Abstract:The key question of applying singular value decomposition (SVD) to signal processing is the construction of the matrix. In order to separate the different frequency components from the original signal through SVD, a recursive SVD algorithm with variable matrix structure is proposed, whose idea is to change the structure of the matrix in the process of SVD recursion decomposition, each time when the SVD is carried out, the structure of the matrix to be decomposed will change regularly to adapt to the different frequency components in the signal, so that the different frequency components can be separated. The signal decomposition algorithm of the variable structure SVD is deduced, and it is proved that the original signal can be decomposed into a linear combination of a series of component signals by this algorithm. Furthermore, the signal separation mechanism of this algorithm is analyzed theoretically, and it is proved that for some frequency structure, variable structure SVD can separate the each single frequency component successively from the original signal. Finally, the separation examples of the simulation signal and actual engineering signal are provided, which demonstrate the good signal separation effect of the variable structure SVD algorithm. The comparison with wavelet analysis and multi-resolution SVD method shows that variable structure SVD can achieve the better signal separation results than these two methods.