted in the Mallat algorithm. Even thoughthe wavelet single-band reconstruction algorithm was proposed later, the frequencyaliasing still exists. In this paper, the reasons causing the frequency aliasing weredetailedly introduced, after that, a completely anti-aliasing Mallat algorithm wasproposed by this paper, which was proved effective in both simulation experiments andpractical uses.During the process of analyzing and introducing, lots of figures and experimentswere given, apart from mathematical formulas. Finally, this paper concluded the main contents and introduced what’s to bestudied in the future.