Some novel applications of vector biased wavelet to signal processing

Up to now, all the wavelet transforms are inner product representation of Hilbert space. In [1,2,3,4], based on the principle of mathematics and dialectical method, a novel method—VPWT (Vector Product Wavelet Transform) is proposed and studied, it is useful for wavelet theory and signal processing. In [5,6], vector wavelet functions, vector scaling functions and biased wavelet functions are put forward, they are suitable for signal processing. In this paper, combined [1,2,3,4] with [5,6], a new signal processing way is given out. Numerical tests of the new way by optimal control theory suggest that the new method considerably improve the representation capabilities of wavelet expansions.