The Similarity of Signal Processing Effect between SVD and Wavelet Transform and Its Mechanism Analysis
YE Bang-yan · Dianzi xuebao · 2008
It's pointed out that singular value decomposition(SVD) has the very similar signal processing effect as wavelet transform when Hankel matrix is used.It's proved that original signal can be decomposed into the linear superposition of a series of component signals by SVD using Hankel matrix,and what the component signals reflect essentially are the similarity extent of original signal to standard orthogonal bases of m and n dimension space constituted by left and right orthogonal matrix in SVD.The similarity mechanism of signal processing of SVD and wavelet transform is analyzed from the angle of basis of vector space and characteristic of Hankel matrix.The orthogonality difference of component signals got by SVD and wavelet transform is studied theoretically.It's pointed out that SVD also has the singularity detection ability when Hankel matrix is used,but compared with wavelet transform,SVD has two characteristics in singularity detection,one is that the vanishing moment of SVD component signals is increased progressively and the n'th SVD component signal has the n-1'th order vanishing moment so that singular point with different Lip index can also be detected,the other is that the width of the impulse that indicates the position of singular point will keep the same in all SVD component signals and this width is determined by the column number of Hankel matrix.