The Application Of Multi-wavelet Theory In Signal Processing

Wavelet analysis is a continuation and innovation of Fourier analysis theory,and it started with harmonic analysis,then it became the time-frequency analysis of important analysis tool.Fourier analysis inspired the theory and thought of wavelet analysis.Wavelet analysis came from Fourier analysis,the thought is also derived from the Fourier analysis,and it is the new development of Fourier analysis,it is the product of perfect combination of numerical analysis,with Fourier analysis,spline analysis,harmonic analysis,functional analysis.Wavelet analysis is evergreen,because of its exquisite mathematical thought and extensive application field.In the field of application,especially in the computer application,signal processing,image analysis,speech analysis,nonlinear science,earth science and applied technology,wavelet analysis has a broad influence.For full value of wavelet transform in digital image and audio signal processing advantages,in the MATLAB environment,the use of V.Strela wavelet toolbox,in view of the digital image and audio signal is the application of wavelet theory to achieve more,this is V.Strela professor to continue to develop and promote high le vels of work,the main research idea is as follows: first of all,in the MATLAB environment,by r multi-resolution analysis and wavelet theory,explore the multi-wavelet transform in the application of image enhancement and image fusion,at the same time the fusion image edge detection,and compared before and after the transformation of image.Canny edge detection and C-L multi-wavelet were selected as time-frequency analysis tools.Conclusion can detect image edge enhanced image edge clearer than before enhancement;Secondly,the multiple wavelet multi-resolution analysis as the theoretical basis,the experiment of the original audio signal is Windows XP start up sound,in the process of the reconstruction of the audio signal is decomposed,the wavelet as the research tools for the C-L experiment in the MATLAB environment.Through this experiment,each channel of the double channel signal can be deco mposed by multiple wavelets,and it can also be reconstituted as a double channel audio signal.The realization of this technology for later the researchers gave the good e xperimental basis,in the MATLAB environment multi-wavelet to audio signal denoising,video signal processing and other aspects of applications will continue to study as a future direction,and the properties of multi-wavelet good effect in the signal processing can also do further research and application,etc.Finally,based on the multi-resolution analysis theory,the fourth-order balanced multi-wavelet cardbal4 is used as the experimental tool in MATLAB to explore its different applications in the field of digital watermarking.First,the digital watermark is embedded in the image,and the tool is used to balance multi-wavelet cardbal4.This chapter fully embodies the advantages of balancing multiple wavelets and the uniqueness of experimental methods.Later in the study can further explore more in the process of wavelet toolbox,explore more good experimental methods and good properties of multi-wavelet,probe into the application of the experiments performed in MATLAB.