A general method to construct wavelet function on real number field is proposed in this article,which is based on finite length sequence.This finite length sequence is called the seed sequence, and the corresponding wavelet function is called the seed sequence wavelet function.The seed sequence wavelet function is continuous and energy concentrated in both time and frequency domains.That is, it has a finite support set in both time and frequency domains. It is proved that if and only if the seed sequence has 0 mean value, the interpolation function satisfies the admissible condition of wavelet function.The conditions corresponding to the higher order vanishing moment of the seed sequence wavelet function are also given in this article. On this basis, the concept of random wavelet function is proposed, and the condition of the regularity of random wavelet is discussed.

In this paper, an orthogonal mode decomposition method is proposed to decompose finite length real signals on both the real and imaginary axes of the complex plane. The interpolation function space of finite length discrete signal is constructed, and the relationship between the dimensionality of the interpolation function space and its subspaces and the band width of the interpolation function is analyzed. It is proved that the intrinsic mode is actually the narrow band signal whose intrinsic instantaneous frequency is always positive (or always negative). Thus, the eigenmode decomposition problem is transformed into the orthogonal projection problem of interpolation function space to its low frequency subspace or narrow band subspace. Different from the existing mode decomposition methods, the orthogonal modal decomposition is a local time-frequency domain algorithm. Each operation extracts a specific mode. The global decomposition results obtained under the precise definition of eigenmodes have uniqueness and orthogonality. The computational complexity of the orthogonal mode decomposition method is also much smaller than that of the existing mode decomposition methods.