Orthogonal Mode Decomposition for Finite Discrete Signals (2409.07242v3)

Abstract: In this paper, an orthogonal mode decomposition method is proposed to decompose ffnite length real signals on both the real and imaginary axes of the complex plane. The interpolation function space of ffnite 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 speciffc mode. The global decomposition results obtained under the precise deffnition 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.