Wavelet transform (WT) is a new transform analysis method. It inherits and develops the idea of ​​localization of short-time Fourier transform. At the same time, it overcomes the shortcomings of window size and frequency variation, and can provide a change with frequency. The “Time-Frequency†window is an ideal tool for signal time-frequency analysis and processing. Its main feature is that it can fully highlight some aspects of the problem through transformation, can localize the analysis of time (space) frequency, and gradually multi-scale the signal (function) through the telescopic translation operation, and finally reach the high frequency. Time subdivision, frequency subdivision at low frequency, can automatically adapt to the requirements of time-frequency signal analysis, so that it can focus on any detail of the signal, solve the difficult problem of Fourier transform, and become a major breakthrough in scientific methods since the Fourier transform. The traditional signal theory is based on Fourier analysis, and the Fourier transform has certain limitations as a global change. In practical applications, people began to make various improvements to the Fourier transform, and wavelet analysis was produced. Wavelet analysis is an emerging branch of mathematics, which is the perfect crystallization of general functions, Fourier analysis, harmonic analysis, and numerical analysis; in application fields, especially in signal processing, image processing, speech processing, and many nonlinear science fields. It is considered to be another effective time-frequency analysis method after Fourier analysis. Compared with the Fourier transform, the wavelet transform is a local and time domain transform, which can effectively extract information from the signal, and perform multi-scale refinement analysis on functions or signals through operations such as scaling and translation. Solved many difficult problems that the Fourier transform can't solve. Wavelet is the basis of analysis of multiresolution theory. The multi-resolution theory is related to signal representation and analysis at multiple resolutions, and its advantages are obvious - features that cannot be found at one resolution will be easily found at another resolution. Looking at the wavelet transform from a multi-resolution perspective, although there are many ways to interpret the wavelet transform, this approach simplifies the mathematical and physical interpretation process. There are many applications for wavelets. The direction I am learning is mainly image processing, so here I use the application of images as an example. For images, it is important to know that the quantization level determines the resolution of the image. The higher the quantization level, the clearer the image and the higher the resolution of the image. First, the wavelet status Wavelets have been hot for a while, but wavelets are not omnipotent. In some applications, wavelets are not suitable for solving differential equations. Pure numbers and physical status are not as good as FT. Second, the application of impact sound detection in engine sound in signal detection Fourier analysis: Time-averaged effect blurs the local characteristics of the signal Gabor transform: still requires a long window to contain the oscillating waveform wavelet transform: the wavelet base can be arbitrarily narrow Third, noise reduction application 1. Applicable occasions Classical filtering: requires that the signal and noise frequencies are narrow enough and do not coincide Gaussian noise and impulse noise - broadband noise - wavelet denoising 2, the filter effect 1 classic filter: lost waveform sharp information 2 wavelet noise reduction: basically retain the information of the waveform sharp point (related to wavelet base selection) 3, filtering means 1 traditional method: Prony parameter modeling method 2 wavelet noise reduction b, can prove its statistical optimality c. Threshold comparison (threshold T can be based on signal standard deviation) 4. Wavelet basis selection: The wavelet base should be similar to the main signal. The higher the similarity, the larger the main wavelet coefficient and the smaller the noise figure. NI Signal Processing Toolbox SMP series Rack-mounted DC Power Supplies are economical, MOSFETs-based, high switching speed, high power density DC power supplies with output power covering 300W ~ 6KW, and maximum voltage up to 800VDC.
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